A genetic algorithm and cell mapping hybrid method for multi-objective optimization problems

Abstract

In this paper, a hybrid multi-objective optimization (MOO) algorithm consisting of an integration of the genetic algorithm (GA) and the simple cell mapping (SCM) is proposed. The GA converges quickly toward a solution neighborhood, but it takes a considerable amount of time to converge to the Pareto set. The SCM can find the global solution because it sweeps the whole space of interest. However, the computational effort grows exponentially with the dimension of the design space. In the hybrid algorithm, the GA is used initially to find a rough solution for the multi-objective optimization problem (MOP). Then, the SCM method takes over to find the non-dominated solutions in each region returned by the GA. It should be pointed out that one point near or on the Pareto set is enough for the SCM to recover the rest of the solution in the region. For comparison purpose, the hybrid algorithm, the GA and SCM methods are applied to solve some of benchmark problems with the Hausdorff distance, number of function evaluations and CPU time as performance metrics. The results show that the hybrid algorithm outperforms other methods with a modest computational time increase. Although the hybrid algorithm does not guarantee finding the global solution, it has much improved chance as demonstrated by one of the benchmark problems.