Multi-objective Optimization of the Distributed Permutation Flow Shop Scheduling Problem with Transportation and Eligibility Constraints

In this paper,we consider the distributed permutation flow shop scheduling problem(DPFSSP)with transportation and eligibility constrains.Three objectives are taken into account,i.e.,makespan,maximum lateness and total costs(transportation costs and setup costs).To the best of our knowledge,there is no published work on multi-objective optimization of the DPFSSP with transportation and eligibility constraints.First,we present the mathematics model and constructive heuristics for single objective;then,we propose an improved The Nondominated Sorting Genetic Algorithm II(NSGA-II)for the multi-objective DPFSSP to find Pareto optimal solutions,in which a novel solution representation,a new population re-/initialization,effective crossover and mutation operators,as well as local search methods are developed.Based on extensive computational and statistical experiments,the proposed algorithm performs better than the well-known NSGA-II and the Strength Pareto Evolutionary Algorithm 2(SPEA2).