Theoretical basis of parameter tuning for finding optima near the boundaries of search spaces in real-coded genetic algorithms

Studies on parameter tuning in evolutionary algorithms are essential for achieving efficient adaptive searches. This paper discusses parameter tuning in real-valued crossover operators theoretically. The theoretical analysis is devoted to improving robustness of real-coded genetic algorithms (RCGAs) for finding optima near the boundaries of bounded search spaces, which can be found in most real-world applications. The proposed technique for crossover-parameter tuning is expressed mathematically, and thus enables us to control the dispersion of child distribution quantitatively. The universal applicability and effect have been confirmed theoretically and verified empirically with five crossover operators. Statistical properties of several practical RCGAs are also investigated numerically. Performance comparison with various parameter values has been conducted on test functions with the optima placed not only at the center but also in a corner of the search space. Although the parameter-tuning technique is fairly simple, the experimental results have shown the great effectiveness.