C语言差分进化算法及优化实例

D I F F E R E N T I A L E V O L U T I O N C-code in the file de.c implements Differential Evolution (DE) algorithm, more precisely DE/rand/1/bin [1,2,3] version of the method. This DE variation is probably the most used DE variation and perform well with arbitrary problems. Whole algorithm is in the file de.c and you may implement your optimization problem to a separate file. You do not have to make any changes to the de.c file, all the problem specific definitions are to be made only the file where objective function is in function func. See for example file rastrigin_2d.c for problem description. You can compile the program with command: gcc -Wall -pedantic -ansi -O -o de de.c problem.c -lm , where you replace problem.c file with the file name containing your optimization problem. All the parameters for the program are given on command line and you can run ./de -h to see usage. You may run this program also without any parameters using default values. Basic control parameters are: -N NP (20*D) defines size of the population NP (20*dimension of the problem is default) -G Gmax (1000) defines number of generations -C CR (0.9) defines crossover constant -F F (0.9) defines mutation scaling factor Other parameter for the program are: -u -h usage of the problem -o <fname> output file name for the final population -s uses same random number generator seed Format of output file is such that every row contains one member of the population, first are decision variables and final value is the objective function value, i.e., x1_1 x1_2 x1_3 ... x1_D f1 x2_1 x2_2 x2_3 ... x2_D f2 x3_1 x3_2 x3_3 ... x3_D f3 : : : : xN_1 xN_2 xN_3 ... xN_D fN Parameter CR controls the crossover operation and its value is [0.0, 1.0]. Parameter F is a scaling factor for the mutation and its value is typically (0,1+]. In practice, CR controls the rotational invariance of the search, and its small value (e.g. 0.1) is practicable with separable problems and larger values (e.g 0.9) are practicable for non-separable problems. Control parameter F controls the speed and robustness of the search, i.e., lower value for F increases the convergence rate but also the risk of stacking into a local optimum. If nothing is known about problem characteristics then it might be good to use the control parameter values CR = F = 0.9 which give slow convergence but provide the global optimum reliable. You may try out following commands: gcc -Wall -pedantic -ansi -O -o de de.c rastrigin_20d.c -lm ./de -N 20 -G 500 -C 0.0 -F 0.5 gcc -Wall -pedantic -ansi -O -o de de.c rastrigin_20d_skewed.c -lm ./de -N 100 -G 10000 -C 0.2 -F 0.5 gcc -Wall -pedantic -ansi -O -o de de.c schwefel_20d.c -lm ./de -N 50 -G 400 -C 0.2 -F 0.5 Author and copyright: Saku Kukkonen Lappeenranta University of Technology Department of Information Technology P.O.Box 20, FIN-53851 LAPPEENRANTA, Finland E-mail: saku.kukkonen@lut.fi Code is free for scientific and academic use. Use for other purpose is not allowed without a permission of the author. There is no warranty of any kind about correctness of the code and if you find a bug, please, inform the author. Please, acknowledge and inform the author if you use this code. References: [1] Rainer Storn and Kenneth V. Price, Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces, Technical Report, TR-95-012, ICSI, March, 1995, [Online] Available: www.icsi.berkeley.edu/ftp/global/pub/techreports/1995/tr-95-012.pdf, 14.6.2005. [2] Rainer Storn and Kenneth V. Price, Differential evolution - a Simple and Efficient Adaptive Scheme for Global Optimization Over paces, Journal of Global Optimization, 11 (4), pp. 341-359, Dec, 1997, Kluwer Academic Publisher. [3] Kenneth V. Price, Rainer Storn, and Jouni Lampinen, Differential Evolution: A Practical Approach to Global Optimization, Springer-Verlag, Berlin, ISBN: 3-540-20950-6, 2005.