34 research outputs found

    Experiments on local search for bi-objective unconstrained binary quadratic programming

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    International audienceThis article reports an experimental analysis on stochastic local search for approximating the Pareto set of bi-objective unconstrained binary quadratic programming problems. First, we investigate two scalarizing strategies that iteratively identify a high-quality solution for a sequence of sub-problems. Each sub-problem is based on a static or adaptive definition of weighted-sum aggregation coefficients, and is addressed by means of a state-of-the-art single-objective tabu search procedure. Next, we design a Pareto local search that iteratively improves a set of solutions based on a neighborhood structure and on the Pareto dominance relation. At last, we hybridize both classes of algorithms by combining a scalarizing and a Pareto local search in a sequential way. A comprehensive experimental analysis reveals the high performance of the proposed approaches, which substantially improve upon previous best-known solutions. Moreover, the obtained results show the superiority of the hybrid algorithm over non-hybrid ones in terms of solution quality, while requiring a competitive computational cost. In addition, a number of structural properties of the problem instances allow us to explain the main difficulties that the different classes of local search algorithms have to face

    A Study of Memetic Search with Multi-parent Combination for UBQP

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    We present a multi-parent hybrid geneticÔÇôtabu 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

    Constrained Entropy Models; Solvability and Sensitivity

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    The paper presents an analysis of the constrained entropy maximization model from the point of view of geometric programming. While the original entropy maximization model consists of maximizing the entropy of a system subject only to constraints that the solution be a probability measure, the models considered here contain an additional set of linear constraints. These constrained models have been the subject of a wide range of applications in transportation and geographical analysis. Using the duality theory of geometric programming, we develop the dual to the constrained model, which as in the case of the original model is unconstrained except for the positivity restrictions on the dual variables. In addition, this duality theory enables us to study the solvability of the model and the impact of changes in the model parameters on the solution. The sensitivity analysis provides approximations to the optimal solution to problems with perturbed data without requiring the re-solving of the model. This analysis is appropriate for changes in the right hand sides of the constraints, the coefficients in the constraints, and the objective function coefficients. Since the constraint coefficients correspond to the objective function exponents in the primal geometric program, the analysis provides a means of studying such changes is any geometric program. The computational aspects of the procedures are illustrated on a trip distribution problem.entropy, geometric programming

    On the solution of regional planning models via geometric programming

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    The purpose of this paper is to demonstrate the applicability of geometric programming to regional land-use planning models. The regional models are of the type where the criterion is maximum accessibility, and the model is constrained by population limits on each district. After a brief discussion of geometric programming, the relationships of total accessibility models to geometric programs is developed and a method of obtaining numerical solutions is presented. Several models are analyzed using the geometric programming approach, including a game theoretic model which is used to generate decentralized plans.

    Entropy maximization and geometric programming

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    This paper shows the equivalence of entropy-maximization models to geometric programs. As a result we derive a dual geometric program which consists of the minimization of an unconstrained convex function. We develop the necessary duality equivalences between the two dual programs and show the computational attractiveness of our approach. We also develop some characterizations of the optimal solution of the entropy model which have important implications with regard to postoptimal or sensitivity analysis.