Deriving multiple near-optimal solutions to deterministic reservoir operation problems

Even deterministic reservoir operation problems with a single objective function may have multiple near-optimal solutions (MNOS) whose objective values are equal or sufficiently close to the optimum. MNOS is valuable for practical reservoir operation decisions because having a set of alternatives from which to choose allows reservoir operators to explore multiple options whereas the traditional algorithm that produces a single optimum does not offer them this flexibility. This paper presents three methods: the near-shortest paths (NSP) method, the genetic algorithm (GA) method, and the Markov chain Monte Carlo (MCMC) method, to explore the MNOS. These methods, all of which require a long computation time, find MNOS using different approaches. To reduce the computation time, a narrower subspace, namely a near-optimal space (NOSP, described by the maximum and minimum bounds of MNOS) is derived. By confining the MNOS search within the NOSP, the computation time of the three methods is reduced. The proposed methods are validated with a test function before they are examined with case studies of both a single reservoir (the Three Gorges Reservoir in China) and a multireservoir system (the Qing River Cascade Reservoirs in China). It is found that MNOS exists for the deterministic reservoir operation problems. When comparing the three methods, the NSP method is unsuitable for large-scale problems but provides a benchmark to which solutions of small-and medium-scale problems can be compared. The GA method can produce some MNOS but is not very efficient in terms of the computation time. Finally, the MCMC method performs best in terms of goodness-of-fit to the benchmark and computation time, since it yields a wide variety of MNOS based on all retained intermediate results as potential MNOS. Two case studies demonstrate that the MNOS identified in this study are useful for real-world reservoir operation, such as the identification of important operation time periods and tradeoffs among objectives in multipurpose reservoirs.