Hybrid Genetic Algorithms to Solve the Multidimensional Knapsack Problem

Abstract

This paper introduces solutions to deal with the Multidimensional Knapsack Problem (MKP), which is a NP-hard combinatorial optimisation problem. Two hybrid heuristics based on Genetic Algorithms (GA) are proposed: the Memetic Search Algorithm (MSA) and the Genetic Algorithm Guided by Pretreatment information (GAGP). MSA combines sequentially GA with the Stochastic Local Search-Simulated Annealing algorithm (SLSA). GAGP is composed of two steps, in the first, a ratio-based greedy algorithm extracts useful information and the core concept is utilised to decompose items according to their ratios; In the second, these information are integrated to the operators of a GA allowing to reach the best solutions faster. An operator is added to the GA to dynamically update the ratio values of the items. Two groups of data were used to examine the proposed approaches. A group of simple instances of MKP has been used to examine MSA and a group of complex MKP has been used to examine GAGP. The obtained results indicate that MSA and GAGP have the capability to give solutions of high quality.