Deriving near-optimal solutions to deterministic reservoir operation problems

For a deterministic reservoir operation problem even with a single objective function, there should be some near-optimal solutions whose objective value is greater than or equal to E^*(1 - ε) for a user-specified ε(0 ≤ ε ≤ 1) as E^* is the optima. Near-optimal solutions provide valuable options for decision-making because in practical reservoir operations, it is often more realistic to choose one solution from a set of alternatives with similar or even the same objective value resulting from the same optimization model. Such comparison allows decision makers to consider some aspects that are difficult to include in the optimization model. This paper explores such near-optimal solutions and discusses their statistical characteristics with two steps. (1) Using a dynamic programming (DP) model, the near-optimal space (hereafter denoted as NSO, the minimum and maximum bounds of near-optimal solutions) is derived by building feasible conditions during backtracking. This approach can be incorporated into the discrete differential dynamic programming (DDDP) framework, reducing the computational burden greatly. (2) Following the equifinality concept, the statistical characteristics of the optimal solution can be analyzed by using uncertainty analysis methods with simulation, when the reservoir decisions and the operation performance are treated as model parameters and likelihood function, respectively. With case studies of the China's Three Gorges Reservoir, it is found that the near-optimal solutions do exist for the deterministic reservoir operation problem, and there is great potential benefit in evaluating these solutions and choosing the most realistic one.