The Multiple Knapsack Problem Approached by a Binary Differential Evolution Algorithm with Adaptive Parameters

In this paper the well-known 0-1 Multiple Knapsack Problem (MKP) is approached by an adaptive Binary Differential Evolution (aBDE) algorithm. The MKP is a NP-hard optimization problem and the aim is to maximize the total profit subjected to the total weight in each knapsack that must be less than or equal to a given limit. The aBDE self adjusts two parameters, perturbation and mutation rates, using a linear adaptation procedure that changes their probabilities at each generation. Results were obtained using 11 instances of the problem with different degrees of complexity. The results were compared using aBDE, BDE, a standard Genetic Algorithm (GA) and its adaptive version (aGA), and an island-inspired Genetic Algorithm (IGA) and its adaptive version (aIGA). The results show that aBDE obtained better results than the other algorithms. This indicates that the proposed approach is an interesting and a promising strategy to control the parameters and for optimization of complex problems.

[1]  Xin-She Yang,et al.  Chapter 6 – Differential Evolution , 2014 .

[2]  Jonas Krause,et al.  A Survey of Swarm Algorithms Applied to Discrete Optimization Problems , 2013 .

[3]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[4]  Kenneth de Jong,et al.  Evolutionary computation: a unified approach , 2007, GECCO.

[5]  Oliver Kramer,et al.  Evolutionary self-adaptation: a survey of operators and strategy parameters , 2010, Evol. Intell..

[6]  Zbigniew Michalewicz,et al.  Parameter Control in Evolutionary Algorithms , 2007, Parameter Setting in Evolutionary Algorithms.

[7]  Shengyao Wang,et al.  A novel binary fruit fly optimization algorithm for solving the multidimensional knapsack problem , 2013, Knowl. Based Syst..

[8]  Rafael S. Parpinelli,et al.  Tutorial Sobre o Uso de Técnicas para Controle de Parâmetros em Algoritmos de Inteligência de Enxame e Computação Evolutiva , 2014, RITA.

[9]  Arnaud Fréville,et al.  The multidimensional 0-1 knapsack problem: An overview , 2004, Eur. J. Oper. Res..

[10]  Arild Hoff,et al.  Genetic Algorithms for 0/1 Multidimensional Knapsack Problems , 2005 .

[11]  Dirk Thierens,et al.  An Adaptive Pursuit Strategy for Allocating Operator Probabilities , 2005, BNAIC.

[12]  Kusum Deep,et al.  A Modified Binary Particle Swarm Optimization for Knapsack Problems , 2012, Appl. Math. Comput..

[13]  Ana Maria A. C. Rocha,et al.  Improved binary artificial fish swarm algorithm for the 0-1 multidimensional knapsack problems , 2014, Swarm Evol. Comput..

[14]  Jin-Kao Hao,et al.  A hybrid approach for the 0-1 multidimensional knapsack problem , 2001, IJCAI 2001.

[15]  Michèle Sebag,et al.  Extreme Value Based Adaptive Operator Selection , 2008, PPSN.

[16]  Irene Moser,et al.  Studying feedback mechanisms for adaptive parameter control in evolutionary algorithms , 2013, 2013 IEEE Congress on Evolutionary Computation.