均匀动态规划方法及其在水电系统优化调度中的应用

动态规划(Dynamic Programming,DP)是求解多维多阶段复杂决策问题的有效方法,然而维数灾问题极大地限制了它的应用。为缓解这一问题,结合均匀试验设计提出均匀动态规划(Uniform Dynamic Programming,UDP)。UDP以DP为基础框架,将各阶段不同维度离散状态的组合视为多因素多水平试验,利用均匀设计表从全部状态变量中优选少数极具代表性、在可行域内均匀散布的状态变量进行计算,大幅降低各阶段状态变量集合基数。分析表明,UDP空间复杂度和时间复杂度由DP指数增长分别降至线性和平方增长,存储量和运算量显著减少,同时澜沧江梯级水电站群仿真测试结果验证了UDP的高效性和实用性。

Uniform dynamic programming and its application in optimal operation of hydropower system

In order to overcome the dimension disaster of Dynamic Programming (DP) for solving multi-di- mension and multi-stage decision problems, Uniform Dynamic Programming(UDP) is presented on the basis of uniform experimental design and DP. UDP starts from the initial feasible solution in the state space and takes advantage of uniform design table to choose small but representative state vectors of each stage from all the vectors, and then DP is employed to obtain a better solution. UDP won't terminate the calculation until the termination condition is satisfied. The analysis indicates that the space complexity and time com- plexity of UDP are reduced to linear and square growth instead of exponential growth of DP. The simula- tion results of cascaded hydroelectric plants in the Lancanjiang River show that UDP is a novel method for multi-dimension and multi-stage complex decision problems.