An intelligent genetic algorithm designed for global optimization of multi-minima functions

Abstract

Many practical problems often lead to large non-convex non-linear programming problems that have multi-minima. The global optimization algorithms of these problems have received much attention over the last few years. Generally, stochastic algorithms are suitable for these problems, but not efficient when there are too many minima. Genetic algorithms are stochastic search approaches based on randomized operators, such as selection, crossover and mutation, inspired by the natural reproduction and evolution of the living creatures. However, the existing genetic algorithms cannot solve global optimization of multi-minima functions effectively. A new algorithm called intelligent genetic algorithm (IGA) is proposed for the global optimization of multi-minima functions. IGA integrates many cross operator, mutation operator and reattempt operation. It can select the appropriate cross operator, mutation operator or reattempt operation according to the current optimization result. It converges to the global optimization solution without the influence of random searching process. At first, this paper introduces the foundation for designing intelligent genetic algorithm; secondly, this paper reports on the development of an intelligent genetic algorithm approach for global optimization problems; thirdly, the proposed method is illustrated by means of some numerical examples; finally, the conclusions of this study are drawn with possible directions for subsequent studies. The feasibility, the efficiency and the effectiveness of IGA are tested in detail through a set of benchmark multi-modal functions, of which global and local minima are known. The experimental results suggest that results from IGA are better than results from other methods. In conclusion, the performance of IGA is better than that of other methods, IGA results are satisfactory for all the functions.