Contrastive analysis of three parallel modes in multi-dimensional dynamic programming and its application in cascade reservoirs operation

•We implement the parallel computing of DP among the operation stages by a new way.•Three parallel modes of DP are compared and analyzed in this paper.•Results show that state combinations parallel mode is much better than the other two.

SummaryThe “curse of dimensionality” of dynamic programming (DP) has always been a great challenge to the cascade reservoirs operation optimization (CROO) because computer memory and computational time increase exponentially with the increasing number of reservoirs. It is an effective measure to combine DP with the parallel processing technology to improve the performance. This paper proposes three parallel modes for multi-dimensional dynamic programming (MDP) based on .NET4 Parallel Extensions, i.e., the stages parallel mode, state combinations parallel mode and hybrid parallel mode. A cascade reservoirs of Li Xiangjiang River in China is used as the study instance in this paper, and a detailed contrastive analysis of the three parallel modes on run-time, parallel acceleration ratio, parallel efficiency and memory usage has been implemented based on the parallel computing results. Results show that all the three parallel modes can effectively shorten the run-time so that to alleviate the “curse of dimensionality” of MDP, but relatively, the state combinations parallel mode is the optimal, the hybrid parallel is suboptimal and the stages parallel mode is poor.