A Multiagent Genetic Algorithm for Global Numerical Optimization

In this paper, multiagent systems and genetic algorithms are integrated to form a new algorithm, multiagent 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 analyzes show that MAGA converges to the global optimum. In the first part of the experiments, ten benchmark functions are used to test the performance of MAGA, and 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 20-10,000. 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 good scalability and is a competent algorithm for solving high dimensional optimization problems. To the best of our knowledge, no researchers have ever optimized the functions with 10,000 dimensions by means of evolution. In the second part of the experiments, MAGA is applied to a practical case, the approximation of linear systems, with a satisfactory result.