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 kk are available for processing the specific subset 𝒪k of the given operations. Each set 𝒪k may be partitioned into subsets for their processing on the machines of type k. Solving the hybrid job-shop problem implies the solution of two subproblems: an assignment of all operations from the set 𝒪k to the machines of type k 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%.