改进区间线性规划及其在湖泊流域管理中的应用

Modified interval linear programming for lake watershed management

针对不确定性优化提出了改进区间线性规划(MILP)模型及其算法,从理论上证明了MILP模型的解空间绝对可行,从而弥补了以往区间线性规划的缺陷,为后续决策过程提供了有利的可行性条件.针对四川邛海流域综合管理,以水污染综合防治的投资成本与运行成本最小化为目标,以总磷环境容量等11个管理目标为约束,建立了20个子流域3个阶段的MILP模型,最终得到10个备选污染控制方案的最优规模、投资和TP削减能力.结果表明:①最优的总投资和TP最优削减量分别达到[620×106,1148×106]元和[57.43,59.95]t·a-1,重点方案为污水处理厂工程、农村污染控制工程和中度侵蚀水土流失防治工程;②实施基于最优区间解生成的决策方案时,需要严格保证TP环境容量约束,才能实现各阶段的水质达标.

A modified interval linear programming （MILP） model and its solution algorithm are developed for optimization under uncertainty. This study shows theoretically that the MILP model is a more effective approach to obtain optimal and feasible solutions than previous ILP models. The MILP model was applied to the Lake Qionghal watershed to minimize the capital/ operating costs of pollution control, subject to eleven constraints including total phosphorus assimilative capacity. The final results are the optimal solutions for ten watershed management strategies in twenty sub-watersheds through three stages, which indicate that： ① the optimal capital/ operating costs would be [ 620, 1148 ] × 10^6 for TP reductions of [ 57.43, 59.95 ] t· a^-1 ②municipal wastewater treatment, rural pollution control and moderate water-soil erosion control are the measures of higher priority; ③ it is essential to meet the constraints of TP assimilative capacity for improving water quality in all the stages when generating decision alternatives based on optimal solutions.