A model-based evolutionary algorithm for bi-objective optimization

The Pareto optimal solutions to a multi-objective optimization problem often distribute very regularly in both the decision space and the objective space. Most existing evolutionary algorithms do not explicitly take advantage of such a regularity. This paper proposed a model-based evolutionary algorithm (M-MOEA) for bi-objective optimization problems. Inspired by the ideas from estimation of distribution algorithms, M-MOEA uses a probability model to capture the regularity of the distribution of the Pareto optimal solutions. The local principal component analysis (local PCA) and the least-squares method are employed for building the model. New solutions are sampled from the model thus built. At alternate generations, M-MOEA uses crossover and mutation to produce new solutions. The selection in M-MOEA is the same as in non-dominated sorting genetic algorithm-II (NSGA-II). Therefore, MOEA can be regarded as a combination of EDA and NSGA-II. The preliminary experimental results show that M-MOEA performs better than NSGA-II.