The need for improving the exploration operators for constrained optimization problems

Several specific methods have been proposed for handling nonlinear constraints. These methods have to bring individuals in the feasible space, and help to explore and exploit efficiently the feasible domain. However, even if this domain is not sparse, this paper demonstrates that the exploration capacity of standard reproduction operators is not optimal when solving constrained problems. The logarithmic mutation operator presented in this paper has been conceived to explore both locally and globally the search space. As expected, it exhibits a robust and efficient behavior on a constrained version of the Sphere problem, compared to some other standard operators. Associated with BLX-0.5 crossover and a special ranking selection taking the constraints into account, the logarithmic mutation allows a GA to often reach better performance than several well known methods on a set of classical test cases.