Modified Dung Beetle Optimizer with Multi-strategy for Uncertain Multi-modal Transport Path Problem

Abstract Uncertain multi-modal transport path optimization (UMTPO) is a combined optimization non-deterministic polynomial-time hard problem. Its goal is to determine a path with the lowest total transportation cost and carbon emissions from the starting point to the destination. To effectively address this issue, this article proposes a modified dung beetle optimizer (DBO) to address it. DBO is a swarm-based metaheuristic optimization algorithm that has the features of a fast convergence rate and high solution accuracy. Despite this, the disadvantages of weak global exploration capability and falling easily into local optima exist. In this article, we propose a modified DBO called MSHDBO for function optimization and to solve the UMTPO problem. However, for the vast majority of metaheuristic algorithms, they are designed for continuous problems and cannot directly solve discrete problems. Therefore, this article employs a priority based encoding and decoding method to solve the UMTPO problem. To verify the performance and effectiveness of the MSHDBO algorithm, we compared it with other improved versions of the DBO algorithm used in the literature. We confirmed the excellent performance of MSHDBO using 41 benchmark test functions from the IEEE CEC 2017 test suite and IEEE CEC 2022 test suite. Additionally, we compared the MSHDBO algorithm with 10 other state-of-the-art metaheuristic optimization algorithms through a practical UMTPO problem. The experimental results indicated that the MSHDBO algorithm achieved very good performance when solving the UMTPO problem.