Competitive genetic algorithms for the open-shop scheduling problem

For more than two machines, and when preemption is forbidden, the computation of minimum makespan schedules for the open-shop problem is NP-hard. Compared to the flow-shop and the job-shop, the open-shop has free job routes which lead to a much larger solution space, to smaller gaps between the optimal makespan and the lower bounds, and to disappointing results for the algorithms based on the disjunctive graph model. For instance, the best existing branch and bound method cannot solve some 7 ×7 hard instances to optimality, and all published metaheuristics (working by reversing some disjunctions already fixed) do not better than some greedy or steepest-descent heuristics which need a much smaller computational effort. In this context, the intrinsic parallelism of genetic algorithms (GAs) seems well adapted, for detecting global optima disseminated among many quasi-optimal schedules. This paper presents several GAs for the open-shop problem. It is shown that even simple and fast versions can compete with the best known heuristics and metaheuristics, thanks to two key-features: a population in which each individual has a distinct makespan, and a special procedure which reorders every new chromosome. Using problem-specific heuristics, it is possible to design more powerful GAs which give excellent results, even on the hardest benchmarks of the literature: for instance, all hard open instances from Taillard are broken, except one for which the best known solution is improved.