Effectiveness of genetic multistep searches in interpolation and extrapolation domains on multiobjective optimization

In the design of reproduction operators of genetic algorithm (GA), it is important to consider the inheritance and acquisition of characteristics especially in solving combinatorial problems. Genetic multistep search, deterministic Multi-step Crossover Fusion (dMSXF) and deterministic Multi-step Mutation Fusion (dMSMF) are effective crossover methods in single-objective combinatorial problems; the former exploits parents´ characteristics and the latter explores outside the distribution of the population. In this paper, we extend these crossovers for multiobjective optimization problems. A selection strategy focusing on a dominance relation of solution sets for dMSXF and dMSMF is introduced to obtain non-dominated solutions that well approximates the Pareto front. We show the effectiveness of dMSXF and dMSMF in multiobjective NK models and examine their performance against increase in landscape complexity by tuning epistasis intensity.