Reference point reconstruction-based firefly algorithm for irregular multi-objective optimization

Reference point-based environmental selection has achieved promising performance in multi-objective optimization problems. However, when solving the irregular multi-objective optimization problems, the performance of environmental selection is affected. This is because the irregular Pareto front is often degraded, disconnected, inverted, or with sharp tails, resulting in some reference points not located in appropriate region. This releases the selection pressure. Therefore, adjusting or generating some points is necessary to tackle this problem. However, how to identify the region of interest and how to generate new points in the appropriate region are the current problems to be solved. In this paper, a region-based reconstruction for reference points is proposed. For simplicity, the smallest region which consists of M reference points ( M is the dimension of objective space) in the hyperplane of reference point is identified as the unit region. If the vertexes of the region all belong to active reference points, the region will be identified as region of interest and new reference points will be reconstructed in this region. In addition, the process is activated in the later stage of the algorithm operation, while the efficient of the search algorithm is weak. In order to find more valuable individuals in the neighborhood region of selected individuals, thereby, firefly algorithm is employed as search algorithm because of its search mechanism which has strong indicative features. Several experiments are designed to verify the performance of the proposed method. The experiment results show that the proposed method is effective.