Floating-point to integer mapping schemes in differential evolution for permutation flow shop scheduling

For over 50 years now, the famous problem of permutation flow shop scheduling has been attracting the attention of researchers in operations research, engineering and computer science. Over the past several years, there has been a spurt of interest in computational intelligence heuristics and metaheuristics for solving this problem – ranging from genetic algorithms to tabu search to complex hybrid techniques. Most recently, differential evolution, one of the newest members of the evolutionary algorithm family, has emerged as a popular technique for application to this problem. The main problem in applying differential evolution to the permutation flow shop is that differential evolution works on continuous, or real-valued, parameters (it is a continuous optimisation method), whereas the flow shop problem involves finding sequences or schedules of n jobs, expressed as permutations of n distinct objects (integers). A mapping, or encoding, of floating-point numbers to integer permutations is therefore necessary for differential evolution to be applied to this problem. This paper provides a review and evaluation of the best-known encoding schemes in the literature.