Knowledge-based Genetic Algorithm for the 0–1 Multidimensional Knapsack Problem

Abstract

This paper presents an improved version of Genetic Algorithm (GA) to solve the 0–1 Multidimensional Knapsack Problem (MKP01), which is a well-known NP-hard combinatorial optimisation problem. In combinatorial optimisation problems, the best solutions have usually a common partial structure. For MKP01, this structure contains the items with a high values and low weights. The proposed algorithm called Genetic Algorithm Guided by Pretreatment information (GAGP) calculates these items and uses this information to guide the search process. Therefore, GAGP is divided into two steps, in the first, a greedy algorithm based on the efficiency of each item determines the subset of items that are likely to appear in the best solutions. In the second, this knowledge is utilised to guide the GA process. Strategies to generate the initial population and calculate the fitness function of the GA are proposed based on the pretreatment information. Also, an operator to update the efficiency of each item is suggested. The pretreatment information has been investigated using the CPLEX deterministic optimiser. In addition, GAGP has been examined on the most used MKP01 data-sets, and compared to several other approaches. The obtained results showed that the pretreatment succeeded to extract the most part of the important information. It has been shown, that GAGP is a simple but very competitive solution.