Real-coded Genetic Algorithms with Simulated Binary Crossover: Studies on Multimodal and Multiobjective Problems
Kalyanmoy Deb
Amarendra Kumar
Department of Mechanical Engineering,
Indian Institute of Technology,
Kanpur, UP 208 016, India
Abstract
Real-coded genetic algorithms (GAs) do not use any coding of the problem variables, instead they work directly with the variables. The main difference in the implementation of real-coded GAs and binary-coded GAs is in their recombination operators. Although a number of real-coded crossover implementations were suggested, most of them were developed with intuition and without much analysis. Recently, a real-coded crossover operator has been developed based on the search characteristics of the single-point crossover operator used in binary-coded GAs. This simulated binary crossover (SBX) operator has been found to work well in many test problems having continuous search space when compared to existing real-coded crossover implementations. In this paper the performance of the real-coded GA with SBX in solving multimodal and multiobjective problems is further investigated. Sharing function approach and nondominated sorting implementations are included in the real-coded GA with SBX to solve multimodal and multiobjective problems, respectively. It is observed that the real-coded GAs perform equally well or better than binary-coded GAs in solving a number of test problems. One advantage of the SBX operator is that it can restrict children solutions to any arbitrary closeness to the parent solutions, thereby not requiring any separate mating restriction scheme for better performance. Finally, real-coded GAs with SBX have been successfully used to find multiple Pareto-optimal solutions in solving a welded beam design problem. These simulation results are encouraging and suggest the application of real-coded GAs with SBX operator to real-world optimization problems at large.
