Abstract
Short-term operation of a multi-objective reservoir system under inflow uncertainty has been receiving increasing attention, however, major challenges for the optimization of this system still remain due to the multiple and often conflicting objectives, highly nonlinear constraints and uncertain parameters in which derivative information may not be directly available. Population-based optimization methods do not rely on derivatives while generally have a slow convergence. This study presents a hybrid optimization model for short-term operation of multi-objective reservoirs under uncertainty that is derivative free and has a relatively fast convergence. The model incorporates a local improvement method called Mesh Adaptive Direct Search (MADS) into a population-based method NSGA-II and has no requirement for differentiability, convexity and continuity of the optimization problem. The operation of a multi-objective and multi-reservoir system on the Columbia River under inflow uncertainty is used as a case study. Overall, the hybrid model outperforms optimization models based on either the NSGA-II only or the MADS only. The model is intended for conditions where derivative information of the optimization problem is unavailable, which could have a wide array of applications in water resources systems.
Highlights
Short-term operation of reservoirs normally considers multiple purposes and face various uncertainties e.g., forecasted inflow
This means that power deficit to the demand is decreased and extra power for heavy load hours is increased, which results are desirable for the decision maker
The hypervolume index is improved by nearly 10% at an increase of computational cost of less than 0.1% compared to the NSGA-II
Summary
Short-term operation of reservoirs normally considers multiple purposes and face various uncertainties e.g., forecasted inflow. The objective and/or constraint functions may be nonconvex, discontinuous (Labadie 2004; Geressu and Harou 2015) or noisy as uncertainty is incorporated (Gelati et al 2014). In this context, the derivative information on either objectives or constraints often become unavailable, unreliable or impractical (Chen and Chen 2001; Guan et al 2013), which may present a difficulty to the optimization methods in particular for derivative-based algorithms e.g., steepest descent or Newton method. The aforementioned methods can be seen as strong candidates for optimizing short-term operation of multi-objective reservoirs under inflow uncertainty. The embedded randomness of GA is a key element for global optimality, this method has a slow convergence compared to methods that use derivative information, especially when approaching to the optimal point (Erol and Eksin 2006; Ishibuchi et al 2009)
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