Unweighted Stochastic Local Search can be Effective for Random CSP Benchmarks

We present ULSA, a novel stochastic local search algorithm for random binary constraint satisfaction problems (CSP). ULSA is many times faster than the prior state of the art on a widely-studied suite of random CSP benchmarks. Unlike the best previous methods for these benchmarks, ULSA is a simple unweighted method that does not require dynamic adaptation of weights or penalties. ULSA obtains new record best solutions satisfying 99 of 100 variables in the challenging frb100-40 benchmark instance

CHN and Swap Heuristic to Solve the Maximum Independent Set Problem

We describe a new approach to solve the problem to find the maximum independent set in a given Graph, known also as Max-Stable set problem (MSSP). In this paper, we show how Max-Stable problem can be reformulated into a linear problem under quadratic constraints, and then we resolve the QP result by a hybrid approach based Continuous Hopfeild Neural Network (CHN) and Local Search. In a manner that the solution given by the CHN will be the starting point of the local search. The new approach showed a good performance than the original one which executes a suite of CHN runs, at each execution a new leaner constraint is added into the resolved model. To prove the efficiency of our approach, we present some computational experiments of solving random generated problem and typical MSSP instances of real life problem

Adaptando Uma Solução GRASP ao Problema da Cobertura Mínima de Vértices

O Problema da Cobertura Mínima de Vértices (PCVM) é um problema NP-Difícil de grande interesse prático. Muitos problemas do mundo real podem ser relacionados ao PCVM, por exemplo, escalonamento de tarefas, desenho de circuitos VLSI, problemas de bioinformática, para citar apenas alguns. Este artigo reporta o uso da heurística GRASP associada ao uso de uma técnica de otimização local, denominada LOT. A heurística resultante foi denominada GRASPlot. O objetivo deste artigo é reportar uma série de experimentos computacionais utilizando o GRASPlot para instâncias de grafos encontradas na biblioteca BHOSLIB confrontando os resultados da heurística proposta com soluções ótimas disponibilizadas pela biblioteca

Finding A Small Vertex Cover in Massive Sparse Graphs: Construct, Local Search, and Preprocess

Algorithms and the Foundations of Software technolog

Analysis of combinatorial search spaces for a class of NP-hard problems, An

2011 Spring.Includes bibliographical references.Given a finite but very large set of states X and a real-valued objective function ƒ defined on X, combinatorial optimization refers to the problem of finding elements of X that maximize (or minimize) ƒ. Many combinatorial search algorithms employ some perturbation operator to hill-climb in the search space. Such perturbative local search algorithms are state of the art for many classes of NP-hard combinatorial optimization problems such as maximum k-satisfiability, scheduling, and problems of graph theory. In this thesis we analyze combinatorial search spaces by expanding the objective function into a (sparse) series of basis functions. While most analyses of the distribution of function values in the search space must rely on empirical sampling, the basis function expansion allows us to directly study the distribution of function values across regions of states for combinatorial problems without the need for sampling. We concentrate on objective functions that can be expressed as bounded pseudo-Boolean functions which are NP-hard to solve in general. We use the basis expansion to construct a polynomial-time algorithm for exactly computing constant-degree moments of the objective function ƒ over arbitrarily large regions of the search space. On functions with restricted codomains, these moments are related to the true distribution by a system of linear equations. Given low moments supplied by our algorithm, we construct bounds of the true distribution of ƒ over regions of the space using a linear programming approach. A straightforward relaxation allows us to efficiently approximate the distribution and hence quickly estimate the count of states in a given region that have certain values under the objective function. The analysis is also useful for characterizing properties of specific combinatorial problems. For instance, by connecting search space analysis to the theory of inapproximability, we prove that the bound specified by Grover's maximum principle for the Max-Ek-Lin-2 problem is sharp. Moreover, we use the framework to prove certain configurations are forbidden in regions of the Max-3-Sat search space, supplying the first theoretical confirmation of empirical results by others. Finally, we show that theoretical results can be used to drive the design of algorithms in a principled manner by using the search space analysis developed in this thesis in algorithmic applications. First, information obtained from our moment retrieving algorithm can be used to direct a hill-climbing search across plateaus in the Max-k-Sat search space. Second, the analysis can be used to control the mutation rate on a (1+1) evolutionary algorithm on bounded pseudo-Boolean functions so that the offspring of each search point is maximized in expectation. For these applications, knowledge of the search space structure supplied by the analysis translates to significant gains in the performance of search

Algorithmes d'approximation à mémoire limitée pour le traitement de grands graphes (le problème du Vertex Cover)

Nous nous sommes intéressés à un problème d'optimisation sur des graphes (le problème du Vertex Cover) dans un contexte bien particulier : celui des grandes instances de données. Nous avons défini un modèle de traitement se basant sur trois contraintes (en relation avec la quantité de mémoire limitée, par rapport à la grande masse de données à traiter) et qui reprenait des propriétés issus de plusieurs modèles existants. Nous avons étudié plusieurs algorithmes adaptés à ce modèle. Nous avons analysé, tout d'abord de façon théorique, la qualité de leurs solutions ainsi que leurs complexités. Nous avons ensuite mené une étude expérimentale sur de gros graphes. De manière générale, les travaux menés durant cette thèse peuvent fournir des indicateurs pour choisir le ou les algorithmes qui conviennent le mieux pour traiter le problème du vertex cover sur de gros graphes. Choisir un algorithme (qui plus est d'approximation) qui soit à la foisperformant (en terme de qualité de solution et de complexité) et qui satisfasse les contraintes du modèle que l'on considère est délicat. en effet, les algorithmes les plus performants ne sont pas toujours les mieux adaptés. dans les travaux que nous avons réalisés, nous sommes parvenus à la conclusion qu'il est préférable de choisir au départ l'algorithme qui est le mieux adapté plutôt que de choisir celui qui est le plus performant.We are interested to an optimization problem on graphs (the Vertex Cover problem) in a very specific context : the huge instances of data. We defined a treatment model based on three constraints (in connection with the limited amount of memory compared to the huge amount of data to be processed) and that reproduces properties from several existing models. We studied several algorithms adapted to this model. We examined, first theoretically, their solutions quality and their complexities. We then conducted an experimental study on large graphs. In general, the work made during this thesis may provide indicators for select algorithms that are best suited to resolve the Vertex Cover problem on large graphs. Choose an algorithm (which is approximated) that is both efficient (in terms of quality of solution and complexity) and satisfies the constraints model whether we consider is tricky. in fact, the most efficient algorithms are not always the best adapted. In the work we have done, we reached the conclusion that, at the beginning, it is best to choose the best suited algorithm rather than the more efficient.EVRY-Bib. électronique (912289901) / SudocSudocFranceF

A stochastic local search approach to vertex cover

Abstract. We introduce a novel stochastic local search algorithm for the vertex cover problem. Compared to current exhaustive search techniques, our algorithm achieves excellent performance on a suite of problems drawn from the field of biology. We also evaluate our performance on the commonly used DIMACS benchmarks for the related clique problem, finding that our approach is competitive with the current best stochastic local search algorithm for finding cliques. On three very large problem instances, our algorithm establishes new records in solution quality.