Multi-Agent Evolutionary Model for Global Numerical Optimization

Abstract

Agent-based computation has been studied for several years in the field of distributed artificial intelligence and has been widely used in other branches of computer science. In this chapter, first, multi-agent systems and genetic algorithms are integrated to form a new algorithm, namely Multi-Agent Genetic Algorithm (MAGA), for solving the global numerical optimization problem. An agent in MAGA represents a candidate solution to the optimization problem in hand. All agents live in a latticelike environment, with each agent fixed on a lattice-point. In order to increase energies, they compete or cooperate with their neighbors, and they can also use knowledge. Making use of these agent-agent interactions, MAGA realizes the purpose of minimizing the objective function value. Theoretical analyses show that MAGA converges to the global optimum. Second, Macro-Agent Evolutionary Model (MacroAEM) is proposed with the intrinsic properties of decomposable functions in mind. In this model, a sub-function forms a macro-agent, and 3 new behaviors, namely competition, cooperation, and selfishness, are developed for macro-agents to optimizing objective functions. Finally, the MacroAEM model is integrated with MAGA, which results a new algorithm, namely Hierarchical Multi-Agent Genetic Algorithm (HMAGA), especially for optimizing decomposable functions. The convergence of HMAGA is also analyzed theoretically and the results show that HMAGA also converges to the global optima. To validate the performance of MAGA, MacroAEM, and HMAGA, benchmark functions are used. The scalability of MAGA along the problem dimension is studied with great care. The results show that MAGA achieves a good performance when the dimensions are increased from 20 to 10,000. Moreover, even when the dimensions are increased to as high as 10,000, MAGA still can find high quality solutions at a low computational cost. Therefore, MAGA has a good scalability and is a competent algorithm for solving high dimensional optimization problems. The experimental results about HMAGA show that HMAGA achieves a good performance, too, especially for high-dimensional functions. Apart from this, the analyses on time complexity demonstrate that HMAGA has a good scalability.