Generating multiple reference vectors for a class of many-objective optimization problems with degenerate Pareto fronts

Many-objective optimization problems with degenerate Pareto fronts are hard to solve for most existing many-objective evolutionary algorithms. This is particularly true when the shape of the degenerate Pareto front is very narrow, and there are many dominated solutions near the Pareto front. To solve this particular class of many-objective optimization problems, a new evolutionary algorithm is proposed in this paper. In this algorithm, a set of reference vectors is generated to locate the potential Pareto front and then generate a set of location vectors. With the help of the location vectors, the solutions near the Pareto front are mapped to the hyperplane and clustered to generate more reference vectors pointing to Pareto front. This way, the location vectors are able to efficiently guide the population to converge towards the Pareto front. The effectiveness of the proposed algorithm is examined on two typical test problems with degenerate Pareto fronts, namely DTLZ5 and DTLZ6 with 5–40 objectives. Our experimental results show that the proposed algorithm has a clear advantage in dealing with this class of many-objective optimization problems. In addition, the proposed algorithm has also been successfully applied to optimization of process parameters of polyester fiber filament melt-transportation.