A Comprehensive Approach to Optimized Cislunar Architecture Design Utilizing Capacity
Justin Kim
BAE Systems, Inc.
Naomi Owens-Fahrner
BAE Systems, Inc.
ABSTRACT
Cislunar Space Domain Awareness (SDA) has gained significant attention due to growing interest from government,
scientific, and commercial sectors. However the complex dynamics, large design space, and lack of standard design
methods present a significant challenge to generating effective architectures. Prior work has focused on optimizing
architectures for observability (access), but did not evaluate other critical measures of performance. This paper presents
a framework and method to simultaneously optimize observability and capacity. The resulting sensor tasking-related
metrics more realistically assess mission performance. This study formulates the architecture optimization problem
as a Markov Decision Process (MDP) that is solved with a multi-objective Monte Carlo Tree Search (MCTS). The
capacity optimization problem is formulated as a grid search MDP in which the sensor explores the cislunar volume
with an ε-greedy algorithm. By expanding the optimization problem with critical objectives and constraints, the
simulation method provides a more comprehensive and streamlined approach to architecture design for cislunar SDA.
In this work we present a comprehensive, viable, and extensible framework for the high-level conceptual design and
optimization of cislunar SDA architectures.
1. INTRODUCTION
Ground-based networks for near-Earth SDA are ill-equipped to perform cislunar SDA due to the large volumes, com-
plex dynamics, and observation constraints in the cislunar environment. An effective cislunar SDA architecture will
likely require some combination of collaborative in-space assets [1]; however, the large design space makes this a
challenging problem to address. In particular, the widely varying properties of orbit families in the cislunar regime
makes orbit selection far from obvious [2]. While the desire and need for SDA solutions in the cislunar region is clear,
at present there is no standard approach to design, evaluate, and optimize such architectures [3].
Prior work has formulated the architecture design problem as a multi-objective optimization problem that attempts
to maximize observability of a volume [4] [5] [3]. Observability is the theoretical Field of Regard (FOR), subject
to geometric and radiometric constraints. In the context of this problem, it is the percentage of the volume that is
visible to the architecture over time, and has been considered the standard metric for optimizing cislunar surveillance
networks [6]. Solutions to this problem have been demonstrated with Monte Carlo Tree Search, branch & bound,
particle swarm, simulated annealing, and other evolutionary algorithms [5] [7]. However, we posit that observability
alone is not sufficient to assess mission performance and realistically evaluate architectures.
Capacity is a measure of performance defined by the percentage of the volume that is observed over time by the ar-
chitecture subject to sensor FOV, agility, and tasking constraints, in addition to the observability constraints. Fig. 1
illustrates the difference between observability and capacity. For observability, the entire cardioid FOR is observable
except for an angular keep-out zone around the Earth. For capacity, coverage is determined by the sensor’s slew path
over time, which is constrained by sensor performance parameters such as agility, integration time, and FOV. Incorpo-
rating these factors into the architecture optimization problem is critical to realistically assess mission performance.
A capacity-based cislunar SDA solution is explored by Owens-Fahrner et al. [8], in which the authors initially opti-
mize and select architectures for observability, and then perform a capacity analysis on the best-in-class architectures.
However, this process requires extensive domain knowledge and human-in-the-loop effort to generate and analyze the
architectures.
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Fig. 1: Coverage as a function of observability vs capacity
This paper expands on such work by simultaneously optimizing for observability and capacity. Additional constraints
and objectives are imposed on the optimization problem such as orbit stability, scheduling metrics, and a higher fidelity
radiometric model. Challenges in this problem include the three-body orbital dynamics, line-of-sight constraints, large
volumes, and low SNR [9] [10]. We address such challenges with a comprehensive simulation method that informs
some of the trades that must be considered in optimizing an architecture for cislunar SDA.
As a mixed-integer, multi-objective, non-linear optimization problem, the architecture optimization problem is for-
mulated as a Markov Decision Process (MDP) as in [5]. A Monte Carlo Tree Search solution was demonstrated,
which we expand upon by including sensor tasking optimization and related objectives. Past studies have explored
some these objectives as isolated pieces, while in this work the objective space of the problem is expanded to include
capacity optimization and sensor tasking analysis, which provide metrics and constraints that are critical for assessing
architectures and evaluating mission performance. Simultaneously optimizing for observability and capacity reduces
the effort and mission knowledge required to evaluate cislunar architectures. With this streamlined method, we have
developed a comprehensive framework that more accurately reflects the complex dynamics and expansive trade space
of the problem.
2. BACKGROUND
2.1 Markov Decision Process
Both the architecture optimization and capacity optimization problems are formulated as Markov Decision Processes
(MDP). An MDP is a discrete-time stochastic control process and mathematical framework used to model decision
making. It is represented by the 5-tuple (S, A, T, R, γ) with state space S, action space A, state transition function T ,
reward function R, and discount factor γ. MDPs are memory-less processes, meaning that evolution of the state is
dependent only on the current state, and none of the preceding states. In general an actor, or agent, at state s may
perform an action that induces a transition to a new state s′ according to the transition function. The state-action pair
and associated new state produce an associated reward. The goal of an MDP is to discover a policy π(s) that maps
states to actions such that the cumulative future reward of the process is maximized. A number of different algorithms
can be used to solve an MDP - in this work the architecture optimization problem is solved via Monte-Carlo Tree
Search, and the capacity optimization problem is solved via ε-greedy search.
2.2 Monte-Carlo Tree Search
Monte-Carlo Tree Search is a heuristic search algorithm that can generally be used to solve sequential decision pro-
cesses; its application to this problem is described in [5] and is briefly described here. The state of the architecture
optimization problem is defined by the architecture parameters - namely, the number of observers and their orbital pa-
rameters. An architecture is composed of a set of observers as shown in Eq. 1, with each observer described by a tuple
in Eq. 2 that describes the observer’s orbit. In this work sensor parameters are homogeneous across the architecture
and are not represented in the state space of the problem.
There are only two possible actions in the action space: add another observer, or modify an existing observer’s orbit.
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Rewards are calculated in the simulation step of Fig. 3, and are an output of the capacity optimization process. These
rewards are used to assess the quality of an architecture and its membership in the Pareto-optimal set of solutions.
Nodes of the tree are architecture states, which describe the constituent observer orbits. Branches between nodes
represent the actions and transitions between states. There are four main steps in the Monte-Carlo Tree Search,
described below:
X = [Obs1 , Obs2 , ...] (1)
Obsi = [Orbit Family, Member, Phase] (2)
1. Selection Starting from a root node, traverse the tree via some exploration vs exploitation policy until an unex-
panded node is found.
2. Expansion If the unexpanded node is not terminal, expand it by creating a child node with a chosen action.
3. Simulation Simulate the node (architecture) and compute the associated reward. This is where capacity optimiza-
tion is performed, with reward metrics output from the sensor tasking optimization.
4. Backpropagation Update the estimated node value and visit count on the visited branch.
In this framework the root node can be selected by the decision maker, randomly set, or initialized as an “empty”
architecture. The exploration vs exploitation policy used in this work is the Upper Confidence Bounds for Trees
(UCT) [11]. This policy assesses the value of a node along with the number of times it has been visited, and attempts
to balance the exploration of new states with exploitation of known promising states. It is defined in Eq. 3 where
Q(s, a) is the value estimate of taking action a at state s, N(s) is the number of times s has been visited, N(s, a) is
the number of times action a has been taken at state s, and C is a constant. The first term represents the exploitation
of known states, while the second state represents the preference for exploring states that have not frequently been
visited.
s
lnN(s)
Q(s, a) +C (3)
N(s, a)
Because of the large action space this tree is said to have a high branching factor, which may result in the tree search
being “shallow”. Expansion of a node is constrained by Progressive Widening (PW) [12], which determines whether
a node is expanded or not by limiting the number of actions that can be taken from a node before it is considered “ex-
panded”. This encourages the tree search to reach states deep within the tree early on, while incrementally expanding
the tree horizontally [13]. Hyperparameters in the UCT and PW may be tuned to favor depth or breadth in the tree
search, i.e. exploitation vs exploration.
2.3 Pareto-optimal Set Evaluation
As a multi-objective optimization problem, determining a single optimal solution is typically not possible. Due to
competing objectives, any number of solutions could be considered optimal depending on the decision maker’s prior-
ities. The complete set of optimal solutions is known as the Pareto frontier. The frontier could potentially be infinite
in size, so we identify a subset of the Pareto frontier known as the Pareto-optimal set of solutions. The solutions in
the set, also known as non-dominated solutions, are typically determined by their proximity to the Pareto frontier in
addition to their diversity and spread in the objective space.
In this problem the Pareto-optimal set is determined by a set-quality indicator known as the Hypervolume Indicator
(HVI) as defined in [14]. The HVI maps a point set to the region of the objective space that is weakly dominated by
that set, and bounded below from a given reference point (assuming maximization). In simpler terms it can be thought
of as the size of the space covered by the set in objective space. The HVI is widely used as a set-quality indicator due
to its simplicity and strict monotonicity with respect to set dominance, and its ability to capture set characteristics in a
single real value [14]. Fig. 2 shows a notional HVI in two-dimensional objective space - the HVI (in this case an area)
is upper-bounded by the frontier of non-dominated solutions, and lower-bounded by an arbitrary reference point.
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Fig. 2: HVI in two-dimensional objective space
As the tree search progresses, new solutions are evaluated and mapped onto the objective space - if a new solution
marginally contributes to and increases the size of the HVI, then it is considered Pareto-optimal. Solutions that do not
contribute to the HVI are considered dominated and are not included in the Pareto-optimal set. Due to its simplicity, the
HVI extends with trivial ease to n-dimensional optimization problems. As described in [5] the HVI is incorporated in
the UCT shown in Eq. 4, so that the policy optimizes the set of best solutions, as opposed to any single solution. Now
that the state-action value estimate includes the HVI, the selection policy is compelled to act such that the hypervolume
of the union of the Pareto-optimal set P with the state-action value estimate is maximized.
s
lnN(s)
HV (Q(s, a) ∪ P) +C (4)
N(s, a)
3. METHOD
The central problem being addressed in this work is the optimal design of architectures for cislunar SDA. The pre-
vailing standard for optimizing cislunar surveillance networks has been to use observability to assess architectures [6],
and a general method to address the optimization problem with this metric is described in the previous section. In
this work we demonstrate a critical enhancement to the method, which is to include capacity optimization and sensor
tasking metrics to the architecture optimization problem, thus providing critical performance metrics that are needed
to realistically evaluate mission architectures. This section will detail the augmented method that includes the capacity
optimization routine and sensor tasking metrics.
The first step is to define the scenario. Any search volume may be used that is described by a set of static points in
cislunar space, as in Fig. 6. The volume of interest, point placement, and point density are easily modified and up to
the user to determine. The simulation time is defined and describes temporal parameters for the volume search and
capacity optimization, such as the starting epoch, volume search time, and time step. Viewing constraints for observ-
ability are defined here, and typically include geometric and radiometric constraints. Sensor and target parameters
are used to determine visual magnitude (mv), SNR, and agility for use in the capacity optimization. This work has
incorporated higher-fidelity BAE radiometric models in case detailed SNR calculations are required; for the purpose
of this work, a simple mv constraint is used to model detectability.
The next step is to define the architecture MDP parameters. The design space space of the architecture problem
is determined by the number of observers and orbits that can populate an architecture. This is arbitrarily limited
according to the user’s preferences. Objective metrics must also be defined for the optimization problem to calculate
rewards in the MDP. Relevant metrics were determined and included for the cislunar SDA problem (shown in Table
1), but the MDP formulation is flexible to include any number of additional metrics as long as they are quantifiable.
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Weights are then applied to the metrics to represent a decision maker’s priority.
Parameters for the Monte-Carlo Tree Search are then defined which include the number of iterations and hyperparam-
eters that define the exploration vs exploitation policy. Inputs from steps 1-3 are fed into the MCTS optimization as
depicted in Fig. 3. The critical enhancement in this work is the inclusion of a sensor tasking routine, which performs
the capacity optimization, as described in the next section. The orange highlights in Fig. 3 indicate where the capacity
optimization occurs. The final output of the method is a Pareto-optimal set of solutions, which is presented to the
decision maker to investigate further, or extract insight from results as shown in Section 4.3.
Fig. 3: Multi-objective MCTS flow diagram
3.1 Capacity Optimization
This section generally describes the volume search approach to capacity optimization, where the output is an optimized
slew plan for each sensor. Observability must first be determined in order to evaluate capacity. The set of observers
is instantiated with orbit and sensor parameters, and observer orbits are propagated for the simulation length. The
time-history of observability is then calculated for every observer-target pair in the scenario, subject to the viewing
constraints. Capacity is evaluated with a cooperative volume search among the instantiated observers. Using the
observability data, each observer performs an ε-greedy search of the space. The search is collaborative, meaning that
the observers share information on which targets were observed and when they were observed, so as to not perform
redundant observations.
The volume search subroutine is formulated as a grid search MDP: each observer has a local environment defined as
a Right Ascension / Declination (RA-dec) sphere, centered on the observer in the Earth-Moon Barycentric Rotating
(EMBR) frame shown in Fig. 4. The sphere is discretized according to the sensor’s FOV, with coordinates on the grid
corresponding to sensor pointing angles in the aforementioned local environment.
Figure 5 depicts a notional subsection of the RA-dec coordinate system in two dimensions. The actor’s state is
composed of its position in the RA-dec coordinate system, last observed targets, currently observed targets, a global
history of target observations, simulation time, and cumulative reward. The position on the grid in state si represents
the observer’s current pointing position. The action space consists of four cardinal directions in the RA-dec coordinate
system - the actor can slew up, down, left, or right. From each state si and action ai , there is an associated reward ri . In
this problem the reward is a linear function of the number of observable targets in that angular position, and the time
since each target in that position was last observed. Note that this is modifiable, and any priority function can be used
with the associated state data.
A simple ε-greedy algorithm is used by each actor to explore the space. At each time step, an actor will sample all
possible actions and determine the associated reward. It will greedily pick the action with the highest reward, with a
small probability (ε) of choosing a different random action. The ε parameter is essentially an exploration factor versus
the greedy exploitation. The greedy algorithm serves not only as the transition function, T , but also as the policy
π(s, a). While it is not necessarily optimal, it was selected for its speed and simplicity. Note that other MDP solutions
can be applied such as policy iteration, value iteration, and even MCTS.
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Fig. 4: RA-dec spherical coordinate system
Fig. 5: RA-dec grid discretized by sensor FOV
The result of the capacity optimization is a slew plan and observation history. The ε-greedy search provides a time
history of where each sensor is pointing, what targets are observed, and a cumulative reward generated throughout the
simulation. These results are used to calculated the evaluation metrics which are detailed in the next section.
3.2 Evaluation Metrics
Architectures are evaluated according to the eight metrics in Table 1, which also comprise the objective space of the
architecture optimization problem. The metrics # Observers and Average orbit stability depend only on the archi-
tecture instantiation - the remaining six metrics are outputs of the volume search capacity optimization. All values
are normalized to [0, 1] in the optimization problem and are formulated such that maximization is ideal. A decision
maker may apply weights to each metric to represent their priorities, which are then used to calculated the HVI and
membership in the Pareto-optimal set.
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Table 1: Optimization metrics
Maximum observability [%] Cumulative percentage of the volume that is observable
Maximum capacity [%] Cumulative percentage of the volume that is observed
Time to observe 90% of the volume [s] Time duration to observe 90% of the volume
Mean Time To Access (MTTA) [s] Median MTTA of targets in the volume
Average gap time [s] Median average gap time of targets in the volume
Observations per target [N] Median # of observations per target in the volume
# Observers [N] Count of observers
Average orbit stability [-] Average of each observer’s orbit stability
Maximum observability and Maximum capacity are both measures of cumulative coverage of the volume, subject to the
different constraints as explained in Section 1. Time to observe 90% of the volume captures the objective of observing
the full volume in the shortest amount of time.
Mean time to access is a measure of the response time of the system, and is defined as how long it takes, on average,
for a given target to be observed. Average gap time is the average gap duration in observability for a given target
over the simulation time. Observations per target reflects the objective of frequent revisits in the volume along with
Average gap time. In case a decision maker prioritizes frequent revisits, they can then assign higher weights to these
metrics. Note that these three metrics are calculated for every target, and the median value over the entire target deck
is used in the optimization problem.
# Observers is a proxy for cost, as an ideal architecture will use the fewest number of observers to sufficiently observe
the volume. Orbit stability is also considered a proxy for cost due to station-keeping and delta-V requirements that are
not modeled in this work. Stability values are taken from the JPL Three-body Orbit Catalog [15] where a value of 1
indicates a perfectly stable orbit and larger values indicate greater instability. Orbits with stability index greater than 2
are filtered out of the design space.
4. RESULTS
4.1 Scenario Description
The cislunar SDA scenario for this work is presented as a volume search in cislunar space. In these results we define
the volume as a 4x GEO shell with a 1x GEO inner radius - note that any static volume in the EMBR frame can be used.
All scenario plots are presented in the EMBR frame with dimensionless units of length (LU) as shown in Fig. 6. The
search time for the capacity optimization routine is set to one hour. The additional viewing constraints in the scenario
require us to consider temporal affects on observability i.e. the position of the sun will affect viewing geometry and
target detectability. Each instance of architecture simulation is performed at 4 different epochs, which are evenly
spaced across one Earth-Moon synodic period - this accounts for the varying position of the Sun in the EMBR frame.
The final computed objective values during evaluation are average values over the Epochs per simulation.
Assuming a visual sensor we impose the following viewing constraints: solar exclusion is defined as an angular keep-
out zone from the vector between the observer and the Sun, and is set to 30◦ . Due to stray light interference, similar
constraints are applied for Earth and Lunar exclusion zones where the angular keep-out is defined from the vector
between the observer and the limb of the body. Both the Earth-limb and Lunar-limb exclusion angles are set to 5◦ . A
visual sensor with absolute visual magnitude sensitivity of 20 is used for this analysis. A sunlit constraint is applied
to the targets in order to be observable, and a range-by-phase constraint is applied to the sensor. The sensor’s range is
a function of its visual magnitude sensitivity, solar phase angle, and target parameters as in [16].
The architecture optimization MDP reward space has eight dimensions, which is the number of optimization objectives
included in the HVI. For the purpose of demonstration, the architecture design space was limited to 4 observers,
8 phases per orbit, 35 orbit families, and 10 members per orbit family. This is an artificial constraint to reduce a
technically infinite design space to an amenable number. Weightings are applied to the objective metrics, with higher
priority placed on Maximum capacity, and # Observers as a proxy for cost. The Monte-Carlo Tree Search was run for
a total of 1,000 iterations, with every iteration producing a unique architecture.
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Fig. 6: EMBR frame and cislunar volume
4.2 Individual Architecture Results
This section will describe the outputs from the evaluation of a single optimized architecture. The outputs shown are
from an architecture consisting of two observers - one at a 4x GEO circular orbit and one at a Distant Prograde Orbit
(DPO). The results and plots in the section were from a single simulation at one epoch. The observability heatmap in
Fig. 7 is a cumulative binary plot of observability over the simulation time. A cone of non-observable points (in red)
is seen around the Earth due to the Earth-exclusion angle constraint.
Fig. 7: Observability heatmap: 4xGEO + Distant Prograde Orbit observers
Volume search results from the capacity optimization can be seen in the observation count heatmap in Fig. 8. This
figure shows the cumulative observation count per target over the simulation time. The DPO observer can be seen
circling the moon, and the 4xGEO orbit observer can be seen on the green trace around the GEO shell. The resultant
sensor slew plan can be seen in Fig. 9, which shows a visit count heatmap of each observer’s local RA-dec coordinate
system. This is a two-dimensional representation of each observer’s pointing coordinates, centered on the respective
observer. The heatmap is colored to indicate the frequency of visits on each grid space, showing where and how
frequently the observer was pointing at a given angular coordinate. Gaps in each observer’s search can be seen centered
around the Earth which is consistent with the Earth-exclusion viewing constraint. The higher search frequency around
the Earth is likely because the observer’s priority function searches for regions of higher density in the volume.
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Fig. 8: Observation count heatmap: 4xGEO + Distant Prograde Orbit observers
Fig. 9: Local environment visit count heatmap: 4xGEO + Distant Prograde Orbit observers
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A time history of the observability and capacity coverage is shown in Fig. 10. The coverage depicted is a result of
the collaborative search, meaning capacity contributions from all observers in the architecture. As expected, the ob-
servability is relatively constant and much greater than the capacity. Capacity, being a cumulative measure, continues
to increase as the observer searches the volume. The results shown thus far are for a single epoch evaluation i.e. the
architecture evaluated at only one starting time for a one hour search window.
Fig. 10: Coverage vs time: 4xGEO + Distant Prograde Orbit observers
Aggregate results of the objective metrics are shown in Table 2, with true dimensioned values. As noted in Section 3.2,
these values are averaged over several epochs to account for the varying position of the Sun. Note again that the MTTA,
Average gap time, and Observations per target are median values of the entire target deck. As shown in Fig. 10 the
architecture never achieves 90% capacity in the one hour search time, therefore the Time to observe 90% of the volume
is the maximum simulation time of 3,600 seconds. Depending on its orbit phase around the moon, the DPO observer is
able to see much of the volume, but is limited by range. The 4xGEO observer does not have such limitations; however,
due to its proximity to the volume and narrow FOV, only small arc segments of the volume can be seen at any given
moment which results in a slow search of the space. In this example, the observers are complementary to each other
and achieve good coverage of the volume without requiring a large number of observers.
Table 2: Objective results - 4xxGEO + Distant Prograde Orbit
Maximum observability 98.80%
Maximum capacity 78.34%
# Observers 2
Average orbit stability 1.001
Time to observe 90% of the volume 3600 s
MTTA 368 s
Average gap time 713 s
Observations per target 4
4.3 Pareto-optimal Results
The overall result of the architecture optimization process is a Pareto-optimal set of architectures. This set, and the
associated HVI, evolve as the tree search iterates as shown in Fig. 11. With enough iterations the MCTS is guaranteed
to converge on the global optimum; this would however require a number of iterations approaching the number of
total possible architectures. The advantage of MCTS is its ability to quickly explore breadth in the tree while also
remembering and exploiting valuable solutions. Among the 28,000 possible architectures, several optimized solutions
were found within the 1,000 architecture evaluations. In reality the design space and number of possible architectures
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is technically infinite, thus the possible architectures and number of iterations were limited to a tractable number for
the purposes of demonstration.
Fig. 11: HVI history
A Pareto plot of the objective space is shown in Fig. 12 for selected metrics. Each dot represents a unique architecture,
with grey dots representing dominated solutions and colored dots representing the Pareto-optimal solutions. Note again
that the objective values have been normalized between [0, 1] with weighting factors applied, and are formulated such
that maximization is ideal. A roughly linear trend between observability and capacity can be seen, with a similar trend
between capacity and gap time. In general, Pareto plots in the objective space can be useful to identify relationships
between objectives that are not obviously correlated.
Fig. 12: Pareto plot of selected metrics in the objective space
A coverage versus time plot for selected architectures in the Pareto-optimal set is shown in Fig. 13. Individual results
for the 4xGEO - DPO architecture are shown in the previous section. While it did not achieve as high capacity as
the other architectures, it achieved almost as much capacity with one fewer observer. If the # Observers metrics is
weighted heavily such results may be expected. Fig. 14 shows a histogram of orbit families that appear in the Pareto-
optimal set - depending on the scenario, this can vary and inform decision about candidate architectures. Because
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this example scenario uses a GEO shell volume, we may expect families of orbits that remain relatively close to the
Earth to perform well, which is consistent with the high frequency of xGEO and Low Prograde Orbits seen in the
Pareto-optimal set.
Fig. 13: Coverage vs time for selected Pareto-optimal solutions
Fig. 14: Histogram of orbit families in the Pareto-optimal set
With information on the Pareto-optimal set, an analyst or decision maker can infer broad insights into the solution
space of the problem. High-performing architectures and orbit families are identified for further investigation, and
relationships can be identified between objective metrics. Additionally, determining a Pareto-optimal set of solutions
allows one to identify and visualize trades in a high-dimensional objective space. The method and framework is
designed to be flexible and extensible, and allow analysis on a wide variety of cislunar SDA problems. Different
search volumes, optimization algorithms, objective metrics, and radiometric models can be implemented with ease.
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5. CONCLUSION
While the need for cislunar SDA is present, the architecture design problem remains complex and challenging due
to the complex dynamics and large design space. This work demonstrates a simulation framework that addresses the
complexity of the problem with a streamlined and comprehensive approach to evaluating mission performance. The
addition of capacity optimization in the problem provides critical measures of performance, allowing architectures to
be evaluated with more realistic objectives and constraints. The approach shown greatly reduces the domain knowledge
required to design cislunar missions, as well as the human-in-the-loop effort required to sustain such efforts. The
demonstrated framework is extensible, and can be used to evaluate a variety of scenarios with different search volumes,
optimization algorithms, sensor models, viewing constraints, and optimization metrics.
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