An improved SAT formulation for the social golfer problem

Abstract

The Social Golfer Problem (SGP) is a sports scheduling problem that exhibits a lot of symmetry and has recently attracted significant attention. In this paper, we first revisit an existing SAT encoding for the SGP and correct some of its clauses. We then propose a change in the encoding that significantly reduces the number of variables for all instances. We achieve considerable performance improvements when solving many SGP instances with common SAT solvers using local search and complete backtracking. This makes SAT formulations a more promising approach for solving the SGP than previously.

An effective greedy heuristic for the Social Golfer Problem

“…Other approaches include a SAT encoding (Gent and Lynce 2005;Triska and Musliu 2010), which so far is not competitive with other methods, and various constraint-based formulations including sophisticated dynamic symmetry breaking techniques (Barnier and Brisset 2005;Fahle et al 2001).…”

Set constraint model and automated encoding into SAT: application to the social golfer problem

“…Coding set constraints directly into SAT is a tedious tasks (see for example [20] or [13]). Moreover, when one wants to optimize its model in terms of variables and clauses this quickly leads to very complicated and unreadable models in which errors can easily appear.…”

“…An instance of the problem is then given by a triple g − p − w. Various instances of the Social Golfer Problem are still open, and the problem is attractive since it is related to problems such as encryption and covering problems. Compared to direct encodings (such as the one of [20]), the instances we generate are smaller (less clauses), and also contain less variables using unit propagation. The introduction of symmetry breaking is simplified with our technique and can be done by adding constraints to the initial model or by refining the initial model.…”

“…Concerning applications, i.e., the Social Golfer Problem, the closest work is [20] which is a revision and improvement of [13]. Whereas these works are hand-written modeling of the Social Golfer Problem directly in SAT, we are concerned with a higher-level model language which is automatically transformed into SAT instances.…”

“…We apply our technique to the Social Golfer Problem and we also use it to break symmetries of the problem.Our technique is simpler, more declarative, and less error-prone than direct and improved hand modeling. The SAT instances that we automatically generate contain less clauses than improved hand-written instances such as in [20], and with unit propagation they also contain less variables. Moreover, they are well-suited for SAT solvers and they are solved faster as shown when solving difficult instances of the Social Golfer Problem.…”