An Efficient Dynamic Resource Allocation Framework for Evolutionary Bilevel Optimization

TL;DR

DRC-BLEA achieves competitive accuracy across diverse problem sets and real-world scenarios, while significantly reducing the number of function evaluations and overall running time.

Abstract

Bilevel optimization problems are characterized by an interactive hierarchical structure, where the upper level seeks to optimize its strategy while simultaneously considering the response of the lower level. Evolutionary algorithms are commonly used to solve complex bilevel problems in practical scenarios, but they face significant resource consumption challenges due to the nested structure imposed by the implicit lower-level optimality condition. This challenge becomes even more pronounced as problem dimensions increase. Although recent methods have enhanced bilevel convergence through task-level knowledge sharing, further efficiency improvements are still hindered by redundant lower-level iterations that consume excessive resources while generating unpromising solutions. To overcome this challenge, this paper proposes an efficient dynamic resource allocation framework for evolutionary bilevel optimization, named DRC-BLEA. Compared to existing approaches, DRC-BLEA introduces a novel competitive quasi-parallel paradigm, in which multiple lower-level optimization tasks, derived from different upper-level individuals, compete for resources. A continuously updated selection probability is used to prioritize execution opportunities to promising tasks. Additionally, a cooperation mechanism is integrated within the competitive framework to further enhance efficiency and prevent premature convergence. Experimental results compared with chosen state-of-the-art algorithms demonstrate the effectiveness of the proposed method. Specifically, DRC-BLEA achieves competitive accuracy across diverse problem sets and real-world scenarios, while significantly reducing the number of function evaluations and overall running time.

Figures (3)

• Figure 1: Flowchart of the proposed DRC-BLEA. The squares represent the number of times each task has been executed at the lower level. The red square indicates that the corresponding task is selected to be executed, while the yellow square represents the cooperative tasks for the red one. The red-yellow mixed square indicates that the features of the selected task have been improved before execution through cooperation, and the blue square indicates that the task has met the lower-level termination condition.
• Figure 2: The resource allocation of DRC-CMA-ES and the compared algorithms in the experiments on SMD1 with the median FEs results in 21 runs. The dot indicates that the lower-level task is selected and optimized for one lower-level iteration. The early, middle and late stages refer to the first upper-level iteration, and the 40% and 80% mark of the total upper-level iterations, respectively. The tasks are derived from the currently generated upper-level individuals, so tasks with the same index in different sub-figures do not correspond to the same one. The tasks labeled in red indicate that the ($x_u$, $x_l^*$) pairs generated by these tasks survived the subsequent environmental selection. The tasks highlighted with a box are typical examples in which a large amount of lower-level FEs were executed, but the resulting pairs were not competitive enough and were eliminated.
• Figure 3: Average running time of different algorithms on SMD problems with dimension ($m$ = 30, $n$ = 30). For ease of observation, only results within 200 seconds are presented.