求解单目标两层优化问题的一种高效进化算法
Efficient Evolutionary Algorithm for Single-Objective Bilevel Optimization
摘要：
双层优化问题是一类具有挑战性的优化问题，它包含两个层次的优化任务。在这些问题中，下层问题的最优解成为上层问题的可能可行候选。这样的要求使得优化问题难以解决，并且使研究人员忙于设计可以有效处理问题的方法。尽管努力，几乎没有任何有效的方法，这是能够处理一个复杂的双层问题。本文提出了一种基于最优下层变量对上层变量的二次近似的双层进化算法（BLEAQ）。该方法能够在相对较少的函数求值次数下处理不同复杂度的两层问题。从经典优化的思想已经与进化方法杂交，产生一个有效的优化算法的一般双层问题。该算法的有效性已被证明对两组测试问题。第一组是最近提出的SMD测试集，其中包含可控的复杂性的问题，第二组包含从文献中收集的标准测试问题。所提出的方法已被评估对两个基准，并观察到的性能增益是显着的。
英文摘要：
Bilevel optimization problems are a class of challenging optimization problems, which contain two levels of optimization tasks. In these problems, the optimal solutions to the lower level problem become possible feasible candidates to the upper level problem. Such a requirement makes the optimization problem difficult to solve, and has kept the researchers busy towards devising methodologies, which can efficiently handle the problem. Despite the efforts, there hardly exists any effective methodology, which is capable of handling a complex bilevel problem. In this paper, we introduce bilevel evolutionary algorithm based on quadratic approximations (BLEAQ) of optimal lower level variables with respect to the upper level variables. The approach is capable of handling bilevel problems with different kinds of complexities in relatively smaller number of function evaluations. Ideas from classical optimization have been hybridized with evolutionary methods to generate an efficient optimization algorithm for generic bilevel problems. The efficacy of the algorithm has been shown on two sets of test problems. The first set is a recently proposed SMD test set, which contains problems with controllable complexities, and the second set contains standard test problems collected from the literature. The proposed method has been evaluated against two benchmarks, and the performance gain is observed to be significant.
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