A Study on the Convergence of Multiobjective Evolutionary Algorithms

High computational cost has been a major impediment to the widespread use of evolutionary algorithms in industry. While the clock time for optimization using the GA can be reduced by parallelization, the computational cost can only be improved by reducing the number of function evaluations. For single objective optimization problems, the convergence curve can be utilized to obtain a suitable compromise between the computational cost and the quality of the solution. A non-domination criterion based metric that tracks the growth of an archive of non-dominated solutions over a few generations is proposed to generate a convergence curve for multi-objective evolutionary algorithms. Two analytical and two crashworthiness optimization problems were used to demonstrate the practical utility of this measure. It was observed that, similar to single-objective optimization problems, there were significant advances towards the POF in the early phase of evolution and relatively smaller improvements were obtained as the population matured. This information was used to terminate the search to obtain a good trade-off between the computational cost and the quality of the solutions. The paper also demonstrates the successful use of compute clusters for parallel processing to significantly reduce the clock time for optimization.