Binary differential evolution strategies

Differential evolution has shown to be a very powerful, yet simple, population-based optimization approach. The nature of its reproduction operator limits its application to continuous-valued search spaces. However, a simple discretization procedure can be used to convert floating-point solution vectors into discrete-valued vectors. This paper considers three approaches in which differential evolution can be used to solve problems with binary-valued parameters. The first approach is based on a homomorphous mapping, while the second approach interprets the floating-point solution vector as a vector of probabilities, used to decide on the appropriate binary value. The third approach normalizes solution vectors and then discretize these normalized vectors to form a bitstring. Empirical results are provided to illustrate the efficiency of both methods in comparison with particle swarm optimizers.

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

[2]  Frans van den Bergh,et al.  An analysis of particle swarm optimizers , 2002 .

[3]  G. Thierauf,et al.  A combined heuristic optimization technique , 2005, Adv. Eng. Softw..

[4]  James Kennedy,et al.  Particle swarm optimization , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[5]  J. Kennedy,et al.  Population structure and particle swarm performance , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[6]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[7]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization , 1999, Evolutionary Computation.

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

[9]  C. Su,et al.  Network Reconfiguration of Distribution Systems Using Improved Mixed-Integer Hybrid Differential Evolution , 2002, IEEE Power Engineering Review.

[10]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[11]  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.

[12]  R. Storn,et al.  On the usage of differential evolution for function optimization , 1996, Proceedings of North American Fuzzy Information Processing.

[13]  R. Storn,et al.  Differential evolution a simple and efficient adaptive scheme for global optimization over continu , 1997 .

[14]  Ivan Zelinka,et al.  MIXED INTEGER-DISCRETE-CONTINUOUS OPTIMIZATION BY DIFFERENTIAL EVOLUTION Part 1: the optimization method , 2004 .

[15]  Ivan Zelinka,et al.  MIXED INTEGER-DISCRETE-CONTINUOUS OPTIMIZATION BY DIFFERENTIAL EVOLUTION Part 2 : a practical example , 1999 .

[16]  Feng-Sheng Wang,et al.  Fuzzy decision-making design of chemical plant using mixed-integer hybrid differential evolution , 2002 .

[17]  Feng-Sheng Wang,et al.  A hybrid method of evolutionary algorithms for mixed-integer nonlinear optimization problems , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[18]  Stefan Janaqi,et al.  Generalization of the strategies in differential evolution , 2004, 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings..

[19]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .