基于不确定度采样准则的费时问题优化算法

An optimization algorithm with uncertainty-based sampling strategy for expensive problems

在实际工程和控制领域中,许多优化问题的性能评价是费时的,由于进化算法在获得最优解之前需要大量的目标函数评价,无法直接应用其求解这类费时问题.引入代理模型以辅助进化算法是求解计算费时优化问题的有效方法,如何采样新个体对其进行真实的目标函数评价是影响代理模型辅助的进化算法寻优性能的重要因素.鉴于此,利用径向基函数神经网络作为代理模型辅助进化算法,提出一种新的不确定度计算方法,同时结合模型估值构造一种新的填充采样准则以自主地选择新的采样点,从而引导算法在评价次数有限的情况下尽可能地找到目标函数值较好的解.所提出算法与近年来针对计算费时问题的优化算法在7个高达100维的基准问题上进行测试比较,实验结果表明所提出算法在相同评价次数下可以获得更好的优化结果.

Some optimization problems in the practical engineering and controlling fields are normally computationally expensive, which limits the application of evolutionary algorithms for solving these problems because a number of objective evaluations are often required before locating at the optimal solution. The utilization of surrogate models to assist evolutionary algorithms is efficient for solving computationally expensive problems. However, the sampling method, which is used to select solutions to be evaluated using the exact time-consuming objective function, plays a key role to obtain a good performance of the surrogate-assisted evolutionary algorithm. In this paper, the radial basis function network is adopted as the surrogate model, and a new method to evaluate the uncertainty of the approximated value is proposed. Then, a new sampling strategy is given based on the approximation uncertainty and approximated value to adaptively select solutions for exact objective evaluation, which can assist the algorithm to find a better solution in a limited number of objective evaluations. The performance of the proposed method is verified by comparing to some state-of-the-art algorithms published in recent years on seven test problems with a maximum of 100 dimensions. The experimental results show that the proposed method can get better results in the same number of objective evaluations.