Real-coded Genetic Algorithms with Simulated Binary Crossover: Studies on Multimodal and Multiobjective Problems

Real-coded genet ic algorit hms (GAs) do not use any coding of the problem variab les, instead they work dir ectly with the variab les . The main difference in the implementation of real-coded GAs and binary-coded GAs is in their recombination op erators. Alt ho ugh a number of real-cod ed crossover implementations were suggested, most of them were developed wit h intuition and wit hout much analysis. Recen tly, a real-cod ed crossover operator has been developed based on the search characteristics of t he single-point crossover operator used in binary-coded GAs. T his simulated binary crossover (SBX) operator has been found to work well in many test problems having continuous search space when compared to exis t ing real-coded crossover implementations. In this paper the performan ce of the real-cod ed GA with SBX in solving mult imodal and multiob jective problems is further investigated . Sharing function approach and nond ominated sort ing implementati ons are includ ed in the real-coded GA with SBX to solve mult imodal and mult iobjective problems, resp ecti vely. It is observed that the real-coded GAs perform equally well or bet ter than binarycoded GAs in solving a nu mber of test problems . One advant age of the SBX operator is that it can restri ct childr en solut ions to any arb it rary closeness to the parent solutions , t hereby not requi rin g any separate mating restrict ion scheme for bet ter performance. F inally, rea l-coded GAs with SBX have been successfully used to find mu lt iple P aretooptimal solut ions in solving a welded beam design pr oblem . These simulation results ar e encour aging and suggest the applica t ion of realcod ed GAs with SBX operator to rea l-world optimization problems at large. *Electronic mail address: debClliitk. ernet. in. 432 K alyanmoy Deb and Amarendra Kumar