A Novel Cognitively Inspired State Transition Algorithm for Solving the Linear Bi-Level Programming Problem

Linear bi-level programming (LBLP) is a useful tool for modeling decentralized decision-making problems. It has two-level (upper-level and lower-level) objectives. Many studies have shown that the LBLP problem is NP-hard, meaning it is difficult to find a global solution in polynomial time. In this paper, we present a novel cognitively inspired computing method based on the state transition algorithm (STA) to obtain an approximate optimal solution for the LBLP problem in polynomial time. The proposed method is applied to a supply chain model that fits the definition of an LBLP problem. The experimental results indicate that the proposed method is more efficient in terms of solution accuracy through a comparison to other metaheuristic-based methods using four problems from the literature in addition to the supply chain distribution model. In this study, a cognitively inspired STA-based method was proposed for the LBLP problem. In the future, we expect to extent the proposed method for linear multi-level programming problems.