摘要:多偏好向量引导的协同进化算法（PICEA-g）是将目标向量作为偏好，个体支配目标向量的个数作为适应值，以有效降低高维目标空间中非支配解的比例.但PICEA-g所获解集是近似Pareto前沿，而不是决策者真正感兴趣部分的Pareto最优解，导致算法在处理高维优化问题时性能下降和计算资源的浪费.鉴于此，提出一种基于偏好向量引导的高维目标协同进化算法（ASF-PICEA-g）：首先，利用ASF扩展函数将进化种群中的参考点映射至目标空间，并将其作为偏好向量引导种群进化的参考方向；然后，利用偏好区域选择策略获取两个临时参考点，进而构建决策者感兴趣区域（ROI），确定随机偏好集产生的上下界范围，通过协同进化机制引导种群朝偏好区域收敛.将ASF-PICEA-g与g-NSGA-II和r-NSGA-II在3-20维的WFG系列和DTLZ系列测试函数上进行仿真实验，实验结果表明：ASF-PICEA-g在WFG系列测试函数上表现出了良好的性能，所得解集整体上优于对比算法；在DTLZ系列测试函数上略优于对比算法，尤其在10维以上目标空间，ASF-PICEA-g表现出更好的稳定性，所获解集有较好的收敛性和分布性.



Abstract:The preference-inspired co-evolutionary algorithm (PICEA-g) uses goal vectors as preferences, and uses the number of target vectors that the individual can dominated as fitness value, to effectively decrease the proportion of non-dominated solutions in high dimensional space. However, the obtained set is approximate Pareto frontier, not Pareto optimal solution that decision makers are really interested in. This leads to the performance degradation and computational resources waste when dealing with high-dimensional optimization problems. Therefore, a preference vector guided co-evolutionary algorithm for many-objective optimization is proposed in this study. Firstly, the ASF extension function is used to map the ideal point in the evolution population on the objective space, which is used as a preference vector to guide the evolution direction of the population. Then, two temporary points are obtained by preference region selection strategy in order to build region of preference for decision maker (ROI). The range of upper and lower bounds generated by random preference sets is determined, and the co-evolution mechanism is used to guide the population to converge towards the ROI. The ASF-PICEA-g is compared with g-NSGA-II and r-NSGA-II on WFG and DTLZ benchmark test functions based on 3 dimension to 20 dimension. The experimental results demonstrate that ASF-PICEA-g shows sound performance on the WFG series test function, and the obtained solution set is better than the comparison algorithm; it is slightly better than the comparison algorithm in the DTLZ series test function, especially in the 10 dimension or higher dimension. In addition, ASF-PICEA-g shows better stability, and the obtained solution set has better convergence and distribution.



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