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• W128408443 abstract "ABSTRACT The Multiple Knapsack problem (MKP) is a hard combinatorial optimization problem with large application, which embraces many practical problems from different domains, like cargo loading, cutting stock, bin-packing, financial and other management, etc. It also arise as a subproblem in several more complex problems like vehicle routing problem and the algorithms to solve these problems will benefit from any improvement in the field of MKP. The aim of this paper is to compare different kind of heuristic models, statics and dynamics. The heuristics are used by an Ant Colony Optimization (ACO) algorithm to construct solutions to the MKP. KEYWORDS combinatorial optimization, multiple knapsack problem, heuristics 1. INTRODUCTION Combinatorial optimization is the process of finding the best, or optimal solution for problems with a discrete set of feasible solutions. Applications arise in numerous settings involving operations management and logistics. The economic impact of combinatorial optimization is profound, affecting diverse sectors. While much progress has been made in finding exact solutions to some Combinatorial Optimization Problems (COPs), many hard combinatorial problems are still not solved exactly in a reasonable time and require good heuristic methods. The aim of heuristic methods for COPs is to quickly produce good-quality solutions. Modern heuristics include simulated annealing [7], genetic algorithms [4], tabu search [5], ant colony optimization [2,3]. In many practical problems they have proved to be effective and efficient approaches, being flexible to accommodate variations in problem structure and in the objectives considered for the evaluation of solutions. For all these reasons, metaheuristics have probably been one of the most stimulating research topics in optimization for the last two decades. The ACO algorithm were inspired by the observation of real ant colonies. Ants are social insects, that is , insects that live in colonies and whose behavior is directed more to the survival of the colony as a whole than to that of a single individual component of the colony. An important and interesting aspect of ant colonies is how ants can find the shortest path between food sources and their nest. ACO is the recently developed, population-based approach which has been successfully applied to several NP-hard COPs. One of its main ideas is the indirect communication among the individuals of a colony of agents, called ``artificial'' ants, based on an analogy with trails of a chemical substance, called pheromone which real ants use for communication. ACO uses a colony of artificial ants that behaves as cooperative agents in a mathematical space where they are allowed to search and reinforce pathways (solutions) in order to find the optimal ones. Unlike the real-life case, these pathways might contain very complex information. When constructing an initial solution, at each step ants compute a set of feasible moves and select the best one according to some probabilistic rules. These rules are based on the heuristic information and pheromone trail level. The higher value of the pheromone and the heuristic information, the more profitable is to select this move and resume the search. In this paper ACO algorithm for MKP is investigated. The MKP is an important real-life problem. Problems from different industrial fields, can be interpreted like knapsack problem. When the ACO algorithm is applied MKP gives a possibility to use varied heuristic informations. We have concentrated on" @default.
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• W128408443 date "2005-01-01" @default.
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• W128408443 title "HEURISTICS FOR MULTIPLE KNAPSACK PROBLEM" @default.
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