Scheduling Social Golfers with Memetic Evolutionary Programming

Abstract

Abstract. The social golfer problem (SGP) has attracted significant attention in recent years because of its highly symmetrical, constrained, and combinatorial nature. Nowadays, it constitutes one of the standard benchmarks in the area of constraint programming. This paper presents the first evolutionary approach to the SGP. We propose a memetic algorithm (MA) that combines ideas from evolutionary programming and tabu search. In order to lessen the influence of the high number of symmetries present in the problem, the MA does not make use of recombination operators. The search is thus propelled by selection, mutation, and local search. In connection with the latter, we analyze the effect of baldwinian and lamarckian learning in the performance of the MA. An experimental study shows that the MA is capable of improving results reported in the literature, and supports the superiority of lamarckian strategies in this problem.

An improved SAT formulation for the social golfer problem

“…For Walksat, we tried many options and chose the cutoff in such a way that the program had about 20 minutes to solve an instance. This is a reasonable time frame to be competitive, as this is also the limit that was chosen in recently reported other approaches with similar hardware (Cotta et al 2006).…”

“…Metaheuristic approaches towards the SGP include local search with tabu-lists (Dotú and Hentenryck 2005), and an evolutionary approach (Cotta et al 2006).…”

“…Existing metaheuristic methods for the SGP (Dotú and Hentenryck 2005;Cotta et al 2006), are quite simple and perform surprisingly well on many instances, but they are typically incomplete and can therefore not be used to show that an instance cannot be solved. With complete SAT solvers, on the other hand, this is possible, and SAT solvers employing local search can still be used with the same model.…”

Solving Constrained Optimization Problems with Hybrid Evolutionary Algorithms

“…This constraint can also be formulated as a weighted constraint: let # σ (a, b) be the number of times golfers a and b play together in schedule σ, i.e., As already commented symmetries can appear in (and can be removed from) this problem in several forms; see [69,70,71] for more details.…”

“…In [71], we presented, to the best of our knowledge, the first attempt of tackling the SGP by evolutionary techniques; it consisted of a memetic algorithm (MA) that is based on the hybridization of evolutionary programming and tabu search. The flexibility of MAs eased the handling of the problem symmetries.…”