Using computational swarm intelligence for real-time asset allocation [PDF]

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__________________________________________________________________________________________ This is the author's manuscript of the article published in final edited form as:Reynolds, J., Christopher, L., Eberhart, R., & Shaffer, P. (2015). Using computational swarm intelligence for real-time asset allocation. In 2015 IEEE Symposium on Computational Intelligence for Security and Defense Applications (CISDA) (pp. 1–5). http://doi.org/10.1109/CISDA.2015.7208619

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component, we observed cases where one asset that had relatively few signals assigned to it would be placed an infinite distance (if the boundaries were removed) from the signals. In these cases, the optimizer sacrificed one of the assets by causing its power contribution to become almost non-existent in order to gain an increase in the fitness spread component. Attempts to counter this behavior by adj usting weights on the fitness components were not very successful. Increasing the weight on the power component or decreasing the weight on the spread component had the effect of causing the assets to congregate too close to the receivers. Thus it was difficult to achieve a good middle ground. The addition of the fitness distance component gave more stability to the solutions obtained. This component is calculated by taking the mean of the distances between each asset and the center of mass of the transmitters that it is receiving as shown in the equation below. In this equation, De;>represents the distance between receiver(i) and the center of mass of the transmitters that receiver(i) is receiving. This distance, D(i) is subtracted from a constant Max Distance to so that a higher score is given to smaller distances and so that a positive value is always returned. Fil11u1s

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G. Receiver keep away Finally, a keep-away penalty has been added to keep all the assets outside of a spatial boundary, geographically separated from the transmitters. A sharp penalty is added to the overall fitness when any asset enters a pre-defined boundary around the signal sources. The overall fitness is multiplied by 0.5 for each asset inside the boundary. Prior to adding this boundary, at least one of the receivers ended up on top of the transmitter signals in order to achieve a high power score. In addition, the solution space has been limited to keep the receivers in a square of +- 100 Km in the X and Y dimensions. The keep-away boundary is user-selectable between a circular boundary and a straight, linear boundary. Future research will explore the use of a flexible boundary, with the eventual goal of matching it to the battlefield terrain. H. PSO settings

The Particle Swarm Optimization algorithm in [4] was used to converge to the solution. The PSO in this problem was set to 200 particles (population size), uses a neighborhood optimization strategy with a noisy inertia weight. The fitness components were weighted to balance the contribution of the three areas, with a special emphasis placed on the priority assignments. The swarm was run to 1000 generations, although typical convergence was less than 500 generations.

These were used as our test parameters. Experimentation was done with another set of swarm parameters using a population size of 50, a neighborhood size of 1, and a method of terminating the swarm early when convergence is detected. These are our performance parameters. Repeatability and runtimes of the optimizer using the test parameters and performance parameters are examined in the results section. Ill. GRAPIDCAL USER INTERFACE

The Qt software framework was used to develop an interactive GUI for this research. Qt is an open-source and cross-platform framework for UI development in C++. A current version of the GUI is shown in Figur e 1. The Allocation Plot on the top left shows the spatial location of the receivers and transmitters. The receivers are randomly distributed in the center. Color-coding is used to differentiate between the priorities of each transmitter. The keep-away boundary is depicted by a black circle around the transmitters. The PSO will attempt to optimize with highest priority signals (yellow in the spectrum plot) first, and mid priority second (green) and finally low priority (blue). In this test case, the transmitter location, priority and power was set randomly.

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In Figur e 2, by hovering over one of the receivers, the corresponding transmitters are highlighted, and the frequency allocation is highlighted in red. The subplot on the top right shows the fitness value versus the swarm generation. This is helpful to determine how the swarm evolved over generations. Ideally, the swarm should quickly converge to a maximum fitness and then the fitness should remain nearly constant for successive generations. Future work will be done to detect the point at which the swarm reaches a sufficient solution so that the swarm can be terminated.

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B. Run time Analysis Several run-time analyses were performed on the optimizer. Run-times were found for varying problem sizes and varying swarm parameters. For each run-time analysis, the PSO was run 50 times and the resulting run-times were averaged. Tests were run with both sets of PSO parameters as described in Tables 2.1 and 22. All run-time tests were performed on an Intel Core i7-4710HQ processor. All tests were run using a single thread of execution. Table 3 and Table 4 summarize these run-time tests.

Figure 2. PSO Result Highlighted.

TABLE3 Run times Using test PSO Parameters

Other settings that can be changed in the GUI are: the number of transmitters and receivers, the radius of the transmitter distribution, the radius of the keep-away boundary, and the fitness function component weights. Options exist to run the swarm at full speed, or to run the swarm slow enough that a human can observe it converge. After each run, additional textual information at the bottom of the GUI is given showing exact locations and frequencies of the receivers. IV. RESULTS

A. Analyzing Results To understand the distribution of final fitness values, we ran optimizations on a number of different configurations. We calculated the means and variances of the final fitness values for these configurations, which are summarized in Table 1 and Table 2. It is important to note that the fitness values have no physical meaning by themselves. The values listed here are merely useful for comparison between the different tests. TABLE I Fimess Means and Variances Using Test PSO Parameters

Receivers I Transmitters 3,30 4,30 4,50

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804 891 1234

1.18 5.57 11.6

Receivers I Transmitters 3,30 4,30 7,50

Average Runtime (ms) 452 667 1098

TABLE4 . Pro Run tunes U SIDI? e onnance PSOParameters

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C. Repeatability Analysis A special test problem was designed with a known global maximum solution. The test problem was designed to contain local maxima in which the PSO might become stuck. A statistical analysis was run using this test setup to determine how well the PSO finds the global best solution without becoming stuck in local maxima. Figure 3 shows the test case where 4 transmitters of alternating priority and equal power are uniformly spaced along the battlefield line and the global best solution for two assets. Any other solution is a local maximum solution. Using the test PSO parameters, it was found that the optimizer found the global best solution with a probability greater than 0.99. Running the swarm in this configuration for 50 configurations gave a mean fitness value of 645.8 and a standard deviation of 0.001. However, when the performance PSO parameters were used, the probability of finding the global best solution dropped to 0.77. The mean fitness value in this case was 628.9 and the standard deviation of fitness was 37.8.

ACKNOWLEDGMENT

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The authors would like to acknowledge the support from the sponsor, the Expeditionary Electronic Warfare Division, Spectrum Warfare Systems Department, at the Naval Surface Warfare Center (NSWC) Crane. This research was sponsored by Crane NSWC through CRNBAA14-002.

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REFERENCES

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vol.4, no., pp.1942 ,1948 vol.4, Nov/Dec 1995 [2]

Eberhart, R .; Kennedy, J., "A new optimizer using particle swarm theory," Micro Machine and Human Science, 1995. MHS '95., Proceedings of the Sixth International Symposium on , vol., no., pp.39,43, 46Oct1995

[3]

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V. CONCWSIONS

The Particle Swarm Optimization has been shown to be useful for the allocation of scarce resources of receivers in Electronic Warfare. This new research has shown that optimization over both frequency and 2D space is feasible with a very rapid run time of one second or less. A trade-off exists between obtaining repeatable solutions and obtaining solutions quickly. Next, continued research on the optimization in all 3 spatial dimensions will be performed. Future research is planned in the following five areas: expand receivers to multiple layers of assets, include more complex battlefield 3D terrain, restrict the movement of receivers, optimize while the transmitters are in motion, and finally, include humans in the swarm process with respect to the configuration of the exclusion zones.

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