Glowworm Swarm Optimization : A Multimodal Function Optimization Paradigm With Applications To Multiple Signal Source Localization Tasks

Abstract

Multimodal function optimization generally focuses on algorithms to find either a local optimum or the global optimum while avoiding local optima. However, there is another class of optimization problems which have the objective of finding multiple optima with either equal or unequal function values. The knowledge of multiple local and global optima has several advantages such as obtaining an insight into the function landscape and selecting an alternative solution when dynamic nature of constraints in the search space makes a previous optimum solution infeasible to implement. Applications include identification of multiple signal sources like sound, heat, light and leaks in pressurized systems, hazardous plumes/aerosols resulting from nuclear/ chemical spills, fire-origins in forest fires and hazardous chemical discharge in water bodies, oil spills, deep-sea hydrothermal vent plumes, etc. Signals such as sound, light, and other electromagnetic radiations propagate in the form of a wave. Therefore, the nominal source profile that spreads in the environment can be represented as a multimodal function and hence, the problem of localizing their respective origins can be modeled as optimization of multimodal functions. Multimodality in a search and optimization problem gives rise to several attractors and thereby presents a challenge to any optimization algorithm in terms of finding global optimum solutions. However, the problem is compounded when multiple (global and local) optima are sought. This thesis develops a novel glowworm swarm optimization (GSO) algorithm for simultaneous capture of multiple optima of multimodal functions. The algorithm shares some features with the ant-colony optimization (ACO) and particle swarm optimization (PSO) algorithms, but with several significant differences. The agents in the GSO algorithm are thought of as glowworms that carry a luminescence quantity called luciferin along with them. The glowworms encode the function-profile values at their current locations into a luciferin value and broadcast the same to other agents in their neighborhood. The glowworm depends on a variable local decision domain, which is bounded above by a circular sensor range, to identify its neighbors and compute its movements. Each glowworm selects a neighbor that has a luciferin value more than its own, using a probabilistic mechanism, and moves toward it. That is, they are attracted to neighbors that glow brighter. These movements that are based only on local information enable the swarm of glowworms to partition into disjoint subgroups, exhibit simultaneous taxis-behavior towards, and rendezvous at multiple optima (not necessarily equal) of a given multimodal function. Natural glowworms primarily use the bioluminescent light to signal other individuals of the same species for reproduction and to attract prey. The general idea in the GSO algorithm is similar in these aspects in the sense that glowworm agents are assumed to be attracted to move toward other glowworm agents that have brighter luminescence (higher luciferin value). We present the development of the GSO algorithm in terms of its working principle, various algorithmic phases, and evolution of the algorithm from the first version of the algorithm to its present form. Two major phases ¡ splitting of the agent swarm into disjoint subgroups and local convergence of agents in each subgroup to peak locations ¡ are identified at the group level of the algorithm and theoretical performance results related to the latter phase are obtained for a simplified GSO model. Performance of the GSO algorithm against a large class of benchmark multimodal functions is demonstrated through simulation experiments. We categorize the various constants of the algorithm into algorithmic constants and parameters. We show in simulations that fixed values of the algorithmic constants work well for a large class of problems and only two parameters have some influence on algorithmic performance. We also study the performance of the algorithm in the presence of noise. Simulations show that the algorithm exhibits good performance in the presence of fairly high noise levels. We observe graceful degradation only with significant increase in levels of measurement noise. A comparison with the gradient based algorithm reveals the superiority of the GSO algorithm in coping with uncertainty. We conduct embodied robot simulations, by using a multi-robot-simulator called Player/Stage that provides realistic sensor and actuator models, in order to assess the GSO algorithm's suitability for multiple source localization tasks. Next, we extend this work to collective robotics experiments. For this purpose, we use a set of four wheeled robots that are endowed with the capabilities required to implement the various behavioral primitives of the GSO algorithm. We present an experiment where two robots use the GSO algorithm to localize a light source. We discuss an application of GSO to ubiquitous computing based environments. In particular, we propose a hazard-sensing environment using a heterogeneous swarm that consists of stationary agents and mobile agents. The agents deployed in the environment implement a modification of the GSO algorithm. In a graph of mini mum number of mobile agents required for 100% source-capture as a function of the number of stationary agents, we show that deployment of the stationary agents in a grid configuration leads to multiple phase-transitions in the heterogeneous swarm behavior. Finally, we use the GSO algorithm to address the problem of pursuit of multiple mobile signal sources. For the case where the positions of the pursuers and the moving source are collinear, we present a theoretical result that provides an upper bound on the relative speed of the mobile source below which the agents succeed in pursuing the source. We use several simulation scenarios to demonstrate the ecacy of the algorithm in pursuing mobile signal sources. In the case where the positions of the pursuers and the moving source are non-collinear, we use numerical experiments to determine an upper bound on the relative speed of the mobile source below which the pursuers succeed in pursuing the source.