Multi-objective Differential Evolution for the Flow Shop Scheduling Problem with aModified Learning Effect

This paper proposes an effective multi-objective differential evolution algorithm (MDES) to solve apermutation flow shop scheduling problem (PFSSP) with the modified Dejong's learning effect. Theproposed algorithm combines the basic differential evolution (DE) with local search and borrows theselection operator from NSGA-II to improve the general performance. First the problem is encodedwith an appropriate rule to make the continuous nature of DE suitable for flow shop problems. Second,insert based local search is added in the initialization stage, as well as in each iteration to speed upconvergence. The former guarantees that the algorithm commences with better solutions while thelatter focuses the algorithm on promising areas. Third, in each generation, in order to improvediversity, two populations are introduced, current pop and advanced pop. The best solutions of eachiteration are stored in the current pop, while the less than desirable solutions are added to the advancedpop. At the end of each generation, the two are combined and better individuals are selected for thenext generation. The algorithm is then tested on benchmark problems to demonstrate its effectivenessand the results are discussed. Finally, a truncated version of Dejong's learning effect is proposed andMDES is used to solve the permutation flow shop with the modified learning effect