A Comparison of Differential Evolution Algorithm with Binary and Continuous Encoding for the MKP

This paper provides a brief description on how continuous algorithms can be applied to binary problems. Differential Evolution is the continuous algorithm studied and two versions of this algorithm are presented: the Binary Differential Evolution with a binary encoding and the Discretized Differential Evolution with a continuous encoding. Several discretization methods are presented and the most used method in literature is implemented for the solution discretization. Benchmarks with different complexity and search space sizes of the Multiple Knapsack Problem are used to compare the performance of each Differential Evolution algorithm presented and the Genetic Algorithm with binary encoding. Results suggest that continuous methods can be very efficient when discretized for binary spaces.

[1]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[2]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[3]  John E. Beasley,et al.  OR-Library: Distributing Test Problems by Electronic Mail , 1990 .

[4]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[5]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[6]  John E. Beasley,et al.  A Genetic Algorithm for the Multidimensional Knapsack Problem , 1998, J. Heuristics.

[7]  B. V. Babu,et al.  Multiobjective differential evolution (MODE) for optimization of adiabatic styrene reactor , 2005 .

[8]  Andries Petrus Engelbrecht,et al.  Binary Differential Evolution , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[9]  A. Sima Etaner-Uyar,et al.  Experimental analysis of binary differential evolution in dynamic environments , 2007, GECCO '07.

[10]  Andries Petrus Engelbrecht,et al.  Binary differential evolution strategies , 2007, 2007 IEEE Congress on Evolutionary Computation.

[11]  Arthur C. Sanderson,et al.  Differential evolution for discrete optimization: An experimental study on Combinatorial Auction problems , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[12]  Bingyan Zhao,et al.  Novel Binary Differential Evolution Algorithm for Discrete Optimization , 2009, 2009 Fifth International Conference on Natural Computation.

[13]  Josiah Adeyemo,et al.  Differential evolution algorithm for solving multi-objective crop planning model. , 2010 .

[14]  Xuan Ma,et al.  A Novel Binary Differential Evolution for Discrete Optimization , 2010 .

[15]  Daniel Lichtblau Differential Evolution in Discrete Optimization. , 2012 .

[16]  Lingjuan Hou,et al.  A novel discrete differential evolution algorithm , 2013 .

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