A Probability Collectives Approach for Multi-Agent Distributed and Cooperative Optimization with Tolerance for Agent Failure

Centralized systems are vulnerable to single point failures that may severely affect their performance. On the other hand, in the case of a distributed and decentralized algorithm, the system is more robust as it is controlled by its autonomous subsystems or agents. This chapter intends to demonstrate the inherent ability of a distributed and decentralized agent-based optimization technique referred to as Probability Collectives (PC) to accommodate agent failures. The approach of PC is a framework for optimization of complex systems by decomposing them into smaller subsystems to be further treated in a distributed and decentralized way. The system can be viewed as a Multi-Agent System (MAS) with rational and self-interested agents optimizing their local goals. At the core of the PC optimization methodology are the concepts of Deterministic Annealing in Statistical Physics, Game Theory and Nash Equilibrium. A specially developed Circle Packing Problem (CPP) with a known true optimum solution will be solved to demonstrate the ability of the PC approach to tolerate instances of agent failure. The strengths, weaknesses and future research directions of the PC methodology will also be discussed.

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