Abstract
We describe and analyze the Local Charged Particle Swarm Optimization (LCPSO) algorithm, that we designed to solve the problem of tracking a moving target releasing scalar information in a constrained environment using a swarm of agents. This method is inspired by flocking algorithms and the Particle Swarm Optimization (PSO) algorithm for function optimization. Four parameters drive LCPSO—the number of agents; the inertia weight; the attraction/repulsion weight; and the inter-agent distance. Using APF (Artificial Potential Field), we provide a mathematical analysis of the LCPSO algorithm under some simplifying assumptions. First, the swarm will aggregate and attain a stable formation, whatever the initial conditions. Second, the swarm moves thanks to an attractor in the swarm, which serves as a guide for the other agents to head for the target. By focusing on a simple application of target tracking with communication constraints, we then remove those assumptions one by one. We show the algorithm is resilient to constraints on the communication range and the behavior of the target. Results on simulation confirm our theoretical analysis. This provides useful guidelines to understand and control the LCPSO algorithm as a function of swarm characteristics as well as the nature of the target.
Highlights
Ant Colony Optimization (ACO) [6] or Particle Swarm Optimization (PSO) [27] are swarm intelligence algorithms used in the mathematical community of optimization
In [40], for our Mobile Odor Source Localization (MOSL) problem, we proposed an algorithm called Local Charged Particle Swarm Optimization (LCPSO), inspired by CPSO, which takes into account communication constraints in distance between agents that are representative of underwater systems [41]
Simulation results are not treated in higher dimensions, but we assume that the results we present should be close to the results displayed in Dimension 2 because there are no cross-dimensional terms in the PSO equation described below in
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Tanner, Jadbabaie and Pappas, in a two-part article [11,12], made a fundamental mathematical analysis of the Reynolds rules using the Artificial Potential Field (APF) approach They proved that using potentials both attractive and repulsive, the flock becomes homogeneous with equal inter-agent distance and equal speed vectors at equilibrium. Ant Colony Optimization (ACO) [6] or Particle Swarm Optimization (PSO) [27] are swarm intelligence algorithms used in the mathematical community of optimization The strength of these approaches lies in using agents distributed in the workspace, sharing information to search for the optimum of a fitness function. Those hypotheses are removed one by one to show that our algorithm is resilient to a limited communication range.
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