Bi-Objective Optimization for Transportation: Generating Near-Optimal Subsets of Pareto Optimal Solutions - Hongyu Zhang; Qingfang Ruan; Yong Jin; Shuaian Wang (Applied Sciences)
Bi-objective optimization seeks to obtain Pareto optimal solutions that balance two trade-off objectives, providing guidance for decision making in various fields, particularly in the field of transportation. The novelty of this study lies in two aspects. On the one hand, considering that Pareto optimal solutions are often numerous, finding the full set of Pareto optimal solutions is often computationally challenging and unnecessary for practical purposes. Therefore, we shift the focus of bi-objective optimization to finding a subset of Pareto optimal solutions whose resulting set of nondominated objective vectors is the same as, or at least a good approximation of, the full set of nondominated objective vectors for the problem. In particular, we elaborate three methods for generating a near-optimal subset of Pareto optimal solutions, including the revised <semantics>ϵ</semantics>-constraint method, the improved revised <semantics>ϵ</semantics>-constraint method, and the augmented <semantics>ϵ</semantics>-constraint method. More importantly, the near-optimality of the Pareto optimal solution subset obtained by these methods is rigorously analyzed and proved from a mathematical point of view. This study helps to offer theoretical support for future studies to find the subset of Pareto optimal solutions, which reduces the unnecessary workload and improves the efficiency of solving bi-objective optimization problems while guaranteeing a pre-specified tolerance level.