Objective reduction for visualising many-objective solution sets

Visualising a solution set is of high importance in many-objective optimisation. It can help algorithm designers understand the performance of search algorithms and decision makers select their preferred solution(s). In this paper, an objective reduction-based visualisation method (ORV) is proposed to view many-objective solution sets. ORV attempts to map a solution set from a high-dimensional objective space into a low-dimensional space while preserving the distribution and the Pareto dominance relation between solutions in the set. Specifically, ORV sequentially decomposes objective vectors which can be linearly represented by their positively correlated objective vectors until the expected number of preserved objective vectors is reached. ORV formulates the objective reduction as a solvable convex problem. Extensive experiments on both synthetic and real-world problems have verified the effectiveness of the proposed method.