Dichotomous Binary Differential Evolution for Knapsack Problems

Differential evolution (DE) is one of the most popular and powerful evolutionary algorithms for the real-parameter global continuous optimization problems. However, how to adapt into combinatorial optimization problems without sacrificing the original evolution mechanism of DE is harder work to the researchers to design an efficient binary differential evolution (BDE). To tackle this problem, this paper presents a novel BDE based on dichotomous mechanism for knapsack problems, called DBDE, in which two new proposed methods (i.e., dichotomous mutation and dichotomous crossover) are employed. DBDE almost has any difference with original DE and no additional module or computation has been introduced. The experimental studies have been conducted on a suite of 0-1 knapsack problems and multidimensional knapsack problems. Experimental results have verified the quality and effectiveness of DBDE. Comparison with three state-of-the-art BDE variants and other two state-of-the-art binary particle swarm optimization (PSO) algorithms has proved that DBDE is a new competitive algorithm.

[1]  Zhao Yang Dong,et al.  Power system fault diagnosis based on history driven differential evolution and stochastic time domain simulation , 2014, Inf. Sci..

[2]  Ankit Pat,et al.  An adaptive quantum-inspired differential evolution algorithm for 0–1 knapsack problem , 2010, 2010 Second World Congress on Nature and Biologically Inspired Computing (NaBIC).

[3]  Wenyin Gong,et al.  DE/BBO: a hybrid differential evolution with biogeography-based optimization for global numerical optimization , 2010, Soft Comput..

[4]  Chun-Yin Wu,et al.  Topology optimization of structures using modified binary differential evolution , 2010 .

[5]  Ponnuthurai N. Suganthan,et al.  Recent advances in differential evolution - An updated survey , 2016, Swarm Evol. Comput..

[6]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[7]  Swagatam Das,et al.  Simultaneous feature selection and weighting - An evolutionary multi-objective optimization approach , 2015, Pattern Recognit. Lett..

[8]  Minrui Fei,et al.  A novel modified binary differential evolution algorithm and its applications , 2012, Neurocomputing.

[9]  Ramiro Villeda Rodriguez,et al.  ORLIB, an operations research library , 1981 .

[10]  René Thomsen,et al.  A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[11]  Zhijian Wu,et al.  Heterozygous differential evolution with Taguchi local search , 2015, Soft Comput..

[12]  Heitor Silvério Lopes,et al.  Particle Swarm Optimization for the Multidimensional Knapsack Problem , 2007, ICANNGA.

[13]  Lin Han,et al.  A novel binary differential evolution algorithm based on artificial immune system , 2007, 2007 IEEE Congress on Evolutionary Computation.

[14]  Günther R. Raidl,et al.  The Multidimensional Knapsack Problem: Structure and Algorithms , 2010, INFORMS J. Comput..

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

[16]  Yuren Zhou,et al.  A Comparison of GAs Using Penalizing Infeasible Solutions and Repairing Infeasible Solutions on Average Capacity Knapsack , 2007, ISICA.

[17]  H. Iba,et al.  Inferring Gene Regulatory Networks using Differential Evolution with Local Search Heuristics , 2007, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[18]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[19]  Ivanoe De Falco,et al.  Differential Evolution as a viable tool for satellite image registration , 2008, Appl. Soft Comput..

[20]  Mehmet Fatih Tasgetiren,et al.  Differential evolution algorithm with ensemble of parameters and mutation strategies , 2011, Appl. Soft Comput..

[21]  S. Senju,et al.  An Approach to Linear Programming with 0--1 Variables , 1968 .

[22]  Yuren Zhou,et al.  A theoretical assessment of solution quality in evolutionary algorithms for the knapsack problem , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[23]  Choujun Zhan,et al.  A Parameter Estimation Method for Biological Systems modelled by ODE/DDE Models Using Spline Approximation and Differential Evolution Algorithm , 2014, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[24]  Amit Konar,et al.  Differential Evolution Using a Neighborhood-Based Mutation Operator , 2009, IEEE Transactions on Evolutionary Computation.

[25]  Long Li,et al.  Differential evolution based on covariance matrix learning and bimodal distribution parameter setting , 2014, Appl. Soft Comput..

[26]  Wei Shih,et al.  A Branch and Bound Method for the Multiconstraint Zero-One Knapsack Problem , 1979 .

[27]  Bin Li,et al.  Estimation of distribution and differential evolution cooperation for large scale economic load dispatch optimization of power systems , 2010, Inf. Sci..

[28]  H. Martin Weingartner,et al.  Methods for the Solution of the Multidimensional 0/1 Knapsack Problem , 1967, Operational Research.

[29]  Ali R. Yildiz,et al.  A new hybrid differential evolution algorithm for the selection of optimal machining parameters in milling operations , 2013, Appl. Soft Comput..

[30]  Wenyin Gong,et al.  Differential Evolution With Ranking-Based Mutation Operators , 2013, IEEE Transactions on Cybernetics.

[31]  Qingfu Zhang,et al.  DE/EDA: A new evolutionary algorithm for global optimization , 2005, Inf. Sci..

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

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

[34]  Weicheng Xie,et al.  A binary differential evolution algorithm learning from explored solutions , 2014, Neurocomputing.

[35]  Jouni Lampinen,et al.  A Trigonometric Mutation Operation to Differential Evolution , 2003, J. Glob. Optim..

[36]  Tao Gong,et al.  Differential Evolution for Binary Encoding , 2007 .

[37]  Gang Liu,et al.  Self-adaptive differential evolution with global neighborhood search , 2017, Soft Comput..

[38]  Arthur C. Sanderson,et al.  JADE: Adaptive Differential Evolution With Optional External Archive , 2009, IEEE Transactions on Evolutionary Computation.

[39]  Qingfeng Ding,et al.  The Cellular Differential Evolution Based on Chaotic Local Search , 2015 .

[40]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[41]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

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