MIXED VARIABLE NON-LINEAR OPTIMIZATION BY DIFFERENTIAL EVOLUTION

This article discusses solving non-linear programming problems containing integer, discrete and continuous variables. A novel mixed integer-discrete-continuous, non-linear optimization method based on Differential Evolution algorithm is described. Also the required handling techniques for integer, discrete and continuous variables are described including the techniques needed to handle boundary constraints as well as those needed to simultaneously deal with several non-linear and non-trivial constraint functions. Previous experiments and comparisons with other methods for mixed integer-discretecontinuous non-linear optimization have suggested that the described approach is capable of obtaining high quality solutions. The novel method is relatively easy to implement and use. It is found to be effective, efficient and robust, which makes it as an attractive and widely applicable approach for solving practical problems in the field of prediction.

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

[2]  Kenneth V. Price,et al.  An introduction to differential evolution , 1999 .

[3]  Laxmidhar Behera,et al.  Differential Evolution Based Fuzzy Logic Controller for Nonlinear Process Control , 1999, Fundam. Informaticae.

[4]  Asad I. Khan,et al.  Parallel and distributed processing for computational mechanics: an introduction , 2000 .

[5]  E. Sandgren,et al.  Nonlinear Integer and Discrete Programming in Mechanical Design Optimization , 1990 .

[6]  S. Wu,et al.  GENETIC ALGORITHMS FOR NONLINEAR MIXED DISCRETE-INTEGER OPTIMIZATION PROBLEMS VIA META-GENETIC PARAMETER OPTIMIZATION , 1995 .

[7]  Rainer Storn,et al.  Differential Evolution-A simple evolution strategy for fast optimization , 1997 .

[8]  Han Tong Loh,et al.  Computational Implementation and Tests of a Sequential Linearization Algorithm for Mixed-Discrete Nonlinear Design Optimization , 1991 .

[9]  R. Salomon.  Re-evaluating genetic algorithm performance under coordinate rotation of benchmark functions. A survey of some theoretical and practical aspects of genetic algorithms. , 1996, Bio Systems.

[10]  Ivan Zelinka,et al.  Mechanical engineering design optimization by differential evolution , 1999 .

[11]  H. Loh,et al.  A Sequential Linearization Approach for Solving Mixed-Discrete Nonlinear Design Optimization Problems , 1991 .

[12]  Chun Zhang,et al.  Mixed-discrete nonlinear optimization with simulated annealing , 1993 .

[13]  R. G. Fenton,et al.  A MIXED INTEGER-DISCRETE-CONTINUOUS PROGRAMMING METHOD AND ITS APPLICATION TO ENGINEERING DESIGN OPTIMIZATION , 1991 .

[14]  Chun Zhang,et al.  ON MIXED-DISCRETE NONLINEAR OPTIMIZATION PROBLEMS: A COMPARATIVE STUDY , 1995 .

[15]  Jahau Lewis Chen,et al.  Optimal design of machine elements using genetic algorithms , 1993 .

[16]  W. Land,et al.  A new training algorithm for the general regression neural network , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

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

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

[19]  Han-Lin Li,et al.  A GLOBAL APPROACH FOR NONLINEAR MIXED DISCRETE PROGRAMMING IN DESIGN OPTIMIZATION , 1993 .

[20]  Rainer Storn,et al.  Differential evolution design of an IIR-filter , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[21]  J. Cai,et al.  Evolution strategies - parallelisation and application in engineering optimization , 2000 .