الگوریتم ژنتیک ترکیبی بهبود - سیمپلکس برای بهینه سازی عددی جهانی

In this paper, a hybrid simplex-improved genetic algorithm (HSIGA) which combines simplex method (SM) and genetic algorithm (GA) is proposed to solve global numerical optimization problems. In this hybrid algorithm some improved genetic mechanisms, for example, non-linear ranking selection, competition and selection among several crossover offspring, adaptive change of mutation scaling and stage evolution, are adopted; and new population is produced through three approaches, i.e. elitist strategy, modified simplex strategy and improved genetic algorithm (IGA) strategy. Numerical experiments are included to demonstrate effectiveness of the proposed algorithm.

Genetic algorithm (GA) is a stochastic and parallel search technique based on the mechanics of natural selec- tion, genetics and evolution, which was ¯rst developed by Holland in 1970s[1]. In recent years, GA has been widely applied to di®erent areas such as fuzzy systems, neural net- works, etc.[2] Although GA has become one of the popu- lar methods to address some global optimization problems, the major problem of GA is that it may be trapped in the local optima of the objective function when the prob- lem dimension is high and there are numerous local op- tima. This degradation in e±ciency is apparent especially in applications where the parameters being optimized are highly correlated[3]. In order to overcome these °aws and improve the GA0s optimization e±ciency, recent research works have been generally focused on two aspects. One is improvements upon the mechanism of the algorithm, such as modi¯cation of genetic operators, or the use of niche technique[4], etc; the other is combination of GA with other optimization methods, such as BFGS methods[5], simulated annealing (SA), etc. In this paper, a hybrid simplex-improved genetic algo- rithm (HSIGA) is proposed to solve global numerical op- timization problems. In this hybrid algorithm some im- proved genetic mechanisms are adopted, such as non-linear ranking selection, competition and selection among several crossover o®spring, adaptive change of mutation scaling and adaptive stage evolution mechanism, to form an im- proved genetic algorithm (IGA). For further performance enhancement, the IGA algorithm is combined with the simplex method (SM) and the new population is gener- ated through three approaches, i.e. elitist strategy, simplex strategy and IGA strategy. We investigate the e®ectiveness of this proposed algorithm by solving 10 test functions with high dimensions.

In this paper, the HSIGA has been presented to solve global numerical optimization problems.This methodology involves a novel improvement on the genetic mechanism and combination with the modi¯ed simplex method to en- hance the genetic algorithm.The HSIGA has been carried out to solve 10 benchmark problems with high dimensions. Results obtained from 50 trials for each function show that the proposed HSIGA is able to ¯nd optimal or close-to- optimal solutions for all these test functions; moreover the behavior of the algorithm is stable. Comparison of the HSIGA outcome with those from several other global opti- mization algorithms demonstrates that the HSIGA is more competitive than some recent algorithms on the problem studied.