A Fitness Landscape Analysis for the No-Wait Flow Shop Scheduling Problem with Factorial Representation

Abstract

The no-wait flow shop scheduling problem (NWFSP) is one of the essential models in the manufacturing systems. In this paper, the fitness landscape of the factorial representation for NWFSP with the makespan criterion is studied. The encoding and decoding schemes based on the factorial representation are constructed to transfer the permutation domain to the integer domain. The position-type distributions and fitness distance correlation are implemented to analyze the fitness landscape of the classic benchmarks. The multiple big valleys' structure in the fitness landscape is confirmed through the observation of fitness distance plot and the analysis of factorial coding theory. The various local optima and high ruggedness of the fitness landscape are visualized through the statistical results of position-type distributions. The results of fitness landscape analysis show the suitability of the landscape for the searchability with evolutionary algorithms and local search methods for solving NWFSP.