Multiunit water resource systems management by decomposition, optimization and emulated evolution : a case study of seven water supply reservoirs in Tunisia

Being one of the essential elements of almost any water resource system, reservoirs are indispensable in our struggle to harness, utilize and manage natural water resources. Consequently, the derivation of appropriate reservoir operating strategies draws significant attention in water resources planning and management. These operational issues become even more important with the ever increasing scale and complexity of water resource systems. In this respect, the primary obstacle in the analysis of a multiple-reservoir-multiple-user water supply system operation is the dimensionality of the problem. Namely, being a sequential decision making process, the operation of a complex reservoir system over a certain period of time can adequately be described only if all the relevant variables and parameters related to possible system state and decision realizations are taken into account. Clearly, this requirement tends to grow rapidly with the size of the system considered. The computational burden expands even more drastically if the processes involved bear unavoidable stochastic characteristics which are, in this study, assumed to be attributed only to reservoir inflows. With regard to the problem in hand, the methods proposed and analyzed in the study can be divided into three major groups. The first group of methods falls into the family of system decomposition approaches within the optimization and/or simulation of the operation of complex systems. The second one involves the assessment of the impact various simulation alternatives may have on the performance of the adopted iterative decomposition algorithms. Finally, the third part includes the application of genetic algorithms for the derivation of the best water allocation patterns within a multiple-reservoir-multiple-user water supply system. The decomposition models proposed and analyzed in this study are known as sequential decomposition methods. Essentially, to reduce the dimensionality of an optimization problem, they split up a complex system into its elementary units (i.e. reservoirs). Subsequently, the operating strategy of the system is derived in an iterative fashion by applying successive optimization, simulation and release allocation analyses to individual system elements. The optimization method employed within all the decomposition models is stochastic dynamic programming (SDP). Due to the inherent discrete nature of SDP operating policies, the iterative, decomposition-based optimization models have a certain "inaccuracy threshold" which directly affects the performance of the system. Therefore, three different simulation alternatives have been employed to assess the possibility of reducing this negative impact of discretization. It is shown that, by allowing limited policy violations within simulation, the system performance can improve significantly relative to the case when the operating policies are strictly followed. Ultimately, a method based on the theory of genetic algorithms (GA) has been employed to derive the most favourable water allocation patterns within a multiple-reservoir-multiple-user water supply system. Since GAs make use of simulation to guide their search for promising solutions, two distinct GA models have been tested: i) the first one assumes that individual reservoirs are to be operated according to the standard reservoir operating rule; and ii) the second model simulates the operation of the system according to the policies derived by a prior application of an iterative decomposition/SDP-based optimization of the system's operation. Throughout this study, particular emphasis is given to the appraisal of the system performance derived by different methods. Since all of the employed optimization and search models are essentially single-objective optimization techniques, and given the fact that the operation of a reservoir system cannot adequately be appraised on the basis of a single criterion, this study makes use of simulation to evaluate the performance of the system over a number of criteria, and thereby broaden the basis for the comparison of different models. Ultimately, it is believed that the presented results clearly exemplify the fact that performance indicators like reliability of meeting the targeted demand, resilience with regard to the system escaping from failure mode, vulnerability as a measure of the most severe failure and the likes play an essential role in comprehensive assessment of the operation of a complex reservoir system. The analyses performed in this study showed that a complex water resource system decomposition, combined with the appropriate choice of optimization and simulation approaches could provide a sound basis for a transparent, yet efficient and effective operational analysis of very large reservoir systems. In addition, the application of genetic algorithms to solve a rather large resource allocation problem of a multiple-reservoir-multiple-user water supply system proved to be both relatively uncomplicated and remarkably efficient. Furthermore, it is believed that the coupling of a genetic algorithm resource allocation model with a decomposition-based optimization model represents a potentially powerful approach for solving highly complex operational problems related to multiple-reservoir water resource systems.