Multi-objective genetic algorithms for the method of inequalities

Abstract

Global search capability of genetic algorithms (GAs) provides an attractive method for solving inequalities. For multi-objective optimisation, various multi-objective genetic algorithms (MGAs) have been proposed. However, due to the fundamental difference between the method of inequalities and conventional multi-objective optimisation, it is not immediately apparent how MGAs should be used for solving inequalities. In this chapter, the use of MGAs in the method of inequalities is discussed. For the effective use of MGAs, an auxiliary vector performance index, related to the set of inequalities, is introduced. A simple MGA with Pareto ranking is proposed in conjunction with the auxiliary vector index. The performance of the proposed MGA is tested on a special set of test problems and control design benchmark problems. © 2005 Springer-Verlag London Limited.