Accepted Manuscript

Performance Improvement of Teaching-Learning-Based Optimisation

for Robust Machine Layout Design

Srisatja Vitayasak , Pupong Pongcharoen

PII: S0957-4174(18)30005-8
DOI: 10.1016/j.eswa.2018.01.005
Reference: ESWA 11753

To appear in: Expert Systems With Applications

Received date: 16 March 2017

Revised date: 14 December 2017
Accepted date: 2 January 2018

Please cite this article as: Srisatja Vitayasak , Pupong Pongcharoen , Performance Improvement
of Teaching-Learning-Based Optimisation for Robust Machine Layout Design, Expert Systems With
Applications (2018), doi: 10.1016/j.eswa.2018.01.005

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 ACCEPTED MANUSCRIPT

Highlights

 Application of TLBO to solve MLD problems using robust approach is firstly re-
ported.
 Superiority of TLBO modifications has been proposed and demonstrated in this
work.
 Benchmarking datasets used in the computational experiments are provided.
 Comprehensive literature review on metaheuristics applied to solve MLD is pre-
sented.
 Pseudo codes and mechanisms of the proposed methods are illustrated using figures.

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Performance Improvement of Teaching-Learning-Based Optimisation for

Robust Machine Layout Design

Srisatja Vitayasak1 and Pupong Pongcharoen2,*

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1
Centre of Operations Research and Industrial Applications (CORIA), Department of Industrial Engineering,
Faculty of Engineering, Naresuan University, Phitsanulok, Thailand 65000

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Email: srisatjav@nu.ac.th

2
Centre of Operations Research and Industrial Applications (CORIA), Department of Industrial Engineering,
Faculty of Engineering, Naresuan University, Phitsanulok, Thailand 65000

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Email: pupongp@nu.ac.th

*Corresponding Author: pupongp@nu.ac.th

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Abstract
Teaching-Learning-Based Optimisation (TLBO) is one of the more recently developed me-
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taheuristics and has been successfully applied to solve various optimisation problems. How-
ever, TLBO has not been academically reported for solving the robust machine layout design
(MLD) problems with dynamic demand. Considering internal logistics activities, shortening
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material flow distance within a manufacturing area can lead to efficient productivity and a
decrease in related costs. The robust machine layout is concerned with determining the effi-
cient arrangement of machines/facilities located on a manufacturing shop floor under future
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demand fluctuation. A robust designed layout is essential for a company to maintain a high
productivity rate through multiple time-periods of demand uncertainty with minimum effects
related to the re-layout time and cost, manufacturing disruption, and the movement of monu-
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ment machines. The objectives of this paper were to: i) describe the development of a com-
puter aided layout designing tool for minimising the total material flow distance under dy-
namic demand scenario, ii) investigate the appropriate setting of TLBO parameters, and iii)
propose four TLBO modifications for improving its performance. The modified TLBOs were
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inspired by multiple teachers with two types of classes and two approaches to teacher selec-
tion. The numerical experiments were designed and conducted using eleven MLD bench-
marking datasets. Statistical analyses on the experimental results showed a superior perfor-
mance for the proposed modifications.

Keywords: Computational intelligence, Teaching-Learning-Based Optimisation, facili-

ty layout, robust design, dynamic demand.

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1. Introduction
Teaching-Learning Based Optimisation (TLBO) was introduced by Rao et al. (2011),
who was inspired by the teaching-learning phenomenon within a classroom environment.
TLBO can be categorised into population-based optimisation algorithms, in which the promi-
nent algorithms in this category are Ant Colony System (ACS), Artificial Bee Colony (ABC),
Genetic Algorithm (GA), Harmony Search (HS), and Particle Swarm Optimisation (PSO).
TLBO has been successfully applied to solve several optimisation problems, such as design-
ing planar steel frames (Togan, 2012), truss designs (Baghlani & Makiabadi, 2013; Camp &
Farshchin, 2014; Dede, 2014), unconstrained optimisation problems with different dimensions
and search space (Rao & Patel, 2013a), economic dispatch problems (Basu, 2014;
Bhattacharjee, et al., 2014; Durai, et al., 2015; Krishnasamy & Nanjundappan, 2014; Niknam,

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et al., 2013), scheduling problems (Baykasoglu, et al., 2014; Li, et al., 2015a; Lin, et al.,
2015b; Xu, et al., 2015), water level stabilisation (Baghlani, 2014), assembly line balancing

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(Tuncel & Aydin, 2014), and production planning (Kadambur & Kotecha, 2015).
The TLBO algorithm provides many advantages that will be highlighted next (Rao, et

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al., 2011; Rao, et al., 2012). The concept of teaching-learning is easy to understand and im-
plement. TLBO has no specific algorithm parameter (Rao & Patel, 2013a); the computational
effort related to the specific parameters is not needed. It requires only common control pa-
rameters (population size and the number of iterations), which can be defined depending on

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the problem size. The control parameters usually determine the total number of generated
candidate solutions to be searched in a solution space and, therefore, have an influence on the
amount of computational time and resources. TLBO requires fewer candidate solutions be
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used to search in the solution space and still achieves high consistency on the success per-
centage of obtaining optimum solutions (Rao, et al., 2012).
The facilities layout problem (FLP) in manufacturing plants involves “the determination
of the most efficient physical arrangement of a number of interacting facilities on the factory
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floor of a manufacturing system in order to meet one or more objectives - a facility may be a
department, a machine tool, a manufacturing cell, a machine shop, or a warehouse” (Heragu,
1997). An effective layout can decrease material handling distance and manufacturing lead
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times; at the same time, it can increase throughputs and cost effectiveness. An effective layout
can reduce total operating expenses by at least 10-30% (Tompkins, et al., 2010). Solving large
layout design problems is computationally difficult due to combinatorial explosion. For ex-
ample, if there are 20 machines, the number of possible layouts is 20! or 2.4 x 1016 solutions.
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The design task is to find the best effective layout from those possible solutions. However,
there have been no reports in the international academic databases on the TLBO application
for designing robust layouts under a dynamic demand environment.
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The objectives of this work were to: i) describe the development of a computer aided
layout designing tool for minimising material flow distance with demand changing over a
multiple time-periods planning horizon, ii) investigate the optimised setting of TLBO‟s con-
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trol parameters, and iii) propose and demonstrate four TLBO modifications based on multiple
teachers with single/multiple class(es) with/without constraining teacher selection. The supe-
riority of the modified TLBOs was comprehensively demonstrated through eleven bench-
marking datasets and its performance compared with the conventional TLBO and GA in
terms of solution quality and computational time.
The remaining sections are organised as follows: section 2 presents comprehensive lit-
erature reviews, including the applications of metaheuristics to solve facility layout design
problems, robust machine layout design (RMLD) with demand uncertainty, Genetic Algo-
rithm, and Teaching-Learning Based Optimisation followed by the RMLD problem formula-
tion in section 3. Metaheuristics for a RMLD problem are shown in section 4. The experi-

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mental design and analysis are presented in section 5, and finally, conclusions are drawn in
section 6.

2. Comprehensive literature reviews

The following subsections review the applications of metaheuristics (especially the Ge-
netic Algorithm and Teaching-Learning Based Optimisation) to solve facility layout design
under dynamic demand environment.

2.1 Applications of metaheuristics to solve facility layout design problems (FLPs)

In the context of operations research and computational intelligence, a computational
method iteratively seeks better candidate solutions under constraints and limitations. Me-

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taheuristic is formally defined as an iterative generation process which stochastically guides a
subordinate heuristic by intelligently combining concepts for exploring and exploiting the

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search space; learning strategies are used to structure information in order to find efficiently
near-optimal solutions (Osman & Laporte, 1996). Stochastic search algorithms have been

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successfully applied to solve various problems, especially those that are very large in size, but
the algorithms do not guarantee the optimum solution (Pongcharoen, et al., 2002). A literature
survey on applications of metaheuristics to solve FLPs was undertaken on the ISI Web of Sci-
ence database covering the period 2006 to September 2016. Using the facility/machine layout

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design as keywords, the search found 260 papers, in which 141 papers had applied metaheu-
ristics to solve the problems as shown in Table 1. It can be seen that the majority of the arti-
cles found were on the application of conventional metaheuristics, e.g., Artificial Immune
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System (Krishnan, et al., 2009a), Ant Colony Optimisation (Chen & Lo, 2014), Variable
Neighbourhood Search (Abedzadeh, et al., 2013), Artificial Neural Network (Abu Qudeiri, et
al., 2015), improved Genetic Algorithm (Liu & Sun, 2012), and modified Simulated Anneal-
ing (Li, et al., 2015b). It should be noted that a number of articles focused on the improve-
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ment of metaheuristics performance by implementing hybridisation. For instance, local search

procedures have been incorporated into the Genetic Algorithm to improve convergence per-
formance (Ozcelik & Islier, 2006), and the hybrid Genetic Algorithm has been shown to sta-
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tistically outperform Simulated Annealing, Tabu Search, hybrid Tabu-Simulated Annealing,

and hybrid Ant Systems (Pourvaziri & Naderi, 2014).
Benchmarking datasets or test problems always play an important role on computational
experiments in order to demonstrate the efficiency of the proposed methods and performance
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comparison. Most of the literature mentioned only references datasets, such as the QAPLIB
website (Matai, 2015; Pillai, et al., 2011), previous works (Jolai, et al., 2012; Niroomand, et
al., 2015), and real life problems (Cheng & Lien, 2012). Komarudin and Wong (2010) tested
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the proposed algorithm using various problem datasets taken from the literature for solving
unequal area facility layout problems, in which the data included shop floor area, department
area, aspect ratio, and material flow between departments. Saravanan and Arulkumar (2015)
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presented primary data, including machine-part matrix, parts sequence, area of the machines,
and area of the layout for designing the fixed area layout. Some datasets have been generated,
such as the number of trips between pairs of machines (material flow) and the dimensions of
machines for designing loop layout (Tubaileh, 2014). The diversity of datasets indicates the
research contribution and the problem characteristics, e.g., facility type, facility size and
shape, layout configuration, and demand variability.
Facilities can refer to machines, departments, and/or cells, which may be in homogene-
ous (equal) (Ulutas & Islier, 2009) or heterogeneous (unequal) size (Ficko, et al., 2010). Fa-
cilities are arranged in a single row (Lin, 2009), multi-row (Jithavech & Krishnan, 2010), loop
(Ozcelik & Islier, 2011), or U-shape (Moslemipour & Lee, 2012) layout configuration. The
layout design in a cellular manufacturing system (CMS) involves cell formation (Parika, et

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al., 2014; Wu, et al., 2007), intra-cell design (Kia, et al., 2013), and inter-cell design (Hu, et
al., 2007). Production demand can be certain (static) (Nearchou, 2006) or uncertain (dynamic)
(McKendall & Hakobyan, 2010; Pillai, et al., 2011). Static demand refers to unchanged de-
mand throughout the time period by which material flow between machines and total material
handling distance remain the same. However, this situation rarely occurs since market de-
mand is usually affected by changes in product design, shorter product life cycles, the elimi-
nation of existing products, and the introduction of new products. Designing a facility layout
with demand uncertainty has rarely been reported. Only 36 of 141 papers considered uncer-
tainties in production demand, including customer demand and product mix.

Table 1 Applications of metaheuristics to solve facility layout design problems

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Single metaheuristic Hybridisation

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Demand 2006: (Aiello, et al., 2006; Chae & Peters, 2006a; Chae & Peters, 2006b; Chan, 2006: (Ozcelik & Islier, 2006)
certainty et al., 2006; Eklund, et al., 2006; Hicks, 2006; Kapanoglu & Utkan,
2006; Logendran & Kriausakul, 2006; Nearchou, 2006; Paul, et al.,

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2006; Pour & Nosraty, 2006; Zhou, et al., 2006)
2007: (Sirinaovakul & Limudomsuk, 2007) (Hu, et al., 2007; Ioannou, 2007; 2007: (Ye & Zhouz, 2007)
Liu & Meller, 2007; Sirinaovakul & Limudomsuk, 2007; Wu, et al.,
2007)

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2008: (Khilwani, et al., 2008; Kumar, et al., 2008; Liang & Chao, 2008; Ray &
Sarker, 2008; Singh & Sharma, 2008)
2009: (Ariafar & Ismail, 2009; Diego-Mas, et al., 2009; Kumar, et al., 2009;
Lin, 2009; Raman, et al., 2009; Sahin & Turkbey, 2009b; Scholz, et al.,
2009: (Ramkumar, et al., 2009a;
Ramkumar, et al., 2009b)
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2009; Tarkesh, et al., 2009)
2010: (Ficko, et al., 2010; Jaramillo & McKendall, 2010; Komarudin & Wong, 2010: (Wong & See, 2010)
2010; Samarghandi & Eshghi, 2010; Samarghandi, et al., 2010; Scholz,
et al., 2010; Wong & Komarudin, 2010)
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2011: (Datta, et al., 2011; Gress, et al., 2011; Krishnan & Jaafari, 2011; 2011: (Ku, et al., 2011)
Kulturel-Konak & Konak, 2011; Ozcelik & Islier, 2011; Rezapour, et
al., 2011)
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2012: (Aiello, et al., 2012; Arkat, et al., 2012a; Arkat, et al., 2012b; Jolai, et 2012: (Cheng & Lien, 2012)
al., 2012; Kaveh, et al., 2012; Krishnan, et al., 2012; Kulturel-Konak,
2012; Liu & Sun, 2012; Ulutas & Kulturel-Konak, 2012)
2013: (Aiello, et al., 2013; Chandrasekar & Venkumar, 2013; Chang, et al., 2013: (Tuzkaya, et al., 2013)
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2013; Chang & Ku, 2013; Garcia-Hernandez, et al., 2013a; Garcia-

Hernandez, et al., 2013b; Khaksar-Haghani, et al., 2013; Kothari &
Ghosh, 2013a; Kothari & Ghosh, 2013b; Kulturel-Konak & Konak,
2013; Lenin, et al., 2013; Leno, et al., 2013; Matai, et al., 2013; Ulutas
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& Kulturel-Konak, 2013)

2014: (Berlec, et al., 2014; Jabal-Ameli & Moshref-Javadi, 2014; Kothari & 2014: (Jiang, et al., 2014)
Ghosh, 2014; Tubaileh, 2014)
2015: (Abu Qudeiri, et al., 2015; Cardona, et al., 2015; Garcia-Hernandez, et 2015: (Garcia-Hernandez, et al., 2015b;
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al., 2015a; Kia, et al., 2015; Li, et al., 2015b; Matai, 2015; Niroomand, Goncalves & Resende, 2015)
et al., 2015; Palubeckis, 2015a; Palubeckis, 2015b; Saraswat, et al.,
2015; Saravanan & Arulkumar, 2015; Saravanan & Kumar, 2015)
2016: (Ebrahimi, et al., 2016; Kanduc & Rodic, 2016; Mallikarjuna, et al., 2016: (Ghosh, et al., 2016; Guan & Lin,
2016) 2016; Leno, et al., 2016; Zuo, et
al., 2016)
Demand 2006: (Baykasoglu, et al., 2006; McKendall, et al., 2006)
uncertainty 2008: (Sahin, 2008)
2009: (Krishnan, et al., 2009a; Sahin & Turkbey, 2009a; Ulutas & Islier, 2009) 2009: (Dong, et al., 2009; Sahin &
2010: (Jithavech & Krishnan, 2010; McKendall & Hakobyan, 2010) Turkbey, 2009a)
2011: (Pillai, et al., 2011)
2012: (Kia, et al., 2012; McKendall & Liu, 2012; Moslemipour & Lee, 2012)
2013: (Abedzadeh, et al., 2013; Drira, et al., 2013; Emami & Nookabadi, 2013; 2013: (Chen, 2013; Hosseini-Nasab &

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Izui, et al., 2013; Kia, et al., 2013; Mazinani, et al., 2013; Ou-Yang & Emami, 2013; Nageshwaraniyer, et al.,
Utanilma, 2013; Samarghandi, et al., 2013) 2013)
2014: (Chen & Lo, 2014; Kia, et al., 2014; Mohammadi & Forghani, 2014; 2014: (Hosseini, et al., 2014; Kaveh, et
Zhao & Wallace, 2014) al., 2014; Pourvaziri & Naderi, 2014)
2015: (Bozorgi, et al., 2015; Kheirkhah, et al., 2015; Ulutas & Islier, 2015) 2015: (Kulturel-Konak & Konak, 2015)
2016: (Asl, et al., 2016)

2.2 Robust machine layout design

Variability in demand over time period or dynamic demand has resulted in the disrup-
tion of efficient flow of materials between machines (facilities). Dynamic demand can be in

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either deterministic or stochastic form. Deterministic demand means that demand values are
constant (Tavakkoli-Moghaddam, et al., 2005a; Tavakkoli-Moghaddam, et al., 2005b). For

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stochastic scenario, the predicted demand can be generated using forecasting techniques
(Ertay, et al., 2006) or probability distribution functions, for instance, uniform probability

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distribution (Jithavech & Krishnan, 2010; Krishnan, et al., 2009b), normal probability distri-
bution (Tavakkoli-Moghaddam, et al., 2007) and exponential probability distribution (Chan &
Malmborg, 2010). Demand profile can also be presented as flow density matrix with different
probabilities (Dunker, et al., 2005; McKendall Jr. & Hakobyan, 2010) or assigned in the form

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of material flows between facilities using fuzzy numbers (Enea, et al., 2005). The material
flow matrix or estimated demand was considered as input data before starting the optimisation
process (Sahin & Turkbey, 2009b).
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Robust machine layout is concerned with determining the efficient arrangement of ma-
chines/facilities located on a manufacturing shop floor under dynamic demand scenario. Fig-
ure 1 illustrates the concept design for robust layout under demand uncertainty (D1…DP)
through multiple time-periods (T1…TP) planning horizon, where D is demand profile; T is
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time-period; and P is the total number of time-periods under planning horizon. Designing a
robust layout (L) aimed to minimise the total material flow distance based on the fluctuated
demand. The robust layout (L) is a single layout that is robustly designed for a number of
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time-periods under different demand profiles. The robust layout can be applied in all periods
without machine movements between any periods. This proposed design is effective when
machines are difficult to move (called monument machines), the chance of production disrup-
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tion is high due to machine repositioning, and rearrangement costs are too high (Pillai, et al.,
2011). On the other hand, the dynamic layout design assumes that machines are easily relo-
cated, and rearrangement costs are acceptable. The re-layout approach is developed to mini-
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mise the total cost of material handling and rearrangement costs (Chen, 2013; Hosseini, et al.,
2014; Moslemipour & Lee, 2012; Pourvaziri & Naderi, 2014; Ulutas & Islier, 2015;
Vitayasak, et al., 2017). Since the concept design of a robust layout is simply focused on the
minimum effects related to the rearrangement time and cost, manufacturing disruption, and
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the movement of monument machines; the robust design approach is unsurprisingly found as
a favourite choice.

Figure 1 Robust layout designs through multiple time-periods planning horizon

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Benchmarking datasets of dynamic layout design problems are rarely provided and usu-
ally incomplete, e.g., no dimension of departments and cells (Ioannou, 2007), no material
flow between departments (Garcia-Hernandez, et al., 2013a), and no processing sequences
(Ulutas & Islier, 2015). Tavakkoli-Moghaddam et al. (2007) provided the data of stochastic
demand with normal probability distribution, but the machine sizes were dismissed. Krishnan
et al. (2009b) and Jithavech and Krishnan (2010) considered equal-sized department layout
design with stochastic demand based on uniform probability distribution. Kia et al. (2012)
presented numerical examples using probability distributions taken from the literature. A mul-
tiple rows layout was considered in order to locate equal-sized machines in each cell under
dynamic cellular manufacturing environment. Moslemipour and Lee (2012) randomly gener-
ated test problems, in which the product demands for each time period are assumed to be

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normally distributed whilst identical-size machines are laid out in a u-shaped configuration.
Nageshwaraniyer (2013) has shown a benchmark dataset, including the relative flow between

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pairs of department types for each period, and the unit rearrangement cost was different in
each period. Unfortunately, the complete detailed benchmarking datasets of unequal-sized

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facility layout design problems with an uncertainty environment do not exist in the literature.
The eleven datasets used in this work are shown in Appendices A and B.

2.3 Performance of Genetic Algorithm on layout problems

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Genetic Algorithm (GA) (Gen & Cheng, 1997; Goldberg, 1989) is one of the classical
metaheuristics, which has been successfully applied to solve various combinatorial optimisa-
tion problems in many disciplines (Aytug, et al., 2003; Lin, et al., 2015a). Dapa et al. (2013)
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reported that GA outperformed the Bat Algorithm and Shuffled Frog Leaping Algorithm in a
multiple rows layout design. However, the work was based on demand certainty and constant
production quantity. Lenin et al. (2013) demonstrated the effectiveness of GA by solving a
single-row layout design problem. The results obtained from GA were more favourable than
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other approaches, e.g., Simulated Annealing. Kia et al. (2014) proposed that GA can find
near-optimal solutions in much less computational time than CPLEX for most problems.
Ebrahimi et al. (2016) stated that GA found a better solution than Branch and Bound in much
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less time for solving a cellular manufacturing system considering machine layout and part
scheduling problems simultaneously. Mallikarjuna et al. (2016) showed GA performance in a
loop layout design that gave optimised solutions and provided the best solution compared to
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Simulated Annealing.

2.4 Teaching-Learning Based Optimisation (TLBO)

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Teaching-Learning Based Optimisation is based on the influence of a teacher on the

quality of learners in the class (Rao, et al., 2011). A class consists of a group of learners,
which refers to a population for TLBO. The quality of learners is considered in terms of
grades or solution quality. A teacher shares his/her knowledge with learners, which leads to
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better results or higher scores of the learners. Moreover, learners can gain knowledge through
interaction among themselves by group discussions, presentations, or formal communication.
After undergoing the academic activities, the learners‟ quality is expected to be improved.
The TLBO mechanism consists of two parts: Teacher phase and Learner phase. The
„Teacher phase‟ means learning from the teacher or tutor. The knowledge level of the whole
class (learners) can be increased with teaching delivered by the best learner (as a tutor).
Changing the existing solution in the population using the best solution of the iteration in-
creases the convergence rate. In the „Learner phase‟, a learner interacts randomly with other
learners. A new learner (candidate solution) is accepted if the learner is improved.
TLBO terminology is simple and unique. Table 2 illustrates the TLBO terms with a
comparison to one of the most classical metaheuristics (Genetic Algorithm) terminology.

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TLBO has only two common control parameters: population size and number of generations.
TLBO does not require any algorithm parameters to be tuned. In comparison, GA has four
parameters (population size, number of generations, probability of crossover, and probability
of mutation). For each generation of the search process, TLBO exploits the best solution with-
in the population and also explores different parts of the solution space simultaneously by the
Teacher phase and the Learner phase, respectively.

Table 2 Terminology comparison between GA and TLBO.

Terminology Genetic Algorithm (GA) TLBO

Candidate solution(s) Chromosomes Learners

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Size of candidate solutions Population Population

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Amount of iterative search Number of generations Number of generations
Proportional selection for exploi- Probability of crossover/mutation No probability
tation/exploration

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Intensification Crossover operation Teacher phase
Diversification Mutation operation Learner phase

Two main mechanisms (intensification and diversification) commonly conducted within

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any metaheuristics algorithm play an important role in performance (Blum & Roli, 2003) and
potentially lead to its strengths and weaknesses. Intensification generally refers to the exploi-
tation of the accumulated search experience, whilst diversification refers to the exploration of
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the solution space. Rao and Savsani (2012) suggested that the high convergence rate on the
optimum solutions was based on the balance of exploitation and exploration. This is because
the nature-inspired concepts adopted within the metaheuristics mechanisms have their own
unique properties with their goal to avoid the disadvantages of iterative search improvement
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of getting trapped in local optima and simultaneously guiding the search in a more intelligent
direction than providing a random search.
Advantages and disadvantages of the classical algorithms, including Ant Colony Opti-
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misation (ACO), Genetic Algorithm (GA), Particle Swarm Optimisation (PSO), and TLBO
are shown in Table 3.
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Table 3 Advantages and disadvantages of ACO, GA, PSO, and TLBO

Algorithms Advantages Disadvantages

ACO - Good global search ability because of - Tuning the specific parameters
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mutation and fitness-related selection - Slow convergence rate because of

(Yang, 2014) pheromone updating strategies (Kalra
& Singh, 2015)
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- Low exploitation because of lack of

crossover (Yang, 2014)
GA - Enhance convergence because of cross- - Tuning the specific parameters
over operation and elitism (Yang, 2014) - Premature convergence because of
fixed mutation probability (Kalra &
Singh, 2015)
- Slow convergence rate and high com-
putational cost (Patel, et al., 2017)
PSO - Speed up the convergence by drawing - Tuning the specific parameters
the current best solution. (Yang, 2014) - Slow convergence rate (Kalra &
- High degree of exploration (Yang, 2014) Singh, 2015)
because of adjusting particle‟s velocity - Long computational time (Kalra &

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on the best position of each particle Singh, 2015)

(Kalra & Singh, 2015; Rezazadeh, et al., - Premature convergence (Yang, 2014)
2009) - Uncertain time of convergence (Azimi
- Better exploitation (Patel, et al., 2017) & Saberi, 2013)
because of using the global best solution
of the population for searching a new
candidate (Kalra & Singh, 2015)

Table 3 Advantages and disadvantages of ACO, GA, PSO, and TLBO (Continued)

Algorithms Advantages Disadvantages

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TLBO - No algorithm specific parameters (Rao, - Unbalanced exploitation and explora-
et al., 2011) tion ability (Ji, et al., 2017)

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- Less computational effort to achieve the - Trap in local optimal (Teacher phase)
global optimum solution (Zhou & Yao, (Yu, et al., 2016)

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2017) - Inefficient convergence performance
- Rapid convergence (Wang, et al., 2016) (Learner phase) (Zou, et al., 2014b)
- Easily implemented and requires less - Lose the exploration ability (Ji, et al.,
computational memory (Garcia & Mena, 2017)
2013)
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al., 2013)
- Slow convergence rate (Satapathy, et
al., 2013) in Learner phase because of
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the inappropriate interaction among
learners during the learning phase
- Large computational time (Satapathy,
et al., 2013)
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The superiority of TLBO performance has been studied and compared with other popu-
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lation-based optimisation algorithms (e.g., ACS, ABC, GA, HS, PSO and Grenade Explosion
method) based on various optimisation problems. Performance comparisons have been stud-
ied by Rao, et al. (Rao, et al., 2011; Rao, et al., 2012) on the application to solve constrained
mechanical design optimisation problems and continuous non-linear large-scale problems. It
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was reported that the success percentage and convergence rate of TLBO performance for find-
ing optimum solutions was in high consistency with fewer candidate solutions generated dur-
ing the evolution process. Togan (2012) has applied TLBO to design a series of benchmark-
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type low-weight planar steel frame optimisation problems and demonstrated the advantages of
TLBO performance over HS, GA, ACO and improved ACO. Pawar and Rao (2013) have ap-
plied TLBO to design the best parameter settings for optimising the machining processes re-
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lated to abrasive water-jet machining, grinding, and milling. It has been reported that the
TLBO algorithm outperformed GA and SA in terms of convergence rate and accuracy of the
solutions obtained.
The performance comparison of TLBO and other metaheuristics have been investigated
in the area of electrical power and energy systems. Roy (2013) reported that TLBO perfor-
mance is significantly better than Differential Evolution (DE) and PSO for solving short-term
hydrothermal scheduling problems when considering valve point effect and prohibited dis-
charge constraint. Bouchekara et al. (2014) illustrated that TLBO was more effective and ro-
bust than other techniques (e.g., Biogeography-Based Optimisation, Tabu Search, and evolu-
tionary programming) for solving the optimal power flow problem with different complexi-
ties. Banerjee et al. (2015) applied TLBO to design optimal power generation units to meet

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the load demand while satisfying different operational constraints and found that TLBO re-
ported lower total generation costs than those obtained from GA, SA, and its hybridisation.
However, TLBO is ineffective for many real life problems (Patel & Savsani, 2015) because of
the imbalance between exploitation and exploration ability.
Improvement of TLBO performance has been studied in Teacher phase, Learner phase,
and both by either modifying or hybridising (Rao, et al., 2012). The modified Teacher phase
in TLBO has been proposed with the concept of number of teachers and adaptive teaching
factor (Rao & Patel, 2013b) for which the convergence of the modified TLBO is quicker than
TLBO, but the best-so-far solutions obtained from both algorithms showed no difference. In
the Learner phase, a self-adaptive learning mechanism has been introduced by using learner
probability from the previous iteration and using a weigh accumulator to choose a mutation

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strategy (Niknam, et al., 2013). This mechanism has resulted in quicker convergence to a bet-
ter solution with a lower maximum iteration number and less execution time. A learning

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method for interaction between learners can be developed using the cognition of learner
groups (Niknam, et al., 2012). The experimental results showed that the modified TLBO pro-

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duced a better solution in terms of total fuel cost and total emission of generations with better
convergence characteristics. The Learner phase modified with self-adapting wavelet mutation
strategy and application of a fuzzy clustering technique in population selection for the next
iteration has been investigated in multi-objective optimal power flow problems (Shabanpour-

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Haghighi, et al., 2014). The simulation results indicated that the modified TLBO produced
lower total cost of generation and lower total emission of the units than TLBO.
TLBO modification has been introduced to the Teacher phase and Learner phase simul-
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taneously using a perturbed scheme and a global crossover strategy, respectively (Ouyang, et
al., 2015). The numerical results demonstrated that the solution quality obtained from the
modified TLBO was better than the standard TLBO, PSO variants, DE variants, and ABC
variants. Moreover, TLBO can be improved by other methods, e.g., applying the producer-
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scrounger model generated higher TLBO performance than some other algorithms in terms of
accuracy, convergence speed, and success rate (Chen, et al., 2015). The mutation phase
(Martin Garcia & Gil Mena, 2013), Self-learning phase, Diversified learning, and Teacher‟s
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learning steps (Kanwar, et al., 2015) have been operated next to the Learner phase and these
processes led to better solutions.
TLBO hybridisation has been a favourite choice of performing with several algorithms
or techniques, e.g., Taguchi's method (Yildiz, 2013), Chebyshev polynomials (Baghlani,
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2014), Imperialist Competitive Algorithm (Ghasemi, et al., 2014), the sequential quadratic
programming (SQP) method (Krishnasamy & Nanjundappan, 2014), DE (Wang, et al., 2014),
a variable neighbourhood search (Tang, et al., 2015; Xie, et al., 2014), Gaussian sampling
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learning based on neighbourhood search (Zou, et al., 2014a), robust Tabu Search (Dokeroglu,
2015), and Cuckoo Search algorithm (Huang, et al., 2015). Nevertheless, both TLBO and im-
proved TLBO have not been developed for solving the robust machine layout design problem.
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3. Problem formulation
In this work, the following assumptions were made in order to formulate the robust ma-
chine layout design (RMLD) problem: i) Rectangular-shaped machines were placed and ar-
ranged in multiple rows; ii) There was enough space on the shop floor area for machine
placement; iii) Material flow distance between machines was determined using the rectilinear
distance between the machines‟ centroids; iv) A one-metre gap (empty space) between ma-
chines and rows was constant; vi) Demand profiles were defined by using exponential, nor-
mal, or uniform distribution or known in advance with changes over time periods (product
demand distributions defined for each dataset are stated in Appendix A); vii) A machine was
located in one orientation, where machine length was parallel to the x-axis, and machine

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width was parallel to the y-axis; and viii) Practical constraints, including processing time,
transporting time, plant safety, floor resistance, and human operator needs were negligible.
Figure 2 illustrates an example of a 14-machine placement procedure on a shop floor
area with length as (FL) and width as (FW). Machine sequence for placement on the shop floor
was M5-M2-M10-M6-M9-M12-M4-M7-M8-M1-M3-M11-M13-M14. Machines were se-
quentially arranged row by row, from left to right, starting at the first row with respect to the
length (FL) of the shop floor area with the a predefined gap (G) between machines and rows.
The gap size usually depends on the size of the objects flowing through the gap. When there
was not enough area for placing the next machine at the end of the row, it was then placed in
the next row. Machine placement in the first row (Row 1) started with M5, M2, M10, M6, and
M9. M12 was placed in the next row because there was not enough space for M12. The row

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width (RW) refers to the maximum width of machines in the row, e.g. in the row 1; the RW
for row 1 (RW1) equals the width of machines 2 (M2) and 6 (M6). The maximum length of a

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row (RL) depends on the gap (G) and floor length (FL). Material flows between rows were
routed either by moving to the left or the right side of the row and then moving up or down to

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the destination row. A route for transporting material between machines was evaluated for the
shortest distance.

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Figure 2 Multi-row machine placement procedure and route selection

Rectilinear distance measurement between machines can be classified into two cases: I)
Material handling movements between machine i and j are in the same row; the distance
measured can be determined according to equation (1); and II) Machines i and j are located on
different rows; equations (2), (3) and (4) are used to determine the shortest material handling
distance between machines i and j.

Wi W j
d ij  xi  x j  G   (1)
2 2

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dLij  xi  x j   yi  y j  G 
Wi W j
 (2)
2 2

dRij  RL  xi   RL  x j   yi  y j  G 

Wi W j
 (3)
2 2

d ij  min dLij , dRij  (4)

xi is the coordinate on x-axis of machine i; xj is the coordinate on x-axis of the machine

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j; yi is the coordinate on y-axis of the machine i; yj is the coordinate on y-axis of the machine
j; Wi is the width of the machine i; Wj is the width of the machine j; and RL is the maximum

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length of rows.
For example, in Figure 2, if there is a material flow from machine M10 to machine M6,

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the distance measurement between M10 and M6 (d10,6) can be calculated as follows:

W10 W6
d10,6  x10  x6  G  
2 2

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If there is another case of material flow from machine M4 to machine M11, both of
which are on different rows, the shortest material handling distance between machine M4 to
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machine M11 (d4,11) can be evaluated as follows:

W4 W11
dL4,11  x4  x11   y 4 - y11  G  
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2 2
W4 W11
dR4,11  RL  x4   RL  x11   y 4 - y11  G  
2 2
d 4,11  min dL4,11, dR4,11  = dL4,11
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The evaluation function (Z) on the efficiency of a robust layout design under dynamic
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demand can be used to minimise total material flow distance for all products through multiple
time periods defined by equation (5) (Vitayasak, et al., 2014):
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P N M M
Minimise Z  ∑∑∑∑d ij f ijgk Dgk , (5)
k 1 g 1 i 1 j1
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M is the number of machines; i and j are machine indices (i and j = 1, 2, 3, …, M). N is

the number of product types; g is a product index (g = 1, 2, 3, …, N); P is the number of time
periods; and k is a time period index (k = 1, 2, 3, …, P). dij is the distance from machines i to j
(i ≠ j); fijgk is the frequency of material flow of product g from machines i to j on period k; and
Dgk is the customer demand of product g on period k.

4. Metaheuristics for a robust machine layout design (RMLD) problem

The RMLD program was developed and coded in modular style using Tool Command
Language and Tool Kit (Tcl/Tk) programming language (Ousterhout, 2010). This program is
user-friendly, designed to redefine the parameters for each computational run. The computa-
tional experiments were designed and conducted on a personal computer with Intel Core i7

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3.4 GHz and 16 GB DDR3 RAM. The input data for the RMLD problem included number of
machines (M), dimension of machines (width: MW x length: ML), number of products (N) and
their machine sequences, and demand profiles in each period (Dg1, Dg2, Dg3,…, Dgk) for N
products. The parameters for the RMLD problem consisted of floor length (FL), floor width
(FW), gap between machines (G), and number of periods (P). In this work, two metaheuristics
(GA and TLBO) and four modified TLBOs were applied to design the machine layout prob-
lem as described in the following subsections.

4.1 Genetic Algorithm

The pseudo-code of the proposed GA for the robust machine layout design (RMLD)

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problem shown in Figure 3 can be described in following form:

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Input problem dataset
Parameter setting (Pop, Gen, Pc, Pm, P)
Create demand level (Dgk) for each product associated with demand

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distribution
Randomly create initial population (Pop)
Set l = 1 (first generation)
While l ≤ Gen do

Crossover operation
End loop for
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For r = 1 to cross (cross = round((Pc * Pop)/2))) do

For u = 1 to mute (mute = round(Pm * Pop)) do

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Mutation operation
End loop for
Arrange machines row by row based on FL, FW and G
For k = 1 to Number of periods (P) do
Calculate material flow distance based on demand level (Dgk)
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End loop for

Selection of the best solution using elitist selection
Chromosome selection using roulette wheel method
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l=l+1
End loop while
Output the best solution
Figure 3 Pseudo-code of GA for RMLD problem (Vitayasak & Pongcharoen, 2015).
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Step 1: The problem was encoded in order to produce a list of genes using a numeric
string (seeFigure 4) (Vitayasak & Pongcharoen, 2013). Each gene represented a machine num-
ber. The number of genes was equal to the total number of machines. The candidate solution
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in Figure 4 means one chromosome consisting of ten machines or ten genes.

Step 2: GA parameters were identified: population size (Pop), number of generations
(Gen), probability of crossover (Pc), and probability of mutation (Pm).
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Step 3: The demand levels for each product in each period (Dgk) were created. Product
demands were stochastically generated by using random numbers between 0-1 as a value of
probability density function associated with demand profile. For example, in dataset 10M5N,
the demand distribution function of product 1 was defined in the form of uniform probability
distribution; the demand level is randomly generated between 100 and 200 units
[U(100,200)]. If the random number was generated as 0.5, the demand level would be as-
signed to 150 units.
Step 4: An initial population based on a number of candidate solutions was randomly
generated and defined as Pop. A machine in each sequence was then randomly chosen, e.g.,
machine 5 was initially chosen, so machine no.5 was placed in sequence no.1 (Figure 4). Ma-
chine 1 was chosen last and, therefore, was placed at the end of the sequence.

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Step 5: In each generation (where l was the counter of generation), crossover and muta-
tion operators were applied to generate new offspring according to Pc and Pm, respectively.
Please note that cross and mute were the maximum numbers of operations for crossover and
mutation consecutively whilst r and u were loop-counter indexes for crossover and mutation
operations, sequentially.
Step 6: Machines were placed and arranged row by row based on FL, FW and G as de-
scribed previously in section 3 (see Figure 2).

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Figure 4 Representation of a candidate solution.

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Step 7: The total material flow distance was calculated based on Dgk for P periods.
Step 8: The best chromosome having the shortest material flow distance was selected
using the elitist selection (Gen & Cheng, 1997).
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Step 9: Chromosomes for the next generation were chosen using roulette wheel selec-
tion.
Step 10: The GA process was stopped according to the number of generations. When
the GA process was terminated, the best-so-far solution was reported.
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4.2 Teaching-Learning Based Optimisation

The pseudo-code of the proposed TLBO for the robust machine layout design (RMLD)
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problem shown in Figure 5 can be described in following form:

Step 1: The problem was encoded to produce a list of machines using a numeric string
(see Figure 4). One learner refers to a candidate solution, so that each learner contains a num-
ber of machines to be arranged.
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Input problem dataset

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Set parameters (Pop, Gen, FL, FW, G, P)

Create demand level (Dgk) for each product associated with demand distribution
Randomly create an initial population of learners
Arrange machines row by row based on FL, FW and G
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Calculate material flow distance based on demand level (Dgk) for P periods of all learners
Set l = 1 (first generation)
While l ≤ Gen do
For a = 1 to Pop do
Identify the best solution (Xbest) to be Teacher. Teacher phase
Modify solutions (Xnew,a) based on Teacher (Xbest).
Arrange machines and calculate material flow distance of Xnew,a
If the new solution is better than the existing one,
then accept Xnew,a, , else reject Xnew.a, end.
End

For b = 1 to Pop do
Select any solutions randomly (Xb and Xc) Learner phase
If Xb is better than Xc,
( )
then X new,b = X old ,b + rb X b - X c ,

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else X new,b = X old ,b + rb (X c - X b ) , end.

Arrange machines and calculate total material flow distance of Xnew, b
If Xnew,b is better than Xold,b , then accept Xnew,b
else reject Xnew,b end.
End
l=l+1
End loop while
Print: the best solution
Figure 5 Pseudo-code of TLBO for RMLD problem.
Step 2: Parameters were identified: population size (Pop) and number of generations
(Gen).
Step 3: The demand levels of each product in each period (Dgk) were created.

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Step 4: An initial population based on the defined Pop was randomly generated.
Step 5: Machines were arranged row by row based on FL, FW and G, and total material

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flow distance was calculated for all learners (solutions) in an initial population.
Step 6: The best solution (Xbest: Teacher) was identified.

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Teacher phase:
Step 7: The solution was modified based on the best solution (Xbest) according to the fol-
lowing expression:

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Xnew,a = Xold,a + ra (Xbest - TFXold,a)

Xnew was the new solution. Xold was the existing solution. a was a solution index (a = 1,
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2, 3,…, Pop). ra was a random number in the range [0,1] at ath solution. TF was a teaching
factor. The value of TF can be either 1 or 2, which was recommended by Rao et al. (2011).
Modifying the solution based on the Xbest in Step 7 is illustrated through the example in
Figure 6 and described as follows:
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i) If the TF was equal to 1, which meant that only a single swap operation was re-
quired, two positions were randomly selected for swapping, e.g., position no. 2 (machine
no.3) and 4 (machine no.7) were selected. Two positions were swapped, so TFXold was 1-7-5-
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3-4-9-6-10-2-8.
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Figure 6 Modifying the solution based on the best solution in Step 7 of the Teacher phase.

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ii) Differences in the sequence were calculated as the changes needed to be made
by swapping the individuals (machines) of the TFXold sequence to get the Xbest sequence. Posi-
tion no.1 in Xbest was machine no.4 whilst machine no.4 in TFXold was in position no.5. So,
machine no.4 in position no.5 of TFXold was swapped with machine no.1 in position no.1. The
swapping processes were continued until TFXold was similar to Xbest. Hence, to get the Xbest
sequence from the TFXold sequence, the number of swapping operations was seven, including
(4,1) (2,7) (1,3) (9,3) (10,3) (8,3) and (3,7).
iii) The number of swapping operations was multiplied by a uniform random
number (ra) in the range 0 to 1. If the random number was 0.48, the number of swaps was
7*0.48 = 3.36, which was rounded down to 3. The Xold was modified with three swaps: (4,1),
(2,7), and (1,3). The Xnew is 4-2-5-1-3-9-6-10-7-8.

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Step 8: The material flow distance of Xnew,a was calculated based on the product having
maximum material flow distance.

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Step 9: The Xnew,a was accepted if it was better than Xold,a.

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Learner phase:
Step 10: Solutions were selected randomly (Xb and Xc) where b ≠ c. b is a solution index
(b = 1, 2, 3,…, Pop). c is a solution index (c = 1, 2, 3,…, Pop). Xold,b is Xb and modified to be
Xnew,b. rb is a random number in the range [0,1] at bth solution. Modification of Xold,b is ex-
pressed as
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If Xb is better than Xc, then Xnew,b = Xold,b + rb (Xb – Xc)
else Xnew,b = Xold,b + rb (Xc – Xb), end.
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In the case that Xb is better than Xc, modifying the solution Xold,b in Step 9 is illustrated
through the example in Figure 7 and described as follows:
i) Differences in the sequence were calculated as the changes needed to be made
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by swapping the individuals (machines) of the Xc sequence to get the Xb sequence. Position
no.1 of Xc was machine no.4 whilst machine no.4 of Xb was in position no.2, so machine no.4
in position no.1 of Xc was swapped with machine no.2 in position no.2. The swapping pro-
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cesses were continued until Xc was similar to Xb. Hence, in order to get the Xb sequence from
the Xc sequence, the number of swapping operations were nine, including (4,2) (4,1) (5,8)
(4,9) (3,7) (4,3) (6,4) (10,5) and (6,10).
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Figure 7 Modifying the solution of the Learner phase (step 10) in case of Xb being better
than Xc.
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ii) The number of swapping operations was multiplied by a uniform random num-
ber (ra) in the range 0 to 1. If the random number was 0.6, the number of swaps was 9*0.6 =
5.4, which was rounded down to 5. The Xold,b was modified with five swaps: (4,2) (4,1) (5,8)
(4,9) and (3,7). The Xnew,b was 2-1-8-9-7-4-6-10-3-5.
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In case that Xc was better than Xb, modifying the solution Xold,b in Step 9 is illustrated
through the example in Figure 8 and described as follows:
i) Differences in the sequence were calculated as the changes needed to be made
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by swapping the individuals (machines) of the Xb sequence to get the Xc sequence. Position
no.1 of Xb was machine no.2 whilst machine no.2 of Xc was in position no.2, so machine no.2
in position no.1 of Xb was swapped with machine no. 4 in position no.7. The swapping pro-
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cesses are continued until Xb was similar to Xc. Hence, in order to get the Xc sequence from the
Xb sequence, the number of swapping operations was nine, including (2,4) (1,2) (8,5) (9,1)
(7,3) (7,9) (7,6) (8,10) and (8,7).
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ii) The number of swapping operations was multiplied by a uniform random num-
ber (ra) in the range 0 to 1. If the random number was 0.6, the number of swaps was 9*0.6 =
5.4, which was rounded down to 5. The Xold,b was modified with five swaps (2,4) (1,2) (8,5)
(9,1) and (7,3). The Xnew,b was 4-2-5-1-3-7-9-8-10-6.
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Step 11: Total material flow distance of Xnew,b was calculated, and Xnew,b was accepted if
it gave a better solution.
Step 12: The TLBO process was stopped according to the Gen; otherwise, return to step
6. When the TLBO process was terminated, the best-so-far solution was reported.

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Figure 8 Modifying the solution of the Learner phase (step 10) in case of Xc being better
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than Xb.

4.3 Modified TLBOs (mTLBOs)

In the Teacher phase of TLBO, the best learner is selected to be the teacher for improv-
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ing the knowledge level of the whole class and teaches every subject. The teaching skill of the
best learner may be effective in some subjects. Each learner has differences in scores for each
subject. Multiple-teachers‟ concepts were implemented to modify the proposed TLBO in the
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Teacher phase. Concepts of modification using multiple-teachers were based on selection of

teachers and a number of classes as shown in Figure 9. Teachers were either randomly chosen
(without any constraints) or selected according to sequential quality of solutions (with con-
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straints). Learners were either grouped as a single class (one class for learners) or divided into
several classes (multiple classes) according to the number of classes (Num_class). Pseudo-
codes of Teacher phase for modified TLBOs are compared as shown in Table 4.
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Selection of teachers
No constraints With constraints
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Single class mTLBO1 mTLBO4

Multiple classes mTLBO3 mTLBO2

Figure 9 Concept of TLBO modifications

Table 4 Pseudo-code comparison of Teacher phase for modified TLBOs

Types of class
Single class Multiple classes
mTLBO1 mTLBO4 mTLBO2 mTLBO3
Generate the number of teachers (Num_teacher) Generate the number of classes (Num_class)

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Randomly choose solu- Select the good solutions Select the good solutions Randomly assign solutions
tions (Teachers) accord- (Xbest: Teacher) according (Xbest: Teacher) according (Learners) for each class
ing to Num_teacher to Num_teacher to Num_class
For a = 1 to Pop do, Randomly assign solutions In each class, randomly
For t = 1 to Num_teacher do, (Learners) for each class select Learner to be
Modify solutions (Xnew,a) based on Teach- Teacher
er no.t (Xbest,t) For s = 1 to Num_class do,
Calculate material flow distance of Xnew,a For a = 1 to number of learners in class no.s do,
based on the product having maximum material flow Modify solutions (Xnew,a) based on Teacher in
distance class no.s
If the new solution is better than the exist- Calculate material flow distance of Xnew,a based
ing one, then accept Xnew.a on the product having maximum material flow distance

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Else reject Xnew,a, End If the new solution is better than the existing
End one, then accept Xnew,a

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Select the best Xnew,a Else reject Xnew,a, end
End End
End

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There were four types for TLBO modification: I) A single class of learners without any
constraints on teacher selection (mTLBO1); II) Several classes of learners with constraints on

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teacher selection (mTLBO2); III) Several classes of learners without any constraints on teach-
er selection (mTLBO3); and IV) A single class of learners with constraints on teacher selec-
tion (mTLBO4). The mechanisms of TLBO and mTLBOs are compared as shown in Figure
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10.
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Figure 10 Mechanism comparison of Teacher phase for TLBO and modified TLBOs
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In mTLBO1 and mTLBO4, each learner studied with several teachers, so the number of
learners to number of teachers ratio (Learner:Teacher) was 1:n. The maximum number of
teachers was 10 percent of the population size (Max_value), and the number of teachers was
at least two. The number of teachers (Num_teacher) in each generation was determined in the
range between 2 to Max_value. The number of iterations for improving the process of each
candidate solution was Num_teacher. For mTLBO2 and mTLBO3, each learner studies with
one teacher, so that the Learner:Teacher ratio was 1:1. In the same way, the number of classes
(Num_class) in each generation was determined in the range between 2 to Max_value.

5. Experimental design and analysis

The computational experiments were conducted using eleven testing datasets, all of

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which had different numbers of heterogeneous-size machines with various product types as
shown in Table 5. 40M refers to forty machines, and 20N refers to twenty product types. Ma-

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chine sequence and demand profile for each product were different as shown in Appendix A.
Width and length of machines are presented in Appendix B. Two-step sequential experiments

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were conducted and are reported in the following subsections.
Table 5 Testing datasets
Problem size Datasets Number of machines (M) Number of products (N)
Small

Medium
10M5N
10M10N
20M10N
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10
20
5
10
10
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20M20N 20 20
20M40N 20 40
Large 30M15N 30 15
30M30N 30 30
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40M20N 40 20
Extra large 40M40N 40 40
50M25N 50 25
50M40N 50 40
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5.1 Investigation of TLBO parameter setting

Changing the algorithm‟s parameters usually influences the effectiveness of the
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algorithm. The aim of this experiment was to investigate the appropriate setting of the TLBO
parameters for solving a robust machine layout design (RMLD) problem. The TLBO
parameters include a combination of population size and the number of generations
(Pop*Gen), which were investigated for three levels (25*100, 50*50 and 100*25). The
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evaluation of the layout design was to minimise the total material flow distance. The number
of time periods was set to five periods. Each computational experiment was replicated thirty
times using different random seed numbers. There were eleven datasets, thirty replications
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and three values of Pop*Gen, which gave a total of 11*30*3 = 990 runs.
The results obtained from the computational experiment were analysed using analysis of
variance (ANOVA) for which the F and P values are shown in Table 6. The Pop*Gen had a
significant effect on the total distance with a 95% confidence interval or the P-value < 0.05
(the bold numbers) in 20M20N, 40M40N, 50M25N, and 50M40N. The optimised Pop*Gen
based on the minimum material flow distance shown in Table 7 was suggested to be set at
25*100 for 50M25N and 50M40N, and Pop*Gen: 50*50 for 20M20N and 40M40N. These
results indicated that a small number of learners per generation generated a better solution
than a large number of learners per generation although the total amount of search space was
equal (Pop*Gen = 2,500) in all levels. The Gen led to an increase in the evolution process or
number of learning loops, especially for the extra-large-size problem.

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Table 6 Analysis of Variance (ANOVA) on TLBO parameter

Source DF 10M5N 10M10N 20M10N 20M20N
F P F P F P F P
Pop*Gen 2 0.72 0.488 2.19 0.118 2.29 0.108 4.24 0.017
Error 87
Total 89

Source DF 20M40N 30M15N 30M30N 40M20N

F P F P F P F P
Pop*Gen 2 2.09 0.129 2.12 0.126 2.99 0.055 2.08 0.131
Error 87

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Total 89

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Source DF 40M40N 50M25N 50M40N
F P F P F P
Pop*Gen 2 5.80 0.004 9.79 0.000 7.26 0.001

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Error 87
Total 89

10M5N
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Table 7 Appropriate parameter for each dataset
Datasets Pop*Gen
100*25
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10M10N 50*50
20M10N 50*50
20M20N 50*50
20M40N 50*50
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30M15N 100*25
30M30N 50*50
40M20N 25*100
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40M40N 50*50
50M25N 25*100
50M40N 25*100
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5.2 Performance comparison

Different nature-inspired optimisation mechanisms adopted in metaheuristics affect the
quality of the solution obtained (Moslemipour & Lee, 2012; Rao, et al., 2012). The computa-
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tional experiment conducted in this work was based on the concept of fair comparison. This
means that the number of searches (candidate solutions) carried out by each algorithm must
be similarly predefined. The total number of searches is usually identified by a combination
of population size and number of generations (iterations). In this work, the total number of
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searches carried out by each algorithm was set at 2,500. The optimised setting of TLBO pa-
rameters was adopted from previous experiments. Likewise, the appropriate setting of GA
parameters that was previously investigated by (Vitayasak & Pongcharoen, 2014) (Pop = 25,
Gen = 100, crossover probability = 0.9, and mutation probability = 0.9) was adopted in this
experiment. The genetic operators were the Two-point Centre Crossover (2PCX) and Two
Operation Random Swap (2ORS) (Vitayasak & Pongcharoen, 2011).
The computational results of GA and TLBO were analysed in terms of the mean, stand-
ard deviation (Std. dev.) of material flow distance (MFD) (unit: metres), and computational
time (unit: second) as shown in Table 8. The lowest mean of MFD for each dataset is shown
in bold. The average MFD obtained from TLBO was lower than that obtained from GA for
seven of eleven datasets. These issues led to the idea of TLBO modifications, described in

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section 4.3. The mean computational times required by the TLBO and the GA were slightly
different.

Table 8 Comparison of solutions produced by GA, TLBO, and modified TLBO

Dataset Value GA TLBO mTBLO1 mTBLO2 mTLBO3 mTLBO4
10M5N Mean (m) 307,976.1 308,192.5 310,434.5 308,610.7 305,853.4 303,359.0
Std. dev. 10,632.4 8,925.2 8,273.7 9,185.0 6,808.4 3,845.1
Time (s) 65.0 56.8 137.8 50.6 49.4 121.8
10M10N Mean (m) 771,403.0 771,372.8 792,603.2 769,945.6 771,079.6 769,276.9
Std. dev. 10,557.2 11,116.2 12,206.9 8,796.6 7,666.4 8,472.2
Time (s) 105.8 130.2 323.0 119.2 134.8 337.6

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20M10N Mean (m) 1,616,703.7 1,615,932.6 1,711,775.9 1,610,519.0 1,625,220.8 1,610,299.7
Std. dev. 35,133.2 33,772.3 37,878.4 24,717.4 35,458.5 29,340.0

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Time (s) 266.0 221.6 384.0 217.4 220.2 383.4
20M20N Mean (m) 5,257,786.9 5,293,133.1 5,532,765.3 5,283,189.5 5,318,809.1 5,274,380.1
Std. dev. 99,932.4 74,808.5 133,887.0 90,601.1 77,551.9 92,862.5

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Time (s) 414.0 423.6 781.6 422.4 439.0 757.4
20M40N Mean (m) 10,368,820.1 10,416,073.3 10,754,547.0 10,447,999.9 10,402,487.7 10,385,186.7
Std. dev. 138,117.2 157,116.3 168,287.6 149,535.1 159,734.6 165,841.0
Time (s) 918.2 820.6 1,418.8 801.4 808.8 1,412.4
30M15N

30M30N
Mean (m)
Std. dev.
Time (s)
Mean (m)
3,836,315.3
69,293.5
414.8
8,257,391.9
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3,883,961.1
89,148.5
396.4
8,219,945.7
4,221,868.6
106,137.4
1,030.4
8,745,797.5
3,920,451.5
62,704.8
403.4
8,222,746.0
3,979,078.4
77,504.6
407.8
8,309,603.6
3,843,757.6
89,498.8
975.2
8,111,485.4
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Std. dev. 161,516.4 164,249.8 217,989.5 187,448.7 197,228.8 165,960.8
Time (s) 648.6 722.0 1,373.6 769.0 776.6 1,369.4
40M20N Mean (m) 7,624,618.0 7,489,970.7 7,749,066.3 7,415,087.8 7,511,101.7 7,319,036.6
Std. dev. 186,734.0 193,717.6 239,152.6 203,703.4 182,422.0 227,711.3
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Time (s) 682.0 590.8 823.4 572.4 592.2 800.2

40M40N Mean (m) 14,159,754.1 13,876,258.6 15,115,640.8 14,110,450.3 14,039,551.6 13,767,238.4
Std. dev. 456,916.9 832,971.3 441,234.9 288,911.0 451,167.7 456,251.7
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Time (s) 1,239.6 1,068.8 1,896.6 1,104.2 1,114.0 1,920.4

50M25N Mean (m) 12,516,491.9 12,175,637.4 13,047,868.0 12,169,084.3 11,907,395.1 11,861,712.9
Std. dev. 398,882.1 333,529.7 292,045.6 315,048.4 325,183.6 242,986.9
Time (s) 876.8 2.438 1,156.0 798.4 783.2 1,094.6
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50M40N Mean (m) 18,470,281.4 18,280,861.2 19,445,587.1 18,192,779.5 18,265,764.0 17,662,336.2

Std. dev. 528,513.0 467,368.6 779,717.6 476,277.7 477,343.8 374,696.4
Time (s) 1,074.5 1,040.2 1,659.8 1,199.0 1,161.0 1,636.8
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Four mTLBO algorithms were tested with eleven benchmarking datasets and compared
with GA and TLBO. For each dataset, each algorithm was computationally repeated thirty
times by adopting its optimised parameter setting. The computational results in Table 8 show
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that mTLBO4 produced the lowest average MFD in eight of eleven datasets. The layout area
of the best solution obtained from mTLBO4 was also less than TLBO as shown in Figure 11.
In mTBLO4, the improved process of a candidate solution was iterated in association with the
number of teachers. Multiple good teachers for each learner can bring learners up to the high-
er level of knowledge. This mechanism helped a candidate solution to escape from the local
optimal, so solution quality is better. In contrast, in TLBO, only one teacher acted to improve
learners. This was the reason for the longer execution time in mTLBO4, but the solution qual-
ity was better than those obtained by TLBO. However, mTBLO1 was not able to generate
better solutions compared to TLBO and other mTLBOs because teachers in mTLBO1 were
randomly chosen regardless of quality. Practically, the multi-teacher concept and quality of
teachers should be simultaneously considered.

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(a) TLBO
US (b) mTLBO4
Figure 11 Graphical layout of the best solutions obtained from (a) TBLO and (b) mTLBO4
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The convergences of TLBO and modified TLBO algorithms were investigated by plot-
ting the average best so far solutions in each generation obtained from thirty repeated compu-
tational runs. The convergence graphs for each size of problem are shown in Figure 12 (a)-(d).
The convergences of mTLBO1 were the slowest resulting from teachers chosen randomly. In
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contrast, mTLBO4 converged faster than the others in all problem sizes3 Learners had differ-
ences in skilled and unskilled subjects. Likewise, the teaching skill of each teacher was differ-
ent. Improving the learner with multiple teachers was the best approach.
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In order to compare the performance of the proposed algorithms, the differences in

mean of the total material flow distance obtained from the algorithms were statistically tested
using the Student‟s t-test. There were statistically significant differences in the mean of the
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total distance of TBLO and mTLBO4 in 10M5N, 30M30N, 40M20N, 50M25N, and 50M40N
as shown in Table 9. Although the means of the distances of TLBO and mTLBO4 in 10M10N
were not different (P-value > 0.05), the convergent rate of mTLBO4 was more than TLBO as
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shown in Figure12(a). mTLBO4 was able to find a better solution in a shorter time and the
solution quality obtained from TLBO is statistically better than that obtained from mTLBO1
in almost all datasets; this confirms that inefficient teachers affected the quality of learners.
The TLBO performance was statistically better than GA in some datasets, including 30M15N,
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40M20N, and 50M25N. In practice, TLBO required less parameter setting than GA. The
quality of solutions obtained by mTLBO4 and GA was similar in datasets 10M10N, 20M10N,
20M20N, 20M40N, and 30M15N with P-values of more than 0.05. The quality of the solution
obtained from mTLBO4 was significantly more efficient than that obtained from GA in the
last five datasets, which were in large-size and extra-large-size problems.
One of the great challenges on the application of metaheuristics is to identify the best
balance between exploitation and exploration mechanisms during the iterative search process.
In this work, the TLBO mechanisms were modified in order to improve the balance. The ex-
perimental outcomes from eleven datasets suggested that the majority of the best-so-far solu-
tions were obtained from the mTLBO4, in which a number of performing students (good can-
didate solutions) were selected to act as tutors to improve their classmates. This mechanism

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helps the search process to exploit the solution space using good quality solutions. The high
number of tutors implies the higher exploitive search, but requiring intensive computational
time and resources. In real-world problems that are complex and diverse, it is always ques-
tionable to have a single solution that performs best for all problem sizes across problem do-
mains (Ho & Pepyne, 2001).

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(a) small-size problem (10M10N) (b) medium-size problem (20M40N)

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AN
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(c) large-size problem (40M40N) (d) extra-large-size problem (50M40N)

Figure 12 Convergence graphs
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Table 9 P-value of Student‟s t-test

CEmTLBO1

mTLBO2

mTLBO3

mTLBO4

mTLBO1

mTLBO2
mTLBO1

mTLBO3
mTLBO1

mTLBO4
mTLBO2

mTLBO3
mTLBO2

mTLBO4
mTLBO3

mTLBO4

mTLBO4
TLBO &

TLBO &

TLBO &

TLBO &

TLBO &

& GA

Data
GA
&

&

&

&

&

&

set

10M5 0.317 0.859 0.259 0.010 0.422 0.023 0.000 0.192 0.006 0.087 0.932 0.032
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N
10M10 0.000 0.584 0.906 0.415 0.000 0.000 0.000 0.597 0.765 0.391 0.991 0.393
N
20M10 0.000 0.482 0.303 0.493 0.000 0.000 0.000 0.068 0.975 0.081 0.931 0.447
N
20M20 0.000 0.645 0.197 0.393 0.000 0.000 0.000 0.107 0.711 0.049 0.127 0.508
N
20N40 0.000 0.426 0.741 0.462 0.000 0.000 0.000 0.259 0.129 0.682 0.221 0.679
N
30M15 0.000 0.072 0.000 0.087 0.000 0.000 0.000 0.002 0.000 0.000 0.025 0.720
N
30M30 0.000 0.951 0.061 0.014 0.000 0.000 0.000 0.086 0.018 0.000 0.377 0.001
N
40M20 0.000 0.150 0.665 0.003 0.000 0.000 0.000 0.059 0.091 0.001 0.008 0.000
N
40M40 0.000 0.155 0.350 0.533 0.000 0.000 0.000 0.472 0.001 0.024 0.109 0.002
N
50M25 0.015 0.000 0.000 0.000 0.051 0.051 0.051 0.051 0.051 0.000 0.001 0.000
N
50M40 0.000 0.473 0.902 0.000 0.000 0.000 0.000 0.566 0.000 0.000 0.147 0.000
N

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6. Conclusions
This paper presents the development of a computer aided layout designing program
with the aim to minimise the total material flow distance with dynamic demand under a multi-
period planning horizon using the Teaching-Learning Based Optimisation (TLBO). A com-
prehensive literature review on the application of metaheuristics to solve layout design prob-
lems was also presented. Four modified TLBOs were proposed and comparatively investigat-
ed for their performance with classical metaheuristics by conducting a series of computational
experiments. The experimental results indicated that the majority of the best-so-far solutions
based on eleven benchmarking datasets (provided in the appendix) were obtained from the
proposed algorithms. The superiority of classical metaheuristics‟ performance, however,
comes with the drawback on the intensive requirement of computational time and resources.

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Future research directions may focus on the improvement of metaheuristics perfor-
mance (e.g., options of hybridisation, dynamic parameter tuning and dynamic balance of in-

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tensification, and diversification mechanisms) or investigate other issues of facility layout
design (e.g., considering re-layout approach, multi-criteria layout design, mix layout orienta-

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tion, or uncertainty issues in manufacturing environment).

Acknowledgement
This work was part of research projects supported by the Thailand Research Fund under
grant numbers MRG6080031 and RDG60T0003.

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Appendix

A. Product demand distribution and machine sequences for each dataset

Dataset Product Product demand distribution Machine sequence

10M5N 1 Uniform (100, 200) 2-1-6-5-8-9-3-4
2 Uniform (50, 400) 10-8-7-5-9-6-1
3 Normal (180, 50) 9-2-7-4
4 Normal (300, 120) 8-10-5-9-6
5 Exponential (1/200) 2-4-8-10-7
10M10N 1 Uniform (100, 200) 2-1-6-5-8-9-3-4
2 Uniform (50, 400) 10-8-7-5-9-6-1
3 Normal (180, 50) 9-2-7-4
4 Normal (300, 120) 8-10-5-9-6
5 Exponential (1/200) 2-4-8-10-7
6 Uniform (80, 200) 7-1-6-8-9-9-1-10

T
7 Normal (200, 80) 4-7-1-6-5-3-8-10-6-8
8 Normal (100, 50) 8-4-2-7-5-9-1-10

IP
9 Normal (300, 100) 2-5-1-6-8-4-9-3
10 Exponential (1/200) 3-2-7-10-4-5-6-9
20M10N 1 (100 50 200 45 130) 2-10-6-5-8-19-3-4
2 Uniform (50, 400) 10-8-7-5-9-6-1-19

CR
3 Uniform (100, 300) 9-2-7-4-17-13
4 (100 200 150 300 100) 4-2-3-12-1-9-16-18-20-15-14-6-11
5 (140 220 80 100 300) 10-9-1-3-18-17-6-2-11-4
6 Uniform (80, 200) 17-11-6-8-7-15-16-9-1-20
7 300)Exponential
Normal (200, (1/200)
80) 14-17-11-16-5-13-18-20-19-12-10-6-8-15
8 Normal (100, 50) 18-8-4-5-7-5-9-14-19-1-20-10-16-11-15-13-12

20M20N
9
10
1
2
3
Normal (300, 100)
Exponential (1/200)
(100 50 200 45 130)
Uniform (50, 400)
Uniform (100, 300)
US 2-5-1-6-8-14-9-11-3-15-12
3-2-15-14-11-1-7-10-4-5-13-6-9
2-10-6-5-8-19-3-4
10-8-7-5-9-6-1-19
9-2-7-4-17-13
AN
4 (100 200 150 300 100) 4-2-3-12-1-9-16-18-20-15-14-6-11
5 (140 220 80 100 300) 10-9-1-3-18-17-6-2-11-4
6 Uniform (80, 200) 17-11-6-8-7-15-16-9-1-20
7 300)Exponential
Normal (200, (1/200)
80) 14-17-11-16-5-13-18-20-19-12-10-6-8-15
8 Normal (100, 50) 18-8-4-5-7-5-9-14-19-1-20-10-16-11-15-13-12
9 Normal (300, 100) 2-5-1-6-8-14-9-11-3-15-12
M

10 Exponential (1/200) 3-2-15-14-11-1-7-10-4-5-13-6-9

11 Exponential (1/300) 5-6-11-15-2-12-3-4
12 Uniform(100, 400) 10-9-4-14-2-3-15-8
13 Uniform(200, 400) 11-2-4-14-5-3-15
14 (100 200 300 100 200) 10-12-11-15-13-1-14-4-5-3
ED

15 Normal(200, 80) 5-10-3-7-13-8

16 Exponential(1/200) 7-3-2-8-4-10-15-13-9-1
17 Normal(200, 80) 11-13-20-3-1-12-14-4-8-9-2
18 Normal(400, 200) 6-3-4-18-5-14-12-16-7-11-20-13-17-9-2-8-15
19 Exponential(1/400) 17-9-11-8-10-2-4-3-16-20-6-18-15-12-6-3-7
20 Uniform(200, 500) 13-2-6-9-11-3-14-4-12-158-17-8-1-16-18-10-7-20-19
PT

20M40N 1 (100 50 200 45 130) 2-10-6-5-8-19-3-4

2 Uniform (50, 400) 10-8-7-5-9-6-1-19
3 Uniform (100, 300) 9-2-7-4-17-13
4 (100 200 150 300 100) 4-2-3-12-1-9-16-18-20-15-14-6-11
5 (140 220 80 100 300) 10-9-1-3-18-17-6-2-11-4
CE

6 Uniform (80, 200) 17-11-6-8-7-15-16-9-1-20

7 300)Exponential
Normal (200, (1/200)
80) 14-17-11-16-5-13-18-20-19-12-10-6-8-15
8 Normal (100, 50) 18-8-4-5-7-5-9-14-19-1-20-10-16-11-15-13-12
9 Normal (300, 100) 2-5-1-6-8-14-9-11-3-15-12
10 Exponential (1/200) 3-2-15-14-11-1-7-10-4-5-13-6-9
11 Exponential (1/300) 5-6-11-15-2-12-3-4
AC

12 Uniform(100, 400) 10-9-4-14-2-3-15-8

13 Uniform(200, 400) 11-2-4-14-5-3-15
14 (100 200 300 100 200) 10-12-11-15-13-1-14-4-5-3
15 Normal(200, 80) 5-10-3-7-13-8
16 Exponential(1/200) 7-3-2-8-4-10-15-13-9-1
17 Normal(200, 80) 11-13-20-3-1-12-14-4-8-9-2
18 Normal(400, 200) 6-3-4-18-5-14-12-16-7-11-20-13-17-9-2-8-15
19 Exponential(1/400) 17-9-11-8-10-2-4-3-16-20-6-18-15-12-6-3-7
20 Uniform(200, 500) 13-2-6-9-11-3-14-4-12-158-17-8-1-16-18-10-7-20-19
21 Uniform(100, 300) 4-20-14-1819-2-1-6-5
22 Uniform(150, 400) 5-9-6-1-19-18-15-10-8-7
23 (200 150 300 400 200) 4-3-5-9-2-7-13
24 Exponential(1/150) 9-16-18-5-8-20-15-14-4-2-3-12-1-6-11-17
25 Normal(220, 80) 18-17-6-2-10-9-1-3-11-4
26 Normal(300, 100) 13-1-14-4-5-3-10-12-11-15
27 Normal(200, 90) 10-3-7-13-5-15-8-19
28 (100 200 250 300 100) 3-2-8-4-10-7-6-15-13-9-1
29 (250 100 350 250 100) 12-14-4-8-11-13-20-3-1-9-2

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30 Exponential(1/240) 20-13-6-3-4-18-5-12-16-7-11-10-14
31 Uniform(100, 400) 12-13-10-4-5-14-15
32 Normal(120, 80) 16-7-4-11-20-13-17-9-2-8-15
33 Exponential(1/300) 17-9-11-8-10-2-20-6-18-15-12-6-3-7
34 Uniform(100, 380) 13-2-6-9-11-3-14-4-2-12-19-8-1-16-18
35 Uniform(200, 450) 2-4-8-9-4-12-16-15
36 (200 50 100 300 200) 15-19-5-9-6-1-8
37 Uniform(180, 400) 20-13-15-19-2-7-10
38 Exponential(1/150) 9-16-18-5-8-10-15-14-4-2-3-1
39 Normal(180, 80) 9-14-6-19-1-20-10-16-11-15-13-12
40 Normal(250, 90) 6-18-8-4-2-1-20-10-16-11-15-13-12
30M15N 1 (100 50 200 45 130) 2-1-6-5-18-9-3-4-21-24-28-29
2 Uniform (50, 400) 25-10-8-7-5-19-6-1-30-28
3 Uniform (100, 300) 9-2-17-30-4-23-25
4 (100 200 150 300 100) 4-2-3-12-1-22-9-16-18-5-8-20-15-14-6-11-30
5 (140 220 80 100 300) 10-9-1-3-18-17-30-6-2-27-11-4-24
6 Uniform (80, 200) 17-11-6-8-7-15-16-9-1-20-22-25
7 300)Exponential
Normal (200, (1/200)
80) 14-17-11-21-16-5-13-18-20-19-12-30-10-6-8-15-26

T
8 Normal (100, 50) 6-18-8-4-2-27-5-9-14-26-19-1-20-10-16-11-15-13-12-30-9
9 Normal (300, 100) 4-2-5-1-6-8-14-29-11-3-15-12-28
10 Exponential (1/200) 3-2-26-15-30-14-11-1-7-10-4-5-13-6-9-27-21

IP
11 Exponential (1/300) 5-6-11-22-15-20-12-3-4-19
12 Uniform(100, 400) 23-10-9-24-14-21-3-15-8-28
13 Uniform(200, 400) 24-11-2-4-23-14-16-5-3-15-29
14 (100 200 300 100 200) 10-12-11-25-13-1-14-4-5-3-30

CR
15 Normal(200, 80) 5-25-10-3-7-13-8-30-23-17
30M30N 1 (100 50 200 45 130) 2-1-6-5-18-9-3-4-21-24-28-29
2 Uniform (50, 400) 25-10-8-7-5-19-6-1-30-28
3 Uniform (100, 300) 9-2-17-30-4-23-25
4 (100 200 150 300 100) 4-2-3-12-1-22-9-16-18-5-8-20-15-14-6-11-30

US
5 (140 220 80 100 300) 10-9-1-3-18-17-30-6-2-27-11-4-24
6 Uniform (80, 200) 17-11-6-8-7-15-16-9-1-20-22-25
7 300)Exponential
Normal (200, (1/200)
80) 14-17-11-21-16-5-13-18-20-19-12-30-10-6-8-15-26
8 Normal (100, 50) 6-18-8-4-2-27-5-9-14-26-19-1-20-10-16-11-15-13-12-30-9
9 Normal (300, 100) 4-2-5-1-6-8-14-29-11-3-15-12-28
10 Exponential (1/200) 3-2-26-15-30-14-11-1-7-10-4-5-13-6-9-27-21
AN
11 Exponential (1/300) 5-6-11-22-15-20-12-3-4-19
12 Uniform(100, 400) 23-10-9-24-14-21-3-15-8-28
13 Uniform(200, 400) 24-11-2-4-23-14-16-5-3-15-29
14 (100 200 300 100 200) 10-12-11-25-13-1-14-4-5-3-30
15 Normal(200, 80) 5-25-10-3-7-13-8-30-23-17
16 Exponential(1/200) 17-30-2-8-4-10-15-13-29
M

17 Normal(200, 80) 11-13-20-3-1-12-14-24-8-9-21

18 Normal(400, 200) 6-30-24-18-5-14-12-16-7-11-20-13-17-9-2-8-15
19 Exponential(1/400) 17-9-11-8-10-16-4-20-6-18-15-12-3-27
20 Uniform(200, 500) 13-22-6-9-11-3-14-4-25-17-8-16-18-10-7-20-29
21 Uniform(100, 300) 24-20-14-18-19-2-1-26-5
ED

22 Uniform(150, 400) 5-9-6-21-19-28-25-10-8-7-30

23 (200 150 300 400 200) 24-3-5-19-2-17-13
24 Exponential(1/150) 9-16-18-25-28-15-23-12-21-6-11-17
25 Normal(220, 80) 18-17-6-29-10-9-21-4
26 Normal(300, 100) 13-8-14-5-23-20-12-11-15
27 Normal(200, 90) 10-23-7-13-5-15-8-19
PT

28 (100 200 250 300 100) 3-24-8-30-10-26-15-13-9-1

29 (250 100 350 250 100) 22-14-4-8-11-13-30-29-24
30 Exponential(1/240) 20-13-6-23-4-18-5-12-16-27-11-30-14
40M20N 1 (100 50 200 45 130) 2-1-6-5-8-9-3-4-21-24-28-29
2 Uniform (50, 400) 25-10-8-7-5-9-6-1-39-38
CE

3 Uniform (100, 300) 9-2-7-33-4-23-25

4 (100 200 150 300 100) 4-2-3-12-1-32-9-16-18-5-8-20-15-14-6-11-37
5 (140 220 80 100 300) 10-9-1-3-18-17-35-6-2-27-11-4
6 Uniform (80, 200) 17-11-6-8-7-15-16-9-1-20-22-25
7 300)Exponential
Normal (200, (1/200)
80) 14-17-11-31-16-5-13-18-20-19-12-40-10-6-8-15
AC

8 Normal (100, 50) 36-18-8-4-2-7-5-9-14-26-19-1-20-10-16-11-15-13-12-30-39

9 Normal (300, 100) 34-2-5-1-6-8-14-9-11-3-15-12-38
10 Exponential (1/200) 3-2-26-15-40-14-11-1-7-10-4-5-13-6-9-27-31
11 Exponential (1/300) 5-6-11-22-15-2-12-3-4
12 Uniform(100, 400) 23-10-9-4-14-2-3-15-8-38
13 Uniform(200, 400) 24-11-2-4-14-5-3-15
14 (100 200 300 100 200) 10-12-11-15-13-1-14-4-5-3-35
15 Normal(200, 80) 5-25-10-3-7-13-8-39
16 Exponential(1/200) 7-3-2-8-4-10-36-15-13-9-1
17 Normal(200, 80) 11-13-20-3-1-12-14-14-8-9-2
18 Normal(400, 200) 6-3-4-18-5-30-14-12-18-7-24-11-20-13-17-9-2-8-15
19 Exponential(1/400) 17-9-11-8-10-2-4-3-16-4-20-6-18-15-12-6-3-7
20 Uniform(200, 500) 13-2-6-9-11-3-14-4-32-12-15-17-8-1-16-18-10-7-20-28-19
40M40N 1 (100 50 200 45 130) 2-1-6-5-8-9-3-4-21-24-28-29
2 Uniform (50, 400) 25-10-8-7-5-9-6-1-39-38
3 Uniform (100, 300) 9-2-7-33-4-23-25
4 (100 200 150 300 100) 4-2-3-12-1-32-9-16-18-5-8-20-15-14-6-11-37
5 (140 220 80 100 300) 10-9-1-3-18-17-35-6-2-27-11-4
6 Uniform (80, 200) 17-11-6-8-7-15-16-9-1-20-22-25
300)Exponential (1/200)

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 ACCEPTED MANUSCRIPT

7 Normal (200, 80) 14-17-11-31-16-5-13-18-20-19-12-40-10-6-8-15

8 Normal (100, 50) 36-18-8-4-2-7-5-9-14-26-19-1-20-10-16-11-15-13-12-30-39
9 Normal (300, 100) 34-2-5-1-6-8-14-9-11-3-15-12-38
10 Exponential (1/200) 3-2-26-15-40-14-11-1-7-10-4-5-13-6-9-27-31
11 Exponential (1/300) 5-6-11-22-15-2-12-3-4
12 Uniform(100, 400) 23-10-9-4-14-2-3-15-8-38
13 Uniform(200, 400) 24-11-2-4-14-5-3-15
14 (100 200 300 100 200) 10-12-11-15-13-1-14-4-5-3-35
15 Normal(200, 80) 5-25-10-3-7-13-8-39
16 Exponential(1/200) 7-3-2-8-4-10-36-15-13-9-1
17 Normal(200, 80) 11-13-20-3-1-12-14-14-8-9-2
18 Normal(400, 200) 6-3-4-18-5-30-14-12-18-7-24-11-20-13-17-9-2-8-15
19 Exponential(1/400) 17-9-11-8-10-2-4-3-16-4-20-6-18-15-12-6-3-7
20 Uniform(200, 500) 13-2-6-9-11-3-14-4-32-12-15-17-8-1-16-18-10-7-20-28-19
21 Uniform(100, 300) 4-21-24-28-29-2-1-6-5-8-9-3
22 Uniform(150, 400) 5-9-6-1-39-38-25-10-8-7
23 (200 150 300 400 200) 4-23-25-9-2-7-33
24 Exponential(1/150) 9-16-18-5-8-20-15-14-4-2-3-12-1-32-6-11-37

T
25 Normal(220, 80) 18-17-6-2-10-9-1-3-11-4
26 Normal(300, 100) 13-1-14-4-5-3-10-12-11-15-35
27 Normal(200, 90) 10-3-7-13-5-25-8-39

IP
28 (100 200 250 300 100) 3-2-8-4-10-7-36-15-13-9-1
29 (250 100 350 250 100) 12-14-4-8-11-13-21-3-1-9-2
30 Exponential(1/240) 20-13-6-3-4-18-5-12-16-7-24-11-30-14
31 Uniform(100, 400) 32-23-10-24-35-14-15

CR
32 Normal(120, 80) 16-7-24-11-20-13-17-9-2-8-15
33 Exponential(1/300) 17-9-11-8-10-2-20-6-18-15-12-6-3-7
34 Uniform(100, 380) 13-2-6-9-11-3-14-4-32-12-28-19-8-1-16-18
35 Uniform(200, 450) 21-24-28-29-30-4-2-1-6-5-8
36 (200 50 100 300 200) 15-19-5-9-6-1-39-38-25

US
37 Uniform(180, 400) 40-33-35-19-2-7-10
38 Exponential(1/150) 29-16-18-5-28-10-15-14-4-2-3-1
39 Normal(180, 80) 9-14-26-19-1-20-10-16-11-15-13-12-30-39
40 Normal(250, 90) 36-18-8-4-2-7-5-1-20-10-16-11-15-13-12
50M25N 1 (100 50 200 45 130) 2-1-6-5-8-9-43-40-21-24-28-29
2 Uniform (50, 400) 25-10-8-7-5-9-6-41-39-38
AN
3 Uniform (100, 300) 9-2-7-33-44-23-25
4 (100 200 150 300 100) 40-42-3-12-1-32-9-16-18-5-8-20-15-14-6-11-37
5 (140 220 80 100 300) 10-9-1-43-18-17-35-6-2-27-11-45
6 Uniform (80, 200) 41-47-11-6-8-7-15-16-9-1-20-22-25
7 300)Exponential
Normal (200, (1/200)
80) 14-17-11-31-16-5-13-18-20-19-12-40-10-46-48-15
8 Normal (100, 50) 36-18-8-4-2-7-5-9-14-26-19-1-20-10-16-11-15-13-12-30-49
M

9 Normal (300, 100) 34-2-5-1-6-8-14-49-11-3-15-42-38

10 Exponential (1/200) 3-2-26-15-40-14-11-1-7-10-44-5-13-46-9-27-31
11 Exponential (1/300) 50-46-11-22-15-2-12-3-4
12 Uniform(100, 400) 23-50-49-4-14-2-43-15-8-38-47
13 Uniform(200, 400) 24-11-2-4-14-5-3-15-45
ED

14 (100 200 300 100 200) 10-12-11-15-43-1-14-4-50-3-35

15 Normal(200, 80) 5-25-10-3-47-13-48-39
16 Exponential(1/200) 7-3-2-84-50-36-15-13-9-1
17 Normal(200, 80) 11-13-21-3-1-12-44-4-8-49-50
18 Normal(400, 200) 6-3-4-18-5-30-14-12-16-7-24-11-20-13-17-9-32-48-50
19 Exponential(1/400) 17-9-11-8-10-2-4-3-16-4-20-6-18-15-12-50-33-47
PT

20 Uniform(200, 500) 13-2-6-9-11-43-14-4-32-12-15-17-8-1-1618-10-7-20-28-19

21 Uniform(100, 300) 7-2-6-26-15-38-16-20-1
22 Uniform(150, 400) 3-17-1-2-20-8-46-19-14-11-15-12-7-23-16-10-18-44-13-9-5-36-50
23 (200 150 300 400 200) 3-39-2-42-27-41-45
24 Exponential(1/150) 15-9-19-33-12-3-6-35-48-14-7-42-13-4-16-11-10-18
CE

25 Normal(220, 80) 37-19-50-44-9-16-43-14-1-29-2-1-10-17-12-46-9-45-40

50M40N 1 (100 50 200 45 130) 2-1-6-5-8-9-43-40-21-24-28-29
2 Uniform (50, 400) 25-10-8-7-5-9-6-41-39-38
3 Uniform (100, 300) 9-2-7-33-44-23-25
4 (100 200 150 300 100) 40-42-3-12-1-32-9-16-18-5-8-20-15-14-6-11-37
AC

5 (140 220 80 100 300) 10-9-1-43-18-17-35-6-2-27-11-45

6 Uniform (80, 200) 41-47-11-6-8-7-15-16-9-1-20-22-25
7 300)Exponential
Normal (200, (1/200)
80) 14-17-11-31-16-5-13-18-20-19-12-40-10-46-48-15
8 Normal (100, 50) 36-18-8-4-2-7-5-9-14-26-19-1-20-10-16-11-15-13-12-30-49
9 Normal (300, 100) 34-2-5-1-6-8-14-49-11-3-15-42-38
10 Exponential (1/200) 3-2-26-15-40-14-11-1-7-10-44-5-13-46-9-27-31
11 Exponential (1/300) 50-46-11-22-15-2-12-3-4
12 Uniform(100, 400) 23-50-49-4-14-2-43-15-8-38-47
13 Uniform(200, 400) 24-11-2-4-14-5-3-15-45
14 (100 200 300 100 200) 10-12-11-15-43-1-14-4-50-3-35
15 Normal(200, 80) 5-25-10-3-47-13-48-39
16 Exponential(1/200) 7-3-2-84-50-36-15-13-9-1
17 Normal(200, 80) 11-13-21-3-1-12-44-4-8-49-50
18 Normal(400, 200) 6-3-4-18-5-30-14-12-16-7-24-11-20-13-17-9-32-48-50
19 Exponential(1/400) 17-9-11-8-10-2-4-3-16-4-20-6-18-15-12-50-33-47
20 Uniform(200, 500) 13-2-6-9-11-43-14-4-32-12-15-17-8-1-1618-10-7-20-28-19
21 Uniform(100, 300) 7-2-6-26-15-38-16-20-1
22 Uniform(150, 400) 3-17-1-2-20-8-46-19-14-11-15-12-7-23-16-10-18-44-13-9-5-36-50
23 (200 150 300 400 200) 3-39-2-42-27-41-45

41
 ACCEPTED MANUSCRIPT

24 Exponential(1/150) 15-9-19-33-12-3-6-35-48-14-7-42-13-4-16-11-10-18
25 Normal(220, 80) 37-19-50-44-9-16-43-14-1-29-2-1-10-17-12-46-9-45-40
26 Normal(300, 100) 13-1-14-40-45-3-10-12-11-50-35
27 Normal(200, 90) 10-3-7-13-50-25-8-49
28 (100 200 250 300 100) 3-2-8-42-10-7-36-15-13-9-31
29 (250 100 350 250 100) 12-14-40-8-11-13-21-38-1-9-2
30 Exponential(1/240) 20-3-6-39-44-18-5-12-16-47-24-11-30-14
31 Uniform(100, 400) 32-23-50-24-35-14-15
32 Normal(120, 80) 19-7-24-11-20-13-17-49-42-8-15
33 Exponential(1/300) 17-9-11-8-30-2-20-6-18-50-12-6-43-47
34 Uniform(100, 380) 13-2-6-9-11-2-14-41-32-42-28-19-8-16-18
35 Uniform(200, 450) 21-24-28-29-30-47-2-1-6-5-8
36 (200 50 100 300 200) 15-19-5-49-26-1-39-38-25
37 Uniform(180, 400) 40-33-35-19-2-7-10
38 Exponential(1/150) 29-16-18-5-28-50-15-14-4-42-3-41
39 Normal(180, 80) 9-14-26-47-46-15-13-12-30-49
40 Normal(250, 90) 36-18-48-37-25-20-40-16-11-15-13-42

T
IP
B. Machine width (W) and length (L) (unit in metres)

Number of machines

CR
No. 10 20 30 40 50
W L W L W L W L W L
1 2.50 3.20 2.77 4.43 3.34 3.67 3.34 3.67 3.34 3.67
2 1.30 2.20 2.74 3.29 2.74 3.29 2.74 3.29 2.74 3.29
3 0.80 3.00 1.58 3.64 2.10 2.74 2.10 2.74 2.10 2.74
4 3.00 1.20 3.31 1.89 2.11 2.96 2.11 2.96 2.11 2.96
5
6
7
8
9
3.50
4.00
1.80
2.90
1.20
2.50
4.00
2.40
2.50
3.25
1.47
2.39
1.15
0.96
2.84
1.33
4.29
1.96
2.68
2.03
US0.90
4.05
1.96
2.15
3.31
2.17
2.53
1.15
1.19
1.74
0.90
4.05
1.96
2.15
3.31
2.17
2.53
1.15
1.19
1.74
0.90
4.05
1.96
2.15
3.31
2.17
2.53
1.15
1.19
1.74
AN
10 4.20 3.50 4.82 4.02 6.53 2.97 6.53 2.97 6.53 2.97
11 2.20 2.20 1.42 3.41 1.42 3.41 1.42 3.41
12 3.40 3.40 2.32 3.02 3.24 3.57 3.24 3.57
13 3.00 3.00 1.69 2.37 2.74 3.29 2.74 3.29
14 2.65 2.65 2.99 1.93 2.32 3.02 2.32 3.02
15 2.00 2.00 2.02 1.26 1.69 2.37 1.69 2.37
M

16 2.40 2.40 3.80 3.80 2.99 1.93 2.99 1.93

17 1.60 1.60 2.00 2.00 2.02 1.26 2.02 1.26
18 4.00 4.00 2.70 2.70 5.22 3.07 5.22 3.07
19 3.40 3.40 2.50 2.50 4.56 2.53 4.56 2.53
20 2.00 2.00 2.30 2.30 3.22 1.24 3.22 1.24
ED

21 1.70 1.70 3.80 3.80 3.80 3.80

22 1.90 1.90 2.00 2.00 2.00 2.00
23 3.60 3.60 2.70 2.70 2.70 2.70
24 2.70 2.70 2.50 2.50 2.50 2.50
25 2.20 2.20 2.30 2.30 2.30 2.30
26 4.20 4.20 1.70 1.70 1.70 1.70
PT

27 2.20 2.20 1.90 1.90 1.90 1.90

28 2.50 2.50 3.60 3.60 3.60 3.60
29 3.20 3.20 2.70 2.70 2.70 2.70
30 3.00 3.00 2.20 2.20 2.20 2.20
31 4.20 4.20 4.20 4.20
CE

32 2.20 2.20 2.20 2.20

33 2.50 2.50 2.50 2.50
34 3.20 3.20 3.20 3.20
35 3.00 3.00 3.00 3.00
36 3.50 3.50 3.50 3.50
37 3.80 3.80 3.80 3.80
AC

38 2.40 2.40 2.40 2.40

39 3.30 3.30 3.30 3.30
40 3.90 3.90 3.90 3.90
41 2.77 4.43
42 2.74 3.29
43 1.58 3.64
44 3.31 1.89
45 1.47 1.33
46 2.20 2.20
47 3.40 3.40
48 3.00 3.00
49 2.65 2.65
50 2.00 2.00

42