Trimming, ordering, and similarity check for DSMGA-II: DSMGA-II-TOS

The dependency structure matrix genetic algorithm II (DSMGA-II) is one of the state-of-the-art model-building genetic algorithms capable of solving combinatorial optimization problems by exploiting the underlying structures of the problems. The linkage model generates a series of masks for trial to recombine genes among chromosomes via optimal mixing. This paper proposes three improvements that adaptively adjust the scope, the order, and the receivers of trials. Specifically, the mean of the mask sizes from previous successful recombinations is used to limit the maximum sizes of later trials. Also, successful recombinations prioritize the corresponding mask sizes of trials. Finally, recombinations are confined between chromosomes that pass the proposed similarity check. The ablation study indicates that each proposed technique is indispensable. Combined with these three improvements, DSMGA-II-2E empirically consumes fewer function evaluations on most of the test problems.