A large number of application problems involve two levels of optimization, where one optimization task is nested inside the other. These problems are known as bilevel optimization problems and have been studied by both classical optimization community and evolutionary optimization community. Most of the solution procedures proposed until now are either computationally very expensive or applicable to only small classes of bilevel optimization problems adhering to mathematically simplifying assumptions. In this paper, we propose an evolutionary optimization method that tries to reduce the computational expense by iteratively approximating two important mappings in bilevel optimization; namely, the lower level rational reaction mapping and the lower level optimal value function mapping. The algorithm has been tested on a large number of test problems and comparisons have been performed with other algorithms. The results show the performance gain to be quite significant. To the best knowledge of the authors, a combined theory-based and population-based solution procedure utilizing mappings has not been suggested yet for bilevel problems.

中文翻译：

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基于多重映射迭代逼近的双层优化

大量的应用程序问题涉及两个优化级别，其中一个优化任务嵌套在另一个优化任务中。这些问题被称为双层优化问题，并且已经由经典优化社区和进化优化社区进行了研究。迄今为止，提出的大多数解决方案过程要么在计算上非常昂贵，要么仅适用于坚持数学简化假设的小类双层优化问题。在本文中，我们提出了一种进化优化方法，该方法试图通过迭代逼近双层优化中的两个重要映射来减少计算量。即下层有理反应映射和下层最优值函数映射。该算法已针对大量测试问题进行了测试，并且已与其他算法进行了比较。结果表明，性能提升非常显着。据作者所知，对于双级问题，尚未提出使用映射的基于理论和基于人口的组合求解程序。