Genetic Algorithms, Path Relinking, and the Flowshop Sequencing Problem

Abstract

In a previous paper, a simple genetic algorithm (GA) was developed for finding (approximately) the minimum makespan of the n-job, m-machine permutation flowshop sequencing problem (PFSP). The performance of the algorithm was comparable to that of a naive neighborhood search technique and a proven simulated annealing algorithm. However, recent results have demonstrated the superiority of a tabu search method in solving the PFSP. In this paper, we reconsider the implementation of a GA for this problem and show that by taking into account the features of the landscape generated by the operators used, we are able to improve its performance significantly.

Heuristic algorithms and learning techniques: applications to the graph coloring problem

“…One can find numerous studies investigating the specific local optima properties for the most representative combinatorial optimization problems: boolean satisfiability [Zhang, 2004;], graph coloring Culberson and Gent, 2001], the traveling salesman problem [Stadler and Schnabl, 1992], the 0-1 knapsack problem [Ryan, 1995], graph bi-partitioning [Merz and Freisleben, 2000b], the quadratic assignment problem [Merz and Freisleben, 2000a], job shop or flow shop scheduling [Reeves and Yamada, 1998;Streeter and Smith, 2006], arc crossing minimization in graph drawing ,etc. It seems that the local optimum characteristics of the search space (the number of local optima, their space distribution, the topology of their basins of attraction) may indeed be very different from one problem to another, and even from one instance to another.…”

Applying Multi-Moves in Parallel Genetic Algorithm for the Flow Shop Problem

“…There is the MSXF+MM (Multi -Step Crossover Fusion with Multi-Moves) operator, based on the path-relinking method, used to extend the process of researching for better solutions of the problem. MSXF has been originally described by Reeves and Yamada [5]. Its idea is based on local search, starting from one of the parent solutions, to find a new good solution where the other parent is used as a reference point.…”

Exploiting Problem Structure in Scheduling

“…The path relinking algorithm by Reeves and Yamada (1998) was selected because it has demonstrated some of the best performance to date on the problems from Taillard's test suite and was similar in both implementation and performance to a "path relinking" algorithm that we had been developing in house. Incremental construction refers to algorithms that use heuristics to build up a schedule; this class was included because excellent heuristics are available for the PFSP domain.…”

“…During the process of 'linking' or constructing a path between two local optima, the algorithm can check the intervening area for other optima. Path relinking is the basis for the Reeves/Yamada PFSP algorithm [18], which we denote by pathrelink.…”

“…The shift operator is repeatedly applied, in a next-descent strategy for all the possible pairs of jobs in the permutation, in a random order, until two passes through all the pairs does not result in any improvement. Because the global optima for our problems are unknown, we next computed for each local optimum its average distance to all the other local optima, as was done in the previous study [18].…”