Scatter Search for Graph Coloring

In this paper, we present a first scatter search approach for the Graph Coloring Problem (GCP). The evolutionary strategy scatter search operates on a set of configurations by combining two or more elements. New configurations are improved before replacing others according to their quality (fitness), and sometimes, to their diversity. Scatter search has been applied recently to some combinatorial optimization problems with promising results. Nevertheless, it seems that no attempt of scatter search has been published for the GCP. This paper presents such an investigation and reports experimental results on some wellstudied DIMACS graphs

Sonet Network Design Problems

This paper presents a new method and a constraint-based objective function to solve two problems related to the design of optical telecommunication networks, namely the Synchronous Optical Network Ring Assignment Problem (SRAP) and the Intra-ring Synchronous Optical Network Design Problem (IDP). These network topology problems can be represented as a graph partitioning with capacity constraints as shown in previous works. We present here a new objective function and a new local search algorithm to solve these problems. Experiments conducted in Comet allow us to compare our method to previous ones and show that we obtain better results

Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature

A memetic algorithm for the minimum sum coloring problem

Given an undirected graph $G$, the Minimum Sum Coloring problem (MSCP) is to find a legal assignment of colors (represented by natural numbers) to each vertex of $G$ such that the total sum of the colors assigned to the vertices is minimized. This paper presents a memetic algorithm for MSCP based on a tabu search procedure with two neighborhoods and a multi-parent crossover operator. Experiments on a set of 77 well-known DIMACS and COLOR 2002-2004 benchmark instances show that the proposed algorithm achieves highly competitive results in comparison with five state-of-the-art algorithms. In particular, the proposed algorithm can improve the best known results for 17 instances. We also provide upper bounds for 18 additional instances for the first time.Comment: Submitted manuscrip

Reducing the number of membership functions in linguistic variables

Dissertation presented at Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia in fulfilment of the requirements for the Masters degree in Mathematics and Applications, specialization in Actuarial Sciences, Statistics and Operations ResearchThe purpose of this thesis was to develop algorithms to reduce the number of membership functions in a fuzzy linguistic variable. Groups of similar membership functions to be merged were found using clustering algorithms. By “summarizing” the information given by a similar group of membership functions into a new membership function we obtain a smaller set of membership functions representing the same concept as the initial linguistic variable. The complexity of clustering problems makes it difficult for exact methods to solve them in practical time. Heuristic methods were therefore used to find good quality solutions. A Scatter Search clustering algorithm was implemented in Matlab and compared to a variation of the K-Means algorithm. Computational results on two data sets are discussed. A case study with linguistic variables belonging to a fuzzy inference system automatically constructed from data collected by sensors while drilling in different scenarios is also studied. With these systems already constructed, the task was to reduce the number of membership functions in its linguistic variables without losing performance. A hierarchical clustering algorithm relying on performance measures for the inference system was implemented in Matlab. It was possible not only to simplify the inference system by reducing the number of membership functions in each linguistic variable but also to improve its performance

Scatter search para programação de projetos com custo de disponibilidade de recursos sob incerteza

Orientador: Vinicius Amaral ArmentanoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoDoutorad