Real-coded genetic algorithm with variable rates of cross-over and mutation: a basis of global optimization for multi-modal functions via interval technique

Abstract

A hybrid method consisting of a real-coded genetic algorithm (RCGA) and an interval technique is proposed for optimizing bound constrained non-linear multi-modal functions. This method has two different phases. In phase I, the search space is divided into several subregions and the simple genetic algorithm (SGA) is applied to each subregion to find the one(s) containing the best value of the objective function. In phase II, the selected subregion is divided into two equal halves and the advanced GA, i.e. the RCGA, is applied in each half to reject the subregion where the global solution does not exist. This process is repeated until the interval width of each variable is less than a pre-assigned very small positive number. In the RCGA, we consider rank-based selection, multi-parent whole arithmetical cross-over, and non-uniform mutation depending on the age of the population. However, the cross-over and mutation rates are assumed as variables. Initially, these rates are high and then decrease from generation to generation. Finally, the proposed hybrid method is applied to several standard test functions used in the literature; the results obtained are encouraging. Sensitivity analyses are shown graphically with respect to different parameters on the lower bound of the interval valued objective function of two different problems.

Keywords:

• Global optimization
• Genetic algorithm
• Interval technique
• Multi-modal continuous function

Acknowledgements

The authors would like to acknowledge support for this research provided by the University Grants Commission, India, under DRS phase III programme. The authors are also grateful to the anonymous referees for their constructive and helpful comments and suggestions.