New results for the multi-objective sequence dependent setup times flowshop problem

Although many papers deal with the permutation flowshop scheduling problem with or without setups, according to our knowledge, little has been published tackling multi-objective optimization in presence of sequence dependent setup times. Hence, in this work we cope with this problem considering two pairs of well known independent objectives, the Cmax−TWT (Makespan-Total Weighted Tardiness ) and Cmax−TFT (Makespan-Total Flowtime). An effective algorithm, RIPG (Restarted Iterated Pareto Greedy), has been developed to face this complex scheduling setting. The RIPG is a Pareto evolution of the IG (Iterated Greedy) algorithm, a rather new metaheuristic approach which has shown state-of-the-art performance in single objective optimization for the permutation flowshop problem with [1] and without setups [2]. In essence, it consists of a greedy strategy iteratively applied over an archive of nondominated solutions. The greedy procedure used is an evolution of the well known NEH heuristic [3] and makes use of the Pareto relationship to generate a whole set of nondominated solutions. The rationale of the proposed method is very simple. Roughly, it is possible to divide it into five phases. The first phase is the Initialization, where an initial set of good solutions is generated using a heuristic approach. The remaining four phases are iteratively repeated and constitute the bulk of the algorithm. They are: the Selection phase, where one or more solutions, belonging to the current archive, are selected for the following steps. A modified version of the Crowding Distance Assignment procedure, originally presented in [4], has been developed in order to carry out the selection process. The Pareto greedy improvement phase is then applied over the selected solution and it returns a set of solutions which do not dominate each other. During this step, the current solution is disrupted (Destruction), removing some jobs from the sequence, and a greedy procedure Construction) is applied. The construction procedure reinserts the eliminated jobs into partial sequences similarly to the insertion procedure of the NEH heuristic, returning, a hopefully improved, nondominated solution set. This set is then added to the current Pareto archive and dominated elements are discarded. A Local search phase is hence applied on a selected solution to enrich the process and to improve the current Pareto set in terms of spread and diversity. Lastly, a Restart