Makespan minimization for scheduling unrelated parallel machines: A recovering beam search approach

Size-reduction heuristics for the unrelated parallel machines scheduling problem

“…Woclaw (2006) carried out a comprehensive re-implementation and a computational evaluation of most existing literature for the R//C max , and showed that the Partial method of Mokotoff and Jimeno (2002) produced state-of-the-art results, surpassing all other tested methods. Lately, Ghirardi and Potts (2005) have shown very good results using a Recovering Beam Search (RBS) approach which was already studied earlier by de la Croce et al (2004), based on the Beam Search (BS) method of Ow and Morton (1988). Gairing et al (2007) also proposed a two-phase approach that results in a very fast method but with results that are not able to compete in solution quality with those of Mokotoff and Jimeno (2002) or Ghirardi and Potts (2005).…”

“…These methods were shown to clearly outperform the Partial and RBS methods of Mokotoff and Jimeno (2002) and Ghirardi and Potts (2005) in comprehensive benchmarks. Furthermore, Fanjul-Peyro and Ruiz (2010) also demonstrated that modern commercial solvers, and more specifically, IBM-ILOG CPLEX version 11.0 (simply referred to as CPLEX from now on, although we will make special mention of different version numbers) are capable of outperforming the Partial of Mokotoff and Jimeno (2002) and of producing results that are statistically equivalent to the RBS of Ghirardi and Potts (2005). Note that this good performance of CPLEX was tested with "out-of-the-box" parameters and with the previous simplistic assignment model.…”

A Genetic Algorithm for Minimizing Completion Time with Non-identical Parallel Machines

“…추가적으로 Ghirardi and Potts [13] [12] Gendreau, M., G. Laporte, and E.M. Guimarães, "A divide and merge heuristic for the multiprocessor scheduling problem with sequence dependent setup times," European…”

Hybrid tabu search and a truncated branch-and-bound for the unrelated parallel machine scheduling problem

“…This algorithm is further refined in Mokotoff and Jimeno (2002), where heuristic algorithms based on partial enumeration are presented. This approach was considered to be the most effective approach for R||C max , together with the recovering beam search of Ghirardi and Potts (2005). However, Fanjul-Peyro and Ruiz (2010) present a set of iterated greedy local search based heuristics that outperform the aforementioned state-of-the-art procedures.…”

“…The paper of Martello et al (1997) discusses effective lower bounds for the problem based on Lagrangian relaxation and presents some approximate algorithms. Some efficient heuristic approaches are discussed in Glass et al (1994), Piersma and Van Dijk (1996), Srivastava (1998), Sourd (2001), Mokotoff and Chrétienne (2002), Mokotoff and Jimeno (2002), Ghirardi and Potts (2005), Monien and Woclaw (2006), Guo et al (2007), Fanjul-Peyro and Ruiz (2010), Fanjul-Peyro and Ruiz (2011) and Lin et al (2011). Glass et al (1994) perform a comparison between a genetic algorithm, a simulated annealing approach and a tabu search algorithm.…”