Iterated greedy local search methods for unrelated parallel machine scheduling

Abstract

This work deals with the parallel machines scheduling problem which consists in the assignment of n jobs on m parallel machines. The most general variant of this problem is when the processing time depends on the machine to which each job is assigned to. This case is known as the unrelated parallel machines problem.Similarly to most of the literature, this paper deals with the minimization of the maximum completion time of the jobs, commonly referred to as makespan (C max ).Many algorithms and methods have been proposed for this hard combinatorial problem, including several highly sophisticated procedures. By contrast, in this paper we propose a set of simple iterated greedy local search based metaheuristics that produce solutions of very good quality in a very short amount of time. Extensive computational campaigns show that these solutions are, most of the time, better than the current state-of-the-art methodologies by a statistically significant margin.

Size-reduction heuristics for the unrelated parallel machines scheduling problem

“…For this purpose, we select the best known heuristic for this problem, the already mentioned NVST-IG+ algorithm of Fanjul-Peyro and Ruiz (2010).…”

“…This "brute-force" approach should be seen as the simplest possible multi-core method. Fanjul-Peyro and Ruiz (2010), in their proposed NVST-IG+ algorithm did not propose a parallel version. Here, we test the M-DIG (multicore DIG) which is basically the full DIG heuristic being run multiple times.…”

“…We name this algorithm 3JD. Note that this last method is more complex, as it requires the DIG heuristic (NVST-IG+ algorithm from Fanjul-Peyro and Ruiz, 2010).…”

“…Some of the earlier works on parallel machines are due to McNaughton (1959) and since then, many papers about parallel machines have appeared, as was shown in the reviews of Cheng and Sin (1990) and Mokotoff (2001). A recent short review, more focused in the unrelated parallel machines case is provided by Fanjul-Peyro and Ruiz (2010). Here, a brief summary of the most important related work is commented.…”

“…However, we postulate that given the extremely good performance of CPLEX, even better solutions can be obtained by combining NVST-IG+ with a solver. In this work we challenge the simple and high performing methods of Fanjul-Peyro and Ruiz (2010) and propose new metaheuristics that make extensive use of solvers.…”