Finding the Nondominated Set and Efficient Integer Vectors for a Class of Three-Objective Mixed-Integer Linear Programs
研究一类至少一个目标取离散值的三目标混合整数线性规划，提出目标空间搜索算法生成非支配点或边，并应用于日前电力市场出清问题。
We consider a class of three-objective mixed-integer linear programs (MILPs) where at least one of the objective functions takes only discrete values. These problems commonly occur in MILPs where one or more of the three objective functions contain only integer decision variables. In such problems, the nondominated set consists of the union of nondominated edges and individual nondominated points. The nondominated edges can provide valuable insights on the trade-offs between the two continuous objectives at different levels of the discrete-valued objective. We develop an objective-space search algorithm that keeps partitioning the search space by progressively creating cones in the two-dimensional feasible space of the two continuous objectives for relevant values of the discrete-valued objective. The algorithm generates the nondominated points or edges in the nonincreasing order of the feasible values of the selected discrete-valued objective. Additionally, the algorithm uncovers all efficient integer variable vectors, including different vectors that lead to the same nondominated points or edges. We apply the algorithm to the day-ahead electricity market clearing problem. This paper was accepted by Chung Piaw Teo, optimization. Supplemental Material: The data files and e-companion are available at https://doi.org/10.1287/mnsc.2023.4712 .