An empirical investigation into the effects of chaos on different types of evolutionary crossover operators for efficient global search in complicated landscapes

Abstract

In this study, a comprehensive empirical test is conducted to analyse the effects of two well-known chaotic maps, namely sinusoidal and logistic maps, on the efficacy of double Pareto crossover, Laplace crossover and simulated binary crossover operators for the global optimization of continuous problems. To do so, 13 well-known numerical benchmark problems in three distinctive dimensions, namely 50D, 100D and 200D, are considered and the genetic algorithm (GA) with simple version and chaos-enhanced versions of the mentioned crossover operators are utilized for optimizing these functions. Furthermore, a time complexity analysis is conducted to find out the impact of hybridizing the chaos and the evolutionary operators on the computational complexity of GA. The results of the experimental analysis provide us with fruitful information regarding the scalability, computational complexity and exploration/exploitation capability of the considered rival optimization algorithms, as well as, demonstrate the efficacy of chaos-evolutionary computing for numerical continuous optimizations.

Keywords:

• evolutionary computation
• crossover operator
• chaotic maps
• numerical optimization
• genetic algorithm
• computational complexity

1999 AMS Subject Classifications:

• 68T01
• 68T05
• 68T20