A bi-level evolutionary algorithm with surrogate lower approximation: a case study on a production-distribution problem in supply chain management

Abstract

​Many decision-making situations are characterized by  hierarchical structures with two optimization tasks, modeled as Bi-level Optimization Problem (BOP). These problems are challenging due to the upper-level optimization being constrained by the lower-level solution, making evaluations computationally expensive. For this reason, an interesting search direction might be the designing of new strategies for reducing the lower-level computational cost. In this paper, an efficient evolutionary algorithm with a surrogate-based approach at the lower level, referred as SLABEA, is considered in order to bring down the bi-level computational expense. The basic idea of our proposal is to handle an approximate lower-level evaluation model in order to come up with good upper solution(s) within an acceptable execution time. The comparative statistical analysis demonstrates the effectiveness of SLABEA in solving the bi-level production-distribution planning problem, significantly outperforming competing approaches. Our method achieves a noteworthy convergence rate, highlighting its superiority in addressing this complex optimization problem.