A metaheuristic for solving flowshop problem

Discrete optimization is a class of computational expensive problems that are of practical interest and consequently have attracted the attention of many researchers over the years. Yet no single method has been found that could solve all instances of the problem. The no free launch theorem that confirms that no such general method (that can solve all the instances) could be found, has limited research activities in developing method for a specific class of instances of the problem. In this paper an algorithm for solving discrete optimization is presented. The algorithm is obtained from a hybrid continuous optimization algorithm using a technique devised by Clerc for particle swarm optimization (PSO). In the method, the addition, subtraction and multiplication operators are redefined to support discrete domain. The effectiveness of the algorithm was investigated on the flowshop problem using the makespan as the performance measure and the Taillard benchmark problem instances as the dataset. The result of the investigation is presented in this paper and compared with those from some existing algorithms, including genetic algorithm (GA), ant colony optimization (ACO), simulated annealing (SA), firefly and cockroach algorithms. Based on the experimental results, the algorithm is proposed as a competitive or a viable alternative for solving flowshop problems and possibly discrete optimization problems in general.