基于抽象凸下界估计的群体全局优化算法

针对确定性全局优化算法极高的计算复杂度以及随机性全局优化算法可靠性较低的问题，在群体进化算法框架下，结合抽象凸理论，提出一种基于抽象凸下界估计的群体全局优化算法。首先，对整个初始群体构建抽象凸下界估计松弛模型；然后，利用不断收紧的下界估计信息安全排除部分无效区域，并指导种群更新，同时借助支撑面的下降方向作局部增强；最后，根据进化信息更新支撑面。数值实验结果表明了所提出算法的有效性。

Population-based global optimization algorithm using abstract convex underestimate

To solve the problem of high computation complexity in deterministic global optimization algorithms and low success ratio in stochastic global optimization algorithms, a population-based global optimization algorithm using abstract convex underestimate is proposed. The proposed algorithm combines the abstract convexity theory within the framework of population evolutionary algorithms. The first step of the algorithm is to construct the abstract convex underestimate relaxed model for the whole initial population. Then, relevant tightening underestimate information is used to safely eliminate invalid regions and to guide the population updating. Additionally, descent directions of supporting hyperplanes are employed for local enhancement. Finally, evolutionary information helps to update supporting hyperplanes. Numerical experiment results show the effectiveness of the proposed algorithm.