A Hybrid Competent Multi-swarm Approach for Many-Objective Problems

Many-objective optimization problems (MaOPs) are a class of multi-objective problems that presents more than three functions to be optimized. As most Pareto based algorithms scale poorly according to the number of objectives, researchers are working on alternatives to overcome these limitations. An algorithm that has shown good results in solving MaOPs is the Iterated Multi-swarm (I-Multi) which presents a clever multi-swarm strategy to spread the solutions across different areas of the objective space while keeping a good convergence. As the I-Multi is a very recent algorithm, alternative approaches are yet to be explored. Here we investigate the use of an Estimation of Distribution Algorithm (EDA) in the multi-swarm stage of I-Multi. EDAs create a model based on the best solutions found and sample new solutions based in this model. An EDA that presents good performance is the rBOA which is a real-valued version of the Bayesian optimization algorithm. This work presents an algorithm called C-Multi consisting of a hybrid between the I-Multi and the rBOA with the aim to join the diversity strength of I-Multi and the convergence characteristic of rBOA. An experimental study is conducted using the seven well-known DTLZ test functions with 3, 5, 10, 15 and 20 objectives to evaluate the performance of the algorithms as the number of objectives scales up. The results point that the new algorithm presents superior convergence and diversity on hard problems.