基于既往优化知识的稳健性优化方法
A robust optimization method based on previous optimization knowledge
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摘要:目的 由于直接运用嵌套差分进化算法求解区间不确定性稳健优化问题十分耗时，提出一种能够减少耗时函数调用次数的稳健性设计优化方法。方法 该方法利用临界距离内已经精确计算过的个体响应值的信息近似预测其他个体响应值，以此近似评估个体稳健性指标；利用进化过程中逐步扩充的精确个体响应值的信息，选择性地重新评估已往个体的稳健性，并根据评估误判率自适应调整临界距离。结果 2个数学算例和1个工程算例的验证结果表明，提出的算法在最优目标误差小于2.5%时，节省了94%以上的计算资源。结论 所提方法能够结合既往优化知识，极大地减少精确计算内外层个体响应值的次数，实现个体稳健性评价精度和成本的自适应动态平衡，为区间不确定性稳健设计优化提供一种新的思路和方法。Abstract:Objectives As solving the robust optimization (RO) problem with interval uncertainty is unduly time-consuming when the nested differential evolution algorithm is directly used, a new RO design method is proposed.Methods In the proposed method, individuals' response values that have been accurately calculated within the critical distance are used to approximately predict the response values of other individuals and evaluate the robustness indexes accordingly. The accurate information of individuals' response values, which is gradually expanded in the evolutionary procedure, is also used to selectively re-evaluate the past robustness of individuals, and the critical distance is adaptively reduced on the basis of the robustness misjudgment rate.Results Two numerical and one engineering examples are tested to demonstrate the applicability of the proposed algorithm. The results show that the proposed algorithm saves more than 94% of computational resources, while the estimated error is less than 2.5%.Conclusions The proposed method can greatly reduce the calculation time of individuals' response values in the evolution process and maintain the adaptive balance between the accuracy and cost of robustness evaluation by using previous optimization knowledge, providing a new idea and method for RO design with interval uncertainty.
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