An experimental analysis of a new two-stage crossover operator for multiobjective optimization

Evolutionary algorithms for multiobjective problems utilize three types of operations for progressing toward the higher fitness regions of the search space. Each type of operator contributes in a different way toward the achievement of the common goal. The mutation operation is responsible for diversity maintenance, while the selection operation favors the survival of the fittest. In this paper we focus our attention on the crossover operator. The crossover operator by default is responsible for the search effort and as such deserves our special attention. In particular, we propose a two-stage crossover (TSX) operator for more efficient exploration of the search space. The performance of the proposed TSX operator is assessed in comparison with the simulated binary crossover operator with the assistance of three well-known multiobjective evolutionary algorithms, namely the NSGAII, the SPEA2 and the MOCELL, for the solution of the DTLZ1–7 set of test functions. We also compare the proposed TSX with other popular reproduction operators like the differential evolution and the particle swarm optimization. Finally, we examine the efficacy of the TSX operator in handling problems having five objectives. It is shown with the assistance of the Deb, Thiele, Laumanns and Zitzler set of test functions that the TSX operator can substantially improve the results generated by three popular performance metrics for most of the cases.