Optimizing fuzzy multi-objective problems using fuzzy genetic algorithms, FZDT test functions

Abstract: The following work outlines a robust method for accounting the fuzziness of the objective space while dealing with the real world optimization problems. Use of mean/approximated value of input parameters doesn't account for the variability in the optimized solution inherited due to variability in the input parameters which is very crucial, especially in real world problems. The following work describes and evaluates a unique solution strategy for optimizing fuzzy multi-objective problems by integrating genetic algorithms with concepts of fuzzy logic. The unique way of problem formulation required no tweaking in genetic operators of mutation and crossover but the concept of ranking has been carefully extended to fuzzy domain. The standard benchmark test function, ZDT [4], have been extrapolated to fuzzy domain as FZDT and proposed to be benchmark test function for fuzzy optimization algorithms. The results have been successfully verified with FZDT test functions and were found coherent with ZDT test functions under classical assumptions.