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Bilevel evolutionary algorithms (BLEAs) are a plausible approach for bilevel optimization. However, these algorithms require many fitness evaluations (FEs) and might become unusable if the fitness evaluations are computationally expensive. Therefore, reducing the number of FEs is crucial for designing a BLEA for expensive bilevel optimization (EBLOP). The surrogate-assisted optimization and knowledge transfer mechanisms used in BLEAs have been proven to reduce the number of FEs. This paper proposes a surrogate-assisted bilevel improved multioperator differential evolution algorithm (SA-BL-IMODE), which integrates a classification model-based assisted preselection and environment selection strategy (CPES) for EBLOP. In CPES, promising candidate solutions are prescreened by a classification model, filtering out some unpromising candidate solutions without performing FEs, thus improving the algorithm's performance. Moreover, the classification model also assists environment selection by directly discarding the unpromising offspring solutions before FEs are performed, thus reducing the number of FEs in each iteration. Additionally, an enhanced direct neighbor solution transfer (EDST) mechanism is proposed to identify and utilize the interactions between upper-level and lower-level variables for acquiring knowledge, improving knowledge quality, and reducing the number of FEs further. Experimental studies on two test suite benchmark problems are conducted, and the proposed method is compared with nine state-of-the-art algorithms. The experimental results demonstrate the effectiveness of the proposed mechanisms and show that SA-BL-IMODE has a significant advantage over existing algorithms for expensive bilevel optimization. [ABSTRACT FROM AUTHOR]

Reducing the number of lower-level function evaluations (LFEs) is crucial to designing a bilevel evolutionary algorithm (BLEA) for bilevel optimization. Direct neighbor solution transfer (DST) is regularly used in BLEA because it can improve the lower-level search efficiency and reduce the number of LFEs. But this method still faces the challenge of misleading searches to make the algorithm converge to the wrong optimum. This paper proposes a bilevel improved multi-operator differential evolution algorithm (BL-IMODE) for bilevel optimization, which uses the knowledge transfer and adaptive coordinate systems approach. Specifically, this paper proposes a lower-level search knowledge transfer (LLS-KT) and a lower-level (LL) optimal solution distribution information transfer (LLO-DIT) mechanism to implement knowledge transfer. In LLS-KT, transferring LL solutions to the LL optimizer is similar to DST, but the LLS-KT transfers multiple solutions and thus has less possibility of misleading searches than DST. Moreover, the LLO-DIT transfers the LL optimal solution distribution information to the LL optimizer for generating promising offspring solutions. Since this method does not directly transfer LL solutions, it avoids misleading searches. Additionally, the adaptive coordinate systems (ACS) approach is used in two-level optimizers to suit different fitness landscapes and further reduce the number of LFEs. In ACS, three differential evolution mutation operators are produced in two coordinate systems. An adaptive strategy is used to select the suitable differential evolution mutation operator to generate promising offspring solutions in the Eigen coordinate or original coordinate system. Experimental studies on three test suites benchmark problems for comparison with seven state-of-the-art algorithms are conducted. The results show BL-IMODE has a significant advantage over the comparative algorithms. Finally, BL-IMODE is applied to tackle the inverse optimal control problem. • We propose a bilevel improved multi-operator differential evolution algorithm. • We propose a knowledge transfer approach to avoid misleading search. • We propose an adaptive coordinate systems approach to improve search efficiency. • We outperform all existing approaches in most test instances. [ABSTRACT FROM AUTHOR]