Connectedness and Local Search for Bicriteria Knapsack Problems
نویسندگان
چکیده
This article reports an experimental study on a given structural property of connectedness of optimal solutions for two variants of the bicriteria knapsack problem. A local search algorithm that explores this property is then proposed and its performance is compared against exact algorithms in terms of running time and number of optimal solutions found. The experimental results indicate that this simple local search algorithm is able to find a representative set of optimal solutions in most of the cases, and in much less time than exact approaches.
منابع مشابه
Connectedness of Efficient Solutions in Multiple Objective Combinatorial Optimization
Connectedness of efficient solutions is a powerful property in multiple objective combinatorial optimization since it allows the construction of the complete efficient set using neighborhood search techniques. In this paper we show that, however, most of the classical multiple objective combinatorial optimization problems do not possess the connectedness property in general, including, among ot...
متن کاملOn Beam Search for Multicriteria Combinatorial Optimization Problems
In this article, the beam search approach is extended to multicriteria combinatorial optimization, with particular emphasis on its application to bicriteria { 0,1} knapsack problems. The beam search uses several definitions of upper bounds of knapsack solutions as well as a new selection procedure based on -indicator that allows to discard uninteresting solutions. An in-depth experimental analy...
متن کاملThe Smoothed Number of Pareto Optimal Solutions in Bicriteria Integer Optimization
A well established heuristic approach for solving various bicriteria optimization problems is to enumerate the set of Pareto optimal solutions, typically using some kind of dynamic programming approach. The heuristics following this principle are often successful in practice. Their running time, however, depends on the number of enumerated solutions, which can be exponential in the worst case. ...
متن کاملHard Knapsack Problems That Are Easy for Local Search
Chvv atal (1980) describes a class of zero-one knapsack problems provably diicult for branch and bound and dynamic programming algorithms. Chung et al. (1988) identiies a class of integer knapsack problems hard for branch and bound algorithms. We show that for both classes of problems local search provides optimal solutions quickly.
متن کاملA provably convergent heuristic for stochastic bicriteria integer programming
We propose a general-purpose algorithm APS (Adaptive Pareto-Sampling) for determining the set of Pareto-optimal solutions of bicriteria combinatorial optimization (CO) problems under uncertainty, where the objective functions are expectations of random variables depending on a decision from a finite feasible set. APS is iterative and population-based and combines random sampling with the soluti...
متن کامل