On convergence of multi-objective Pareto front: Perturbation method

A perturbation method is proposed to detect convergence of the Pareto front for multi-objective algorithms and to investigate its effect on the rate of convergence of the optimization. Conventionally, evolutionary algorithms are allowed to run for a fixed number of trial solutions which can result in a premature convergence or in an unnecessary number of calls to a computationally intensive real world problem. Combination of evolutionary multi-objective algorithms with perturbation method will improve the rate of convergence of the optimization. This is a very important characteristic in reducing number of generations and therefore reducing the computational time which is important in real world problems where cost and time constraint prohibit repeated runs of the algorithm and the simulation. The performance of the method will be examined by its application to two water distribution networks from literature. The results will be compared with previously published results from literature and those generated by evolutionary multi-objective algorithm. It will be shown that the method is able to find the Pareto optimal front with less computational effort.