考虑再生循环的多杂质用水网络全局优化

Global optimization for multi-contaminant water networks with regeneration recycling unit

引入再生循环单元可以有效地减少多杂质用水系统整体的新鲜水消耗量和废水排放量。其现有的数学规划模型是一个非凸性严重的混合整数非线性规划问题,直接求解不仅计算难度大而且求解速度慢,这样只能得到局部最优解。本文利用分段线性松弛的方法对该模型进行处理,将双线性等式约束转换成线性约束,从而使复杂的水网络模型转换为对应的混合整数线性规划问题,因现有的商业优化软件对混合整数线性规划问题的求解算法已经非常成熟,这样降低了计算难度并取得全局最优解。算例结果表明分段线性松弛的方法可以使求解简单,能够获得全局最优解。管线费用的减少使年度化费用降低,全局优化能得到一个经济性更好的多杂质水网络,这种方法对于节省设备投资和操作费用,具有重要意义。

The introduction of regeneration recycling unit can largely reduce freshwater consumption and wastewater discharge. The current optimization model of multiple contaminants water networks with regeneration recycling unit is a non-convex mixed-inter nonlinear programming problem （MINLP） . Solving directly without any strategy is very hard, slow and easily trapped into the local optimal solutions. In this paper, a global optimization strategy with piecewise linear relaxation was proposed. With the strategy the complex problem as an MILP model can be reformulated. The computational efforts can be reduced largely and the optimum solution can be obtained. A case study was illustrated to demonstrate the capability of our strategy and the global optimization solution had a significant impact on the total annual cost.