基于角度惩罚距离的收敛因子非线性递减多目标鲸鱼优化改进算法

为了提高多目标鲸鱼优化算法的全局优化性能，提出了一种基于角度惩罚距离的收敛因子非线性递减多目标鲸鱼优化算法IWOA-APD。首先，针对基本多目标鲸鱼算法收敛性和多样性难以平衡的问题，采用角度惩罚距离作为解优劣评价指标。其次，给出了一种基于迭代进度和优化因子的收敛因子指数形式非线性递减策略，该策略可以通过调整优化因子进一步提升优化性能。除此之外，给出了基于融合距离与拥挤度距离的精英集维护机制，从而改善精英集的多样性维护效果。最后，为了验证所提出的算法有效性，基于五种标准测试函数及一种城市轨道列车速度曲线优化实际算例，在MATLAB2016b GUI平台下采用所提出的IWOA-APD与IWOA、MOWOA、dMOPSO进行对比仿真。仿真结果表明，所提出的IWOA-APD寻到了更理想的优化结果。由此说明，相比于一些性能品质良好的优化算法，IWOA-APD还具有更快的计算速度和更高的全局收敛精度。

Improved multi-objective whale optimization algorithm based on angle penalized distance using nonlinear decreasing convergence factor strategy

Aiming at global optimization for multi-objective whale optimization algorithm, this paper proposed an improved multi-objective whale optimization algorithm based on angle penalized distance using a nonlinear decreasing convergence factor strategy IWOA-APD. Firstly, aiming at the problem that the convergence and diversity of the basic whale optimization algorithm were difficult to balance, IWOA-APD used angle penalized distance for evaluating the optimal degree of solutions. Secondly, IWOA-APD given a nonlinear decreasing strategy of convergence factor based on iteration progress and optimization factors, and the strategy can further improve the optimization performance by using optimization factor. In addition, in order to improve the diversity maintenance effect of elite set, IWOA-APD gave an elite maintenance mechanism based on fusion distance and congestion degree distance. Finally, in order to verify the effectiveness of the proposed algorithm, the proposed IWOA-APD was compared with IWOA, MOWOA, dMOSSO in the standard test functions and a practical calculating example of velocity curve optimization for urban rail vehicle on the MATLAB2016a GUI platform. The experimental results show that the proposed algorithm IWOA-APD can obtain more ideal optimization results. Therefore, compared with several optimization algorithms with well performance quality, IWOA-APD has faster calculating efficiency and higher convergence accuracy.