A BRILS metaheuristic for non-smooth flow-shop problems with failure-risk costs. (February 2016) - Ferrer, A.; Guimarans, D.; Ramalhinho, H.; Juan, A.A.
Highlights: Our approach of PFSP includes risk of machine failures due to lack of breaks. We model the problem as a non-smooth optimization problem. We propose the use of a biased-randomized algorithm to solve it. We combine Iterated Local Search with biased randomization of classical heuristics. Our approach outperforms other approaches just based on the makespan. Abstract: This paper analyzes a realistic variant of the Permutation Flow-Shop Problem (PFSP) by considering a non-smooth objective function that takes into account not only the traditional makespan cost but also failure-risk costs due to uninterrupted operation of machines. After completing a literature review on the issue, the paper formulates an original mathematical model to describe this new PFSP variant. Then, a Biased-Randomized Iterated Local Search (BRILS) algorithm is proposed as an efficient solving approach. An oriented (biased) random behavior is introduced in the well-known NEH heuristic to generate an initial solution. From this initial solution, the algorithm is able to generate a large number of alternative good solutions without requiring a complex setting of parameters. The relative simplicity of our approach is particularly useful in the presence of non-smooth objective functions, for which exact optimization methods may fail to reach their full potential. The gains of considering failure-risk costs during the exploration of the solution space are analyzed throughout a series of computational experiments. To promote reproducibility, these experiments are based on a set of traditional benchmark instances. Moreover, the performance of the proposed algorithm is compared against other state-of-the-art metaheuristic approaches, which have been conveniently adapted to consider failure-risk costs during the solving process. The proposed BRILS approach can be easily extended to other combinatorial optimization problems with similar non-smooth objective functions.