摘要 针对耗时计算目标函数的约束优化问题，提出用代理模型来代替耗时计算目标函数的方法，并结合目标函数的信息对约束个体进行选择，从而提出基于代理模型的差分进化约束优化算法。首先，采用拉丁超立方采样方法建立初始种群，用耗时计算目标函数对初始种群进行评估，并以此为样本数据建立目标函数的神经网络代理模型。然后，用差分进化方法为种群中的每一个亲本产生后代，并对后代使用代理模型进行评估，采用可行性规则来比较后代与其亲本并更新种群，根据替换机制将种群中较劣的个体替换为备用存档中较优的个体。最后，当达到最大适应度评估次数时算法停止，给出最优解。该算法与对比算法在10个测试函数上运行的结果表明，该算法得出的结果更精确。将该算法应用于工字梁优化问题的结果表明，相较于优化前的算法，该算法的适应度评估次数减少了80%；相对于FROFI（Feasibility Rule with the incorporation of Objective Function Information）算法，该算法的适应度评估次数减少了36%。运用所提算法进行优化可以有效减少调用耗时计算目标函数的次数，提升优化效率，节约计算成本。
Abstract：In order to solve the constrained optimization problem of objective function with time-consuming computation,a surrogate model was proposed to replace the objective function with time-consuming computation,the constraint individuals were selected based on the information of the objective function,and a surrogate-based differential evolution constrained optimization algorithm was proposed. Firstly,the Latin hypercube sampling method was used to establish the initial population,which was evaluated by the objective function with time-consuming calculation,and the neural network surrogate model of the objective function was established based on these sample data. Then,the differential evolution method was used to generate offsprings for each parent in the population,and the offspring individuals were evaluated by using the surrogate model. The feasibility rule was used to compare the offsprings with their parents and update the population,and the inferior individuals in the population were replaced with the better individuals in the alternate archive according to the replacement mechanism. Finally,the algorithm stopped when the maximum fitness evaluation number was reached,and the optimal solution was obtained. The results of this algorithm and comparison algorithms running on 10 test functions show that the results obtained by this algorithm are more accurate. The results of applying this algorithm to the I-beam optimization problem show that the number of fitness evaluations of this algorithm is reduced by 80% compared with that of the algorithm before optimization,and the number of fitness evaluations of this algorithm is reduced by 36% compared with that of FROFI (Feasibility Rule with the incorporation of Objective Function Information) algorithm. Using the proposed algorithm to realize the optimization can effectively reduce the number of calls for the objective function with time-consuming computation,improve optimization efficiency,and save computational cost.
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2020, Vol. 40 
