改进聚合树的高维多目标降维优化算法

Improved Aggregation-Tree-Based Objective Reduction Optimization for Many-Objective Optimization

对于高维多目标优化问题,降维优化算法通过去除或融合冗余目标的方法解决算法耗时过多的问题,但同时也会导致算法分布性能下降。聚合树算法定义非参数秩冲突从而可以快速计算出各目标间冲突度,但聚合树算法鲁棒性有待提高,且需要用户自行决策去除冗余目标。针对这些问题,提出数组叠加机制并定义冲突趋势和冲突度误差,以提高算法鲁棒性;通过合并冲突度较低的冗余目标的方法来进行目标降维,并定义降维截止冲突度;与NSGA-III算法结合,以达到对高维多目标问题进行完整降维优化的目的。为检验该算法性能,与其他经典高维算法进行对DTLZ测试函数集的优化对比,实验结果表明,该算法在耗时更少的同时,也具有较为优秀的分布性能和收敛性能。

The objective-reduction optimization algorithm solves the problem of consuming too much time by removing or fusing redundant objectives for many-objective optimization problems in practical applications,but the distribution performance of the algorithm will also decline at the same time.Aggregation-tree algorithm defines non-parametric rank conflict and can calculate the conflict value among objectives quickly.However,the robustness of aggregation-tree algorithm needs to be improved,and users need to make decisions to remove redundant objectives by themselves.To solve these problems,an array stacking mechanism is proposed,it defines the trend of conflict and the error of conflict value,and improves the robustness of the algorithm.Objectives combining reduction is proposed by combining redundant objectives with low conflict value,and the cut off conflict value is defined.It is combined with NSGA-III to complete objective reduction optimization for many-objective problems.In order to test the performance of the algorithm in this paper,the optimization of DTLZ test function is compared with other classical many-objective optimization algorithms.The experimental results show that the proposed algorithm has a great advantage in running time,and also ensures excellent distribution performance and convergence performance.