Hybrid Resource Allocation Framework for Large-Scale Multi-Objective Optimization

The resource allocation strategy has been well applied in improving the performance of optimization algorithms. However, most resource allocation methods focus on either the objective space or the decision space. Few reports have been published on establishing adaptive resource allocation model that considers the two spaces simultaneously. In this work, a hybrid resource allocation framework is developed to enhance the performance of large-scale multi-objective optimization algorithms and thus fully use the information of the two spaces to build a reasonable resource allocation model. In objective space, shift-based density estimation strategy is used to allocate the individuals to different groups. In decision space, the decision variables are grouped with Pearson correlation coefficient and k-means clustering. This method does not add significant external computational cost to the algorithm, and the new resource allocation model contains more information than single space resource allocation model does. The adaptability of the resource allocation model is enhanced further by designing an adaptive distribution method to determine the reference resources for the population at different evolution phases. The division speed of the population is adaptive modified, and the diversity and evolution time of individuals in the sub-populations are balanced. In addition, a hybrid environmental selection strategy is designed to balance the quality of offspring and computation cost. Three types of experiments on two benchmark functions and a practical experiment are conducted to prove the effectiveness of the new framework. Statistical results indicate that the new framework can enhance the mean inverted generational distance and hypervolume indicator of the algorithms.