Towards hybrid methods for solving hard combinatorial optimization problems

Tesis doctoral leída en la Escuela Politécnica Superior de la Universidad Autónoma de Madrid el 4 de septiembre de 200

Departamento De Ingenier´ıa Inform ática

Abstract. The scheduling of social tournaments has attracted significant attention in recent years, as they arise in many practical applications and induce highly combinatorial problems. This research proposes a high-level modeling of social tournaments and a local search algorithm for finding solutions to the models. The effectiveness of the approach is demonstrated on three classes of applications: social golfer problems, debating tournaments, and judge assignements. In particular, the approach quickly solves real-life debating tournament and judge assignment problems that were open so far.

Scheduling social golfers locally

Abstract. The scheduling of social golfers has attracted significant attention in recent years because of its highly symmetrical and combinatorial nature. In particular, it has become one of the standard benchmarks for symmetry breaking in constraint programming. This paper presents a very effective, local search, algorithm for scheduling social golfers. The algorithm find the first known solutions to 11 instances and matches, or improves, state-of-the-art results from constraint programming on all but 3 instances. Moreover, most instances of the social golfers are solved within a couple of seconds. Interestingly, the algorithm does not incorporate any symmetry-breaking scheme and illustrates, once again, the nice complementarity between constraint programming and local search on this scheduling application.

TOWARDS HYBRID METHODS FOR SOLVING HARD COMBINATORIAL OPTIMIZATION PROBLEMS

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Scheduling Social Tournaments Locally

Abstract. Tournament scheduling, such as the social golfer problem, has attracted significant attention in recent years because of their highly symmetrical and combinatorial nature. This paper presents an effective local search algorithm for a variety of tournament scheduling problems, including social golfer problems, debating tournaments, judge assignments, and very social golfers. The algorithm finds high-quality solutions on all problems, including new solutions to open problems. Interestingly, the algorithm does not incorporate any symmetrybreaking schemes and is conceptually simple when compared to advanced constraintprogramming solutions.

Rapid prototyping by means of meta-modelling and graph grammars. An example with constraint satisfaction problems

This is an electronic version of the paper presented at the VIII Jornadas de Ingeniería del Software y Bases de Datos, held in Alicante on 2003In this paper, we present our approach for rapid prototyping - by means of meta-modelling and graph grammars - in the multiparadigm modelling tool AToM3. Thisis a tool which allows the graphical definition of formalisms by means of meta-modelling usinf highlevel, graphical notations. As meta-models are stored as attributed, typed graphs, their manipulation (simulation, transformation into another formalism, optimisation and code generation) can be visually and formally expressed as graph transformation. In this way, computations become high-level models, expressed in the graph grammars formalism. As an example of these concepts, we show the automatic generation of a tool (by means of meta-modelling and graph grammars) to graphically define and solve Constraint Satisfaction Problem

M.: Channeling Constraints and Value Ordering in the Quasigroup Completion Problem

The Quasigroup Completion Problem (QCP) is a very challengin

A memetic approach to golomb rulers

Abstract. Finding Golomb rulers is an extremely challenging optimization problem with many practical applications. This problem has been approached by a variety of search methods in recent years. We consider in this work a hybrid evolutionary algorithm that incorporates ideas from greedy randomized adaptive search procedures (GRASP), tabu-based local search methods (TS) and scatter search (SS). In particular, GRASP and TS are embedded into a SS algorithm to serve as initialization and restarting methods for the population and as improvement technique respectively. The resulting memetic algorithm significantly outperforms earlier approaches (including other hybrid EAs, as well as hybridizations of local search and constraint programming), finding optimal rulers where the mentioned techniques failed.

Scheduling Social Golfers with Memetic Evolutionary Programming

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.

Modeling choices in quasigroup completion: SAT vs. CSP

We perform a systematic comparison of SAT and CSP models for a challenging combinatorial problem, quasigroup completion (QCP). Our empirical results clearly indicate the superiority of the 3D SAT encoding (Kautz et al. 2001), with various solvers, over other SAT and CSP models. We propose a partial explanation of the observed performance. Analytically, we focus on the relative conciseness of the 3D model and the pruning power of unit propagation. Empirically, the focus is on the role of the unit-propagation heuristic of the best performing solver, Satz (Li & Anbulagan 1997), which proves crucial to its success, and results in a significant improvement in scalability when imported into the CSP solvers. Our results strongly suggest that SAT encodings of permutation problems (Hnich, Smith, & Walsh 2004) may well prove quite competitive in other domains, in particular when compared with the currently preferred channeling CSP models