68 research outputs found
A Study of Memetic Search with Multi-parent Combination for UBQP
We present a multi-parent hybrid geneticâtabu algorithm (denoted by GTA) for the Unconstrained Binary Quadratic Programming (UBQP) problem, by incorporating tabu search into the framework of genetic algorithm. In this paper, we propose a new multi-parent combination operator for generating offspring solutions. A pool updating strategy based on a quality-and-distance criterion is used to manage the population. Experimental comparisons with leading methods for the UBQP problem on 25 large public instances demonstrate the efficacy of our proposed algorithm in terms of both solution quality and computational efficiency
Elementary landscape decomposition of the 0-1 unconstrained quadratic optimization
Journal of Heuristics, 19(4), pp.711-728Landscapesâ theory provides a formal framework in which combinatorial optimization problems can be theoretically characterized as a sum of an especial kind of landscape called elementary landscape. The elementary landscape decomposition of a combinatorial optimization problem is a useful tool for understanding the problem. Such decomposition provides an additional knowledge on the problem that can be exploited to explain the behavior of some existing algorithms when they are applied to the problem or to create new search methods for the problem. In this paper we analyze the 0-1 Unconstrained Quadratic Optimization from the point of view of landscapesâ theory. We prove that the problem can be written as the sum of two elementary components and we give the exact expressions for these components. We use the landscape decomposition to compute autocorrelation measures of the problem, and show some practical applications of the decomposition.Spanish Ministry of Sci- ence and Innovation and FEDER under contract TIN2008-06491-C04-01 (the Mâ project). Andalusian Government under contract P07-TIC-03044 (DIRICOM project)
Optimal k-fold colorings of webs and antiwebs
A k-fold x-coloring of a graph is an assignment of (at least) k distinct
colors from the set {1, 2, ..., x} to each vertex such that any two adjacent
vertices are assigned disjoint sets of colors. The smallest number x such that
G admits a k-fold x-coloring is the k-th chromatic number of G, denoted by
\chi_k(G). We determine the exact value of this parameter when G is a web or an
antiweb. Our results generalize the known corresponding results for odd cycles
and imply necessary and sufficient conditions under which \chi_k(G) attains its
lower and upper bounds based on the clique, the fractional chromatic and the
chromatic numbers. Additionally, we extend the concept of \chi-critical graphs
to \chi_k-critical graphs. We identify the webs and antiwebs having this
property, for every integer k <= 1.Comment: A short version of this paper was presented at the Simp\'osio
Brasileiro de Pesquisa Operacional, Brazil, 201
An Improved Exact Algorithm for Least-Squares Unidimensional Scaling
Given n objects and an symmetric dissimilarity matrix D with zero main diagonal
and nonnegative off-diagonal entries, the least-squares unidimensional scaling problem
asks to find an arrangement of objects along a straight line such that the pairwise distances
between them reflect dissimilarities represented by the matrix D. In this paper, we propose an improved branch-and-bound algorithm for solving this problem. The main
ingredients of the algorithm include an innovative upper bounding technique relying on
the linear assignment model and a dominance test which allows considerably reducing the
redundancy in the enumeration process. An initial lower bound for the algorithm is provided
by an iterated tabu search heuristic. To enhance the performance of this heuristic
we develop an efficient method for exploring the pairwise interchange neighborhood of a
solution in the search space. The basic principle and formulas of the method are also used
in the implementation of the dominance test. We report computational results for both
randomly generated and real-life based problem instances. In particular, we were able to
solve to guaranteed optimality the problem defined by a Morse code dissimilarity matrix
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