Genetic multi-step search in interpolation and extrapolation domain

Abstract

The deterministic Multi-step Crossover Fusion (dMSXF) is an improved crossover method of MSXF which is a promising method of JSP, and it shows high availability in TSP. Both of these crossover methods introduce a neighborhood structure and distance in each permutation problem and perform multi-step searches in the interpolation domain focusing on inheritance of parents' characteristic. They cannot work effectively when parents stand close each other since they search in interpolation domain. Therefore in the case of the MSXF, the Multi-step Mutation Fusion (MSMF), which is the multi-step search in the extrapolation domain, is combined as the supplementary search to improve its search performance. On the other hand, the search mechanism for acquisition of characteristics, such as MSMF, is not applied to dMSXF. In this paper, we introduce a deterministic MSMF (dMSMF) mechanism as complementary multi-step extrapolation search. We apply dMSXF+dMSMF to TSP and JSP, which have structural difference between their landscapes. Through the experiments it was shown that the deterministic multi-step search in interpolation/extrapolation domain performed effectively in combinatorial problems.

Effectiveness of Multi-step Crossover Fusions in genetic programming

“…dMSMF has been shown to outperform other heuristic methods under the definition of sophisticated neighborhood structures and distance metrics on JSP and traveling salesman problem (TSP) [11].…”

“…This model focuses on a local search performance and it showed effectiveness in combinatorial optimization problems [3], [10], [11]. , xi+1), select the best individual c from offspring C(xi, xi+1) generated by parents (xi, xi+1) and replace the parent xi with c. 6.…”

“…The main difference of these procedures is that the MSXF determines the transition in the local search by Metropolis criterion while dMSXF advances the local search in a deterministic rule. MSXF and dMSXF are defined in a problem-independent manner, and have been successfully applied to various combinatorial optimization problems [10], [11], [12] since the incorporation of local searches into GAs is essential in order to adjust the structural details of solutions [13].…”

Effectiveness of Genetic Multistep Search in Unsupervised Design of Morphological Filters for Noise Removal

“…The acquisition of characteristics that do not appear in the parents can be achieved by incorporating deterministic Multi-step Mutation Fusion (dMSMF) 20) into dMSXF. dMSMF also performs a multistep neighborhood search and explores the external domain of the population distribution.…”

“…Deterministic Multi-step Mutation Fusion (dMSMF) is a complementary search method to dMSXF and explores outside the distribution of the population. It has been shown that the incorporation of dMSMF into dMSXF improves the search performance in several combinatorial problems 20) . In addition, we have shown that the high search performance of both dMSXF and dMSMF was achieved by setting the neighborhood size to a value near the correlation length, which is an indicator of the level of epistasis 21) .…”