A Coordinated Feedback-Based Hierarchical Triangulation Topology Aggregation Optimizer for Bilevel Optimization Problems

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Original abstract

Bilevel optimization problems (BOPs) are widely encountered in hierarchical decision-making, wherein the embedding of the lower-level problem within the upper-level problem poses significant challenges to the solution process. To solve complex BOPs, this paper proposes a coordinated feedback-based hierarchical triangulation topology aggregation optimizer (CFHTTAO). CFHTTAO is developed by constructing a hierarchical solution framework and designing improvement mechanisms to enhance its performance. Specifically, a knowledge-sharing mechanism is established to promote information exchange among triangular topological units, a coordinated feedback mechanism is designed to adaptively select a suitable lower-level search method and feed the obtained lower-level solution back to the upper level, and an elite learning evolution mechanism is used to reduce the risk of premature convergence. CFHTTAO is evaluated on the SMD test suite under different dimensional settings, where the test problems involve various complex characteristics of BOPs. In addition, the Friedman test results show that CFHTTAO achieves the smallest mean ranks, with upper-level mean ranks of 1.08, 1.50, and 1.50 and lower-level mean ranks of 1.00, 1.17, and 1.25 on the SMD(2+3), SMD(5+5), and SMD(10+10) problems, respectively. Finally, CFHTTAO is applied to the inverse optimal control problem as the practical case study. Overall, experimental results demonstrate that CFHTTAO achieves better solution accuracy, stronger stability, and faster convergence when solving complex BOPs, and exhibits strong applicability to the practical bilevel optimization task.

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