Layout optimization of a military operations center using a genetic algorithm

Abstract

A genetic algorithm was developed to support the spatial layout design of military operations centers. Based on an abstract representation of the workplace, the algorithm uses a textual string as the genetic encoding method, two genetic operations (i.e., selection and swap) for simulating an evolution process, a fitness function that reflects a human factors characterization of workplace layout requirements, and an elitist strategy for improving its search efficiency. The effectiveness of the algorithm was demonstrated in the design of a mid-sized operations center that involved a team of 68 operators. This algorithm expands the human factors practitioners’ toolkit and enhances their ability to examine layout options of complex workplaces using modeling and simulation.

Keywords

Military operations center workplace layout genetic algorithm human factors

1. Introduction

The military operations center is a critical facility for a military mission. It is the nervous center of an operation where information from a variety of sources is received, analyzed, and synthesized to support the generation of centralized commands.¹ It is also a complex collaborative work environment where a team of operators works interdependently to support a common set of mission objectives.^2,3

To design such an operations center, an important consideration is its spatial layout, including the position of individual workstations and shared equipment in the workplace. The proximity among operators affects their ability to communicate and interact with one another, which is a key enabler to ensure the successful dissemination of information, development of team situational awareness, and ultimately the commander’s timely decision-making. How to configure the spatial layout of an operations center so that the floor plan best facilitates both individual taskwork and the collaborative effort of the entire team is a task that often requires human factors analysis.

A common design is based on the open-plan concept, which seeks to minimize spatial barriers in the workplace in order to enhance communication. Such a solution is widely applied in the civilian work environment. However, due to the nature of work that is being conducted, a military operations center differs in its design requirements in two significant ways.

Firstly, a close proximity is often preferred to enhance an operator’s ability to communicate. Even with a variety of technology-mediated information exchange methods, face-to-face conversation is still a widely used means for communication in an operations center. To maximize their ability to engage face-to-face, operators often prefer to be positioned in close proximity with frequent collaborators. By contrast, such an arrangement often leads to complaints in a civilian setting for uncontrolled noise and frequent distraction.⁴

Secondly, due to the handling of sensitive information, visual and acoustic privacy is sometimes a prominent concern in the military work environment. As an example, the console screens used by the intelligence team often need to be carefully protected. Consequently, compartmentation is commonly used where workstations with sensitive information are circled by physical walls or high partition dividers.

Due to these requirements, the layout of a military operations center frequently relies on a hybrid design approach, one that is generally based on an open-plan arrangement, with the adoption of compartmentation for specific operators or groups. Such an approach best balances the needs to maximize interaction and communication, while at the same time satisfying the security requirements.

A project was recently completed at Defence Research and Development Canada (DRDC) to optimize the layout of an operations center for a Canadian Armed Forces (CAF) unit. To support the design effort, a customized genetic algorithm was created in this study to search for superior layout solutions based on the hybrid design approach.

The concept of a genetic algorithm represents a family of randomized search and optimization methods that is inspired by the Darwinian evolution theory.⁵ One of its important features is the algorithm’s ability to search through the solution space of a problem by applying the concept of evolution to a pool of solutions.^6,7 Over the years, successful applications of the concept have been reported in numerous studies to resolve design and engineering problems, including to address the facility layout problem in a wide variety of domains, such as construction sites,^8,9 processing plants,¹⁰ wind farms,^11,12 naval ships,^13,14 cellular manufacturing,^15,16 and warehouse distribution centers.¹⁷ In the literature, the layout design challenge is often referred to as the quadratic assignment problem,¹⁸ which is known to be complex and is generally regarded as non-deterministic polynomial-time hard (NP-hard).^19–21 To my knowledge, the current study is the first time such a method has been applied to address the layout design of a military operations center where the quality of design is assessed based on a human factors characterization of operator interaction requirements. To support this study, the customized algorithm was packaged into a software tool, called the Genetic Algorithm for Layout Optimization (GALO). The tool provides graphical user interfaces to facilitate the modeling process. In the rest of this paper, I will describe the modeling of this workplace using the GALO, key features of the genetic algorithm, and its application to design the layout of a mid-sized operations center.

2. Design requirements of a Canadian Armed Forces operations center

The primary objective of this study was to optimize the spatial layout of a mid-sized operations center that needed to accommodate a team of 68 operators. These operators were grouped into five teams based on their functions. Due to the sensitivity of information, the actual names of the teams are not provided in this paper, and general labels are used instead. Table 1 shows the size of each team, the labels used in the model to indicate each team member, and the leader of each team. It is useful to note that many teams can be further divided into sub-groups, for example, Team Echo is comprised of two groups that work on a shift schedule. However, for the sake of brevity, such distinction is not emphasized in this paper.

Table 1.

The team composition of a mid-sized Canadian Armed Forces operations center.

Team	Size	Operator label	Team lead
Alpha	10	Op1–Op10	Op1
Bravo	10	Op11–Op20	Op11
Charlie	9	Op 21–Op29	Op21
Delta	16	Op30–Op 45	Op30
Echo	23	Op46–Op68	Op46
Total	68

Within this operations center, members of the same team have similar technical skills and use the same equipment systems to carry out their regular tasks. Members of the same team often are required to augment one another when task demand becomes high. Across teams, however, members’ skillsets often differ, as do the equipment systems required for their work. Extensive collaboration is frequently required for members across teams.

Figure 1 shows a schematic diagram of the workplace. The room has an irregular shape, and its overall size is approximately 80 feet × 100 feet. It has a main entrance, three emergency exits, and no windows. There is an enclosed room for housing computer servers, which cannot be used as an operator work area. In this study, it was assumed that the key architectural features of this space, such as positions of walls and doors, would not be altered.

Based on safety considerations, it was determined that four pathways were required to provide direct access to the entrance and three exits. These pathways divided the entire workplace into four areas in which individual workstations could be set up.

For each individual operator, a standard workspace of 6 feet × 8 feet was specified to accommodate the setup of the multiple computer systems required by the work. Based on the size of an individual workspace, it was estimated that the space could be configured to house a total of 71 workstations. In addition, a total of 100 square feet would be needed to accommodate common shared equipment, such as printers and shredders. This was approximately twice the size of a standard personal workstation and, as a result, the design problem was transformed to the assignment of 70 entities (i.e., 68 operator workstations and two shared equipment areas) into the available spaces.

3. Workplace representation in the Genetic Algorithm for Layout Optimization

To apply the genetic algorithm, a model of the workplace needs to be first constructed in the GALO. In this tool, a workplace is represented abstractly as a two-dimensional grid with a size of $m rows \times n columns$ . Each grid location, hereby referred to as a cell, can be defined as either an open cell where an operator can be allocated, a barrier cell that causes spatial obstruction, or an unassignable cell that does not cause spatial obstruction but cannot be assigned to an operator. The latter two types of construct are used to represent common architectural features in a workplace, such as walls or pathways.

Figure 2 shows the representation of this CAF operations center in the GALO. Based on the overall dimensions of the workplace and the size of each individual workstation, the room (i.e., as shown in Figure 1) was characterized as a grid space with a size of $16 rows \times 15 columns$ . Among a total of 240 cells that were available, 69 of them (i.e., those with a gray contour) were specified as unassignable to represent the pathways in the room, including both corridors that connect the entrance or exits, and the pathways required in each work area; 100 cells (i.e., those with a black contour) were defined as spatial barriers to indicate spaces that could not be used as operator work areas, such as the server room or partitions for work area compartmentation. The remaining 71 cells were considered open and could be assigned to operators or shared equipment.

After workplace definition was complete, the GALO used Dijkstra’s shortest path algorithm to analyze the proximity between every pair of open cells in the workplace.^22,23 The output of this algorithm was stored internally in an adjacency matrix to represent the transit effort required to move from one location to another in this workplace.

4. Modeling operator interaction

For complex collaborative workplaces such as a military command center, a key layout design objective is to facilitate operator interaction.²⁴ A common analytical method for examining operator interaction is link analysis. Based on this method, each pair of interacting operators is considered to form a link and a distinction between a source and a receiver can be made depending on the direction of information flow for each link.²⁵

This method has been incorporated in the GALO to describe operator interaction. Specifically, a matrix format interface is provided in the tool to define interaction links among all operators. In particular, a priority weight that ranges from zero to nine can be assigned to each source–receiver pair in a model. A larger weight indicates a higher priority for the associated link. A weight of zero means there is no interaction requirement between the associated source and receiver. Notably, the access requirement by an operator to a piece of shared equipment can be analyzed in the same way.

In this study, Subject Matter Experts (SMEs) were consulted to rate the interaction requirements between each pair of operators or between an operator and shared equipment. Based on a total of 70 workstation areas (i.e., 68 for operators and two for shared equipment), a priority weight matrix of 70×70 was created based on SME inputs. The operators were labeled sequentially in this matrix, as shown in Table 1. The two areas reserved for shared equipment were labeled as Op69 and Op70. For the sake of brevity, the complete matrix is not provided in this paper. Table 2 shows the ratings that were used to populate the matrix, which were obtained by averaging the inputs from all SMEs.

Table 2.

The ratings used in a priority weight matrix to indicate interaction requirements between all operators and shared equipment.

Team/equipment	Alpha	Bravo	Charlie	Delta	Echo	Shared equipment
Alpha (Op1–Op10)	9	9	9	7	5	9
Bravo (Op11–Op20)		9	9	3	6	9
Charlie (Op21–Op29)			9	3	3	9
Delta (Op30–Op45)				9	7	9
Echo (Op46–Op68)					9	9
Shared equipment (Op69–Op70)						0

For each pair of operators that belonged to the same team, SMEs generally suggested a strong demand for interaction in all cases. Therefore, the highest rating of 9 was assigned to all pairs of operators who belonged to the same group (i.e., shaded cells in Table 2). As an example, a rating of 9 was assigned to the link between Op1 and Op2 who belonged to the same team Alpha.

By contrast, the demand for interaction varied significantly for operators that belonged to different teams. The value ranged from 3 (e.g., between Bravo and Delta) to 9 (e.g., between Alpha and Bravo). In this study, these ratings were used to specify the interaction links between leaders of each team. For example, an average rating of 9 was obtained for interaction requirements between teams Alpha and Bravo, and this rating was entered into the interaction matrix for a link between Op 1 (leader of Alpha) and Op11 (leader of Bravo). Such an arrangement reflects that interaction among team leads was more frequent than that between regular members and the setup emphasized the clustering of team members as a higher priority in the layout arrangement.

Lastly, for access to shared equipment, a universal rating of 9 was used for all operators; however, a rating of 0 was specified between Op69 and Op70, indicating no requirement to collocate these two areas (see the last column in Table 2).

5. Setup of a customized genetic algorithm

A detailed description of the customized genetic algorithm has been reported elsewhere before.²⁶ In this paper, an overview of the algorithm including the configuration of its key parameters is provided. Specifically, the algorithm uses a textual string as a genetic encoding method to represent a chromosome (i.e., a layout solution), which is a variation of the permutation encoding scheme.⁶ Figure 3 illustrates this scheme using a six-space workplace example. Each space has a unique identifier, in this case labeled as s1–s6. Operators are coded numerically. For example, the string “5 3 6 2 1 4” represents a layout solution in which six operators are assigned to six spaces; in this case, the fifth operator (i.e., Op5) is positioned in the first space, the third operator (i.e., Op3) in the second space, and so on. If there exist fewer operators than available spaces, the code zero could be included in the string to indicate unoccupied spaces. In a valid solution, the codes for all operators should appear (i.e., the rule of completeness) and appear once only (i.e., the rule of non-redundancy), indicating each operator has been assigned to a single space.

In this study, a population of 10,000 layout solutions (i.e., chromosomes), was analyzed in each simulation run. At the beginning of each run, that is, at Generation zero, each solution was randomly created by the algorithm.

As the simulation unfolds, the quality of each layout solution, that is, its fitness, was assessed based on its impact on between-operator interaction effectiveness. This fitness function was developed on an existing model for layout quality assessment that considers human interaction in four domains, that is, visual, auditory, tactile, and movement.²⁵ For each pair of operators, their interaction effectiveness is assessed by a quality measure that considers the distance displacement between the pair, the characteristics of the interaction source and the receiver, and any spatial obstruction between them, as shown in the following equation²⁷:

q (i, j) = r (i, j) s (i, j) \prod_{h = 1}^{n} α (i, j, h)

(1)

where $q (i, j)$ is the quality of interaction between the ith source and jth receiver; $r (i, j)$ and $s (i, j)$ are a strength measure of the receiver and source; and $α (i, j, h)$ represents an attenuation of interaction efficiency due to spatial obstructions.

The total layout cost (J) is then computed by aggregating the cost of all interacting operator pairs in the workplace, based on Equation (2). The importance of each pair of interacting operators is prioritized and a scaling factor is introduced to ensure the total layout cost score ranges between 0 and 1, with a smaller J score (i.e., lower cost) indicating a more effective layout:

\begin{matrix} J = \sum_{i = 1}^{e} \sum_{j = 1}^{e} k_{0}^{(v)} [1 - q^{(v)} (i, j)] p^{(v)} (i, j) + \\ \sum_{i = 1}^{e} \sum_{j = 1}^{e} k_{0}^{(a)} [1 - q^{(a)} (i, j)] p^{(a)} (i, j) + \\ \sum_{i = 1}^{e} \sum_{j = 1}^{e} k_{0}^{(t)} [1 - q^{(t)} (i, j)] p^{(t)} (i, j) + \\ \sum_{i = 1}^{e} \sum_{j = 1}^{e} k_{0}^{(m)} [1 - q^{(m)} (i, j)] p^{(m)} (i, j) \end{matrix}

(2)

where J is the measure of total layout cost; e is the number of operators; $q (i, j)$ and $p (i, j)$ are the quality and priority values for each pair of interacting operators i and j, respectively; $k_{0}^{(.)}$ are combined weighting and scaling factors for each domain of interaction; and superscripts $v, a, t, m$ indicate four interaction domains, that is, visual, auditory, tactile, and movement.

Finally, to apply such a cost model in the genetic algorithm, an inverse transformation was used to construct a fitness function F so that a larger score is better (i.e., fitter), as shown in the following equation:

F = \frac{1}{J}

(3)

Notably, although the fitness function model enables a comprehensive assessment of operator interaction in multiple sensory domains, not all domains are required in a particular analysis. In the current study, due to the nature of operator tasks and the workplace’s architectural characteristics, the analysis was focused mainly on the movement domain.

In each step during a simulated evolution, a genetic operation, selection, was first adopted to ensure that layout solutions with a higher fitness score were more likely to be reproduced in the next generation. The operation generates an identical copy of a parent chromosome in the mating pool based on its fitness score. A mating pool is a construct in a genetic algorithm that holds selected chromosomes for the application of genetic operations. In this model, a roulette wheel method was used to control the selection operation. This method has been used in other studies in the past.²⁸ It involves a two-step procedure. Firstly, the fitness of each solution in a parent generation is computed, and then the proportion of a solution’s fitness of the total population fitness is calculated, and this value is used as the probability for selecting the specific solution for reproduction in the mating pool.

Next, for each chromosome in the mating pool, a second genetic operation called swap could be applied. This operation involves workstation exchange between two random locations in a layout. It alters an existing solution and may create a new one in the mating pool. The probability whether swap is applied to an individual solution was controlled by a user-defined variable, Probability of SWAP (PSWAP). In this study, the value of PSWAP was set at 0.5, based on the findings of previous research.²⁹

The use of genetic operations like swap is accompanied by the risk of destroying a good solution. To reduce such a risk, an elitist strategy was implemented in this algorithm. Such a strategy requires the tracking of the best solution (i.e., the fittest) in each generation and comparing the current best in the mating pool with the best one from the immediate generation before. If the current best is worse, then an exchange is performed that replaces the worst solution in the current mating pool with the best solution from the generation before. Such a strategy ensures the best solution is passed onto the next generation and increases the algorithm’s search efficiency.

After the elitist strategy is applied, all solutions in the mating pool are used to constitute the population of the next generation. At this point, a single step of simulated evolution is complete. In this study, an evolution process that involved 1000 generations was examined. Results from a total of 100 simulation runs were collected. The recommended solutions identified in repeated simulation runs were compared to one another, based on their fitness score, to obtain the overall best solution.

6. Results

Over 100 simulation runs, a total of three unique best layouts were identified. All of them shared the same fitness score, which means that they had the equivalent quality, as measured by the fitness metric used in the algorithm.

Figure 4 shows one of the recommended layout solutions. Notably, the locations of barrier cells (i.e., those with a black contour) and unassignable cells (i.e., those with a gray contour) are identical to those in Figure 2. The lines between operators indicate interaction links.

The following features are revealed in this solution:

operators from the same team are clustered together and allocated to one of the enclosed work areas, supporting the strong within-team interaction requirements;

the leaders from five teams (i.e., Op1, Op11, Op21, Op30, and Op46) are positioned in locations that are adjacent to the main gateway into each work area, and toward the center of the workplace, so that they are closer to each other, reflecting the frequent interaction needs among team leads;

the two cells for housing shared equipment (i.e., Op69 and Op70) are positioned at the center of the room, satisfying the demand from all operators for access to such equipment.

In addition to recommended layouts, the GALO also produced a diagram to display the change of fitness scores during a simulation run. Figure 5 shows such a diagram for the simulation run that generated the above-recommended design. Its horizontal axis represents the simulated evolution timeframe (i.e., generation number) and the vertical axis indicates the fitness score. The two lines are constructed by connecting the fitness scores of the best solution (the black line) and the population average (the gray line) in each generation. The dot (shown at Generation 1000) indicates the fitness score of a recommended solution, that is, an overall best obtained during the entire simulation over 100 runs. It is apparent that the algorithm was able to gradually improve the average quality of all solutions in the population, as well as the quality of the best one.

For the other two layout options that the GALO also recommended, the same design patterns explained above could be identified as well. Compared to the solution shown in Figure 4, one alternative solution switched the location between the two 10-man teams (i.e., Alpha and Bravo) and both involved some exchanges of members’ allocation within the same team. The quality of all three layouts was identical. Based on an analytical examination of the workplace requirement, it could be confirmed that these solutions represented an optimal layout for this design problem.

After the recommended layouts were identified in the GALO, additional transformation was performed to convert them into realistic designs with workstation setups for future implementation. Figure 6 shows the solution that was created based on the design shown in Figure 4.

7. Discussion

The usefulness of this genetic algorithm was confirmed in the current study to support military operations center layout design. Based on independently repeated simulations, the algorithm was able to efficiently identify superior layout solutions for the design problem. The effectiveness of this algorithm has been verified in hypothetical test cases before,²⁶ but this was the first time that this algorithm was applied in a large-scale design project.

In addition to a bespoke fitness function that reflects a human factors characterization of layout requirements, this algorithm differs from other genetic algorithms in two significant ways.

First, it adopts a genetic encoding method that is a variation of the permutation encoding scheme; in other words, it uses a string of numbers to indicate the sequence of workspace assignment. Such a method is different from many other genetic algorithms that use a binary scheme where a solution’s chromosome is comprised of a sequence of binary states (e.g., 0s or 1s).

Second, it uses a customized genetic operation (i.e., swap) as opposed to common operations, such as crossover and mutation, that are widely adopted in many other genetic algorithms, for simulating the evolutionary process. Crossover mimics the natural sexual reproduction process in which gene segments from two parents are combined to form the chromosome of an offspring. Mutation is asexual and applied to a single parent by changing the value at one or more random gene locations. These two genetic operations are not implemented in the current algorithm primarily because they may generate invalid genetic strings that violate the rule of completeness or the rule of non-redundancy. Although there are ways to correct invalid chromosomes,^30,31 such techniques were not introduced in the current algorithm mostly because the adopted swap operation was found to be sufficiently effective. It is useful to point out, however, that due to the lack of conventional genetic operators, such as crossover and mutation, a large value was suggested for the probability of applying swap (in this case, PSWAP = 0.5). This differs from many other genetic algorithms where a more conservative value is recommended for such parameters.

The grid-style workspace representation currently implemented in the GALO is highly abstract. However, with the use of two supporting constructs (i.e., barrier and unassignable cells), it is feasible to model workplaces with irregular shapes, as shown in this study. Currently in the GALO, individual workspaces are assumed to have an identical size and can be assigned to any operator, which was acceptable in this study since a standard workspace footprint was specified for all. However, this is an exception rather than the rule as it is common in many applications where a range of individual workspaces of different sizes or shapes need to be considered. Currently, such requirements cannot be represented in the GALO. A solution to this limitation will require a modification of the tool itself, which will be a topic for future development.

8. Summary

To sum up, the current study is concerned with the layout design of military operations centers. As a complex work environment, such operations centers are critical for military missions. Their layout is a key enabler to facilitate operator interaction and ensure the efficient flow of information in the workplace.

In this paper, I have described the use of a genetic algorithm to assist with the layout design of a mid-sized military operations center. This algorithm uses an encoding scheme and genetic operations that are customized for this problem domain. It adopts a fitness function that quantifies layout quality based on its support to operator interaction and incorporates an elitist strategy to improve the algorithm’s search efficiency. Based on an independently repeated simulation strategy, this study confirmed the effectiveness of this algorithm to generate layout solutions that best facilitate operator interaction both within and across teams. The main contribution of this work is the customization of genetic algorithm techniques to support a military application. The addition of this algorithm to the human factors practitioners’ toolkit enhances their ability to examine layout options of complex workplaces using modeling and simulation.

Footnotes

Acknowledgements

The author would like to thank Kevin Baker and Kelly Forbes for their contribution to the data collection.

Funding

This work was supported by the DRDC Human Centric Cyber project.

ORCID iD

Wenbi Wang

Author biography

Wenbi Wang is a defence scientist at DRDC, which is the Canadian national leader in defense science and technology. He has been a member of the Human Effectiveness section at the Toronto Research Centre since 2003. He received his PhD in Mechanical and Industrial Engineering with specialization in human factors from the University of Toronto. His current research focuses on computational human performance modeling, including the development of evolutionary algorithms to address human systems integration challenges in military applications.

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