Qiqi Liu, Yaochu Jin, Martin Heiderich, Tobias Rodemann, "Coordinated Adaptation of Reference Vectors and Scalarizing Functions in Evolutionary Many-objective Optimization", IEEE Transactions on Systems, Man and Cybernetics: Systems, vol. 53, no. 2, pp. 763-775, 2023.

It is highly desirable to adapt the reference vectors to unknown Pareto fronts in decomposition based evolutionary many-objective optimization. While adapting the reference vectors enhances the diversity of the achieved solutions, it often decelerates the convergence performance. To address this dilemma, we propose to adapt the reference vectors and the scalarizing functions in a coordinated way. On the one hand, the adaptation of the reference vectors is based on a local angle threshold, making the adaptation better tuned to the distribution of the solutions. On the other hand, the weights of the scalarizing functions are adjusted according to the local angle thresholds and the reference vectors’ age, which is calculated by counting the number of generations in which one reference vector has at least one solution assigned to it. Such coordinated adaptation enables the algorithm to achieve a better balance between diversity and convergence, regardless of the shape of the Pareto fronts. Experimental studies on MaF, DTLZ and DPF test suites demonstrate the effectiveness of the proposed algorithm in solving problems with both regular and irregular Pareto fronts.