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A Genetic algorithm to minimize the makespan in the k-stage hybrid flow shop scheduling problem

Besbes W., Teghem J., Loukil T.

Foundations of Computing and Decision Sciences

2010

Vol. 35, No. 1

3-24

In this paper, we consider the k-stage hybrid flow shop scheduling problem where the parallel machines are identical. Our study aims to provide a good approximate solution to this specific problem with the makespan (Cmax) minimization as the objective function. Considering the success of the Genetic Algorithms (GA) developed for scheduling problems, we apply this metaheuristic to deal with this problem. We develop a GA with a new crossover operator. Indeed, it is a combination of two other crossover operator proposed in the literature. The design of our GA is different compared to the classical structure of the genetic algorithm especially in the encoding of solutions. For the calibration of our metaheuristic parameters, we conduct several experimental designs. Our algorithm is tested on a well known benchmark in the literature. The numerical results show that the proposed genetic algorithm is an efficient approach for solving the k-stage hybrid flow shop problem. Furthermore, this computational study shows that our GA, with the proposed crossover operator gives better results than the two other crossover operators.

Solving multi-objective production scheduling problems with Tabu Search

Loukil T., Teghem J., Fortemps P.

Control and Cybernetics

2000

Vol. 29, no 3

819-828

Most of multiple criteria scheduling problems are NP-hard, so that exact procedures can only solve small problems and with two criteria. The complexity and the diversity of multiple criteria scheduling problems resulted in many alternative approaches to solve them. Exact and approximate procedures proposed in the literature are mainly dedicated to the problem to be solved and their performance depends on the problem data, on the criteria optimized, and are generally difficult to implement. We propose in this paper a Tabu Search approach to multiple criteria scheduling problems. The proposed procedure is a general flexible method, able to solve hard multiple criteria scheduling problems, easy to implement, and providing a set of potential efficient schedules. The criteria are any combination chosen from (C[sub max],T[sub max], L, N[sub T] and F).