A Genetic Algorithm for Hybrid Job-Shop Scheduling Problems with Minimizing the Makespan or Mean Flow Time

Abstract

We address a generalization of the classical job-shop problem which is called a hybrid job-shop problem. The criteria under consideration are the minimization of the makespan and mean flow time. In the hybrid job-shop, machines of type [Formula: see text] are available for processing the specific subset [Formula: see text] of the given operations. Each set [Formula: see text] may be partitioned into subsets for their processing on the machines of type [Formula: see text]. Solving the hybrid job-shop problem implies the solution of two subproblems: an assignment of all operations from the set [Formula: see text] to the machines of type [Formula: see text] and finding optimal sequences of the operations for their processing on each machine. In this paper, a genetic algorithm is developed to solve these two subproblems simultaneously. For solving the subproblems, a special chromosome is used in the genetic algorithm based on a mixed graph model. We compare our genetic algorithms with a branch-and-bound algorithm and three other recent heuristic algorithms from the literature. Computational results for benchmark instances with 10 jobs and up to 50 machines show that the proposed genetic algorithm is rather efficient for both criteria. Compared with the other heuristics, the new algorithm gives most often an optimal solution and the average percentage deviation from the optimal function value is about 4%.