Many evolutionary algorithms have been proposed for multi-/many-objective optimization problems; however, the tradeoff of convergence and diversity is still the challenge for optimization algorithms. In this paper, we propose a modified particle swarm optimization based on decomposition framework with different ideal points on each reference vector, called MPSO/DD, for many-objective optimization problems. In the MPSO/DD algorithm, the decomposition strategy is used to ensure the diversity of the population, and the ideal point on each reference vector can draw the population converge faster to the optimal front. The position of each individual will be updated by learning the demonstrators in its neighborhood that have less distance to the ideal point along the reference vector. Eight state-of-the-art evolutionary multi-/many-objective optimization algorithms are adopted to compare the performance with MPSO/DD for solving many-objective optimization problems. The experimental results on seven DTLZ test problems with 3, 5, 8, 10, 15 and 20 objectives, respectively, show the efficiency of our proposed method on solving problems with high-dimensional objective space.

对于多/多目标优化问题，已经提出了许多进化算法。然而，收敛性和多样性的折衷仍然是优化算法的挑战。本文针对多目标优化问题，提出了一种基于分解框架的改进粒子群算法，该算法在每个参考向量上具有不同的理想点，称为MPSO / DD。在MPSO / DD算法中，使用分解策略来确保总体的多样性，并且每个参考矢量上的理想点可以使总体更快地收敛到最优前沿。每个人的位置将通过学习邻近参考点的示教者进行更新，这些示教者与理想点之间的距离较小。采用八种最先进的进化多目标/多目标优化算法，将性能与MPSO / DD进行比较，以解决多目标优化问题。对分别具有3个，5个，8个，10个，15个和20个目标的七个DTLZ测试问题的实验结果表明，我们提出的方法可以解决高维目标空间的问题。