A Systematic Review of Bilevel Optimization Methods Using a Meta-Synthesis Approach: Algorithms, Complexity, and Applications in Resource Allocation
Keywords:
Bilevel optimization, KKT optimality conditions, mathematical program with complementarity constraints (MPCC), conditional value, at, risk (CVaR), meta, synthesisAbstract
This study seeks to provide a comprehensive overview of bilevel optimization methods through a systematic review and meta-synthesis of the literature, focusing on solution algorithms, computational complexity, and applications in resource allocation. Using a meta-synthesis approach and a systematic literature review, the study identifies 64 credible sources from Scopus, Web of Science, and Google Scholar and analyzes them within four main streams: (1) theory and exact and metaheuristic solution algorithms, (2) uncertainty modeling and robust optimization, (3) policy applications in energy and supply chains, and (4) multifollower structures and security games. The analytical criteria include computational complexity, the type of mathematical reformulation (KKT/MPCC), and the approach to uncertainty. Exact methods based on reformulations using the Karush–Kuhn–Tucker (KKT) optimality conditions and mathematical programs with complementarity constraints (MPCC) are highly effective for convex problems, but face computational challenges in nonconvex or large-scale problems. Continuous regularization and smoothing methods strike an appropriate balance between accuracy and scalability. Regarding uncertainty, scenario-based approaches and the conditional value-at-risk (CVaR) measure are less conservative than classical robust optimization and are more suitable for resource allocation problems involving discrete scenarios. A significant research gap was also identified in simultaneously integrating heterogeneous multifollower structures with downside risk control in science and technology policymaking. By proposing a conceptual framework and identifying research gaps, this study paves the way for developing robust bilevel optimization models with a multifollower approach. The proposed framework can serve as a roadmap for researchers working on optimization and its applications in national resource allocation.
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