Swarm Intelligence And Evolutionary Computation For Single And Multiobjective Optimization In Water Resource Systems

Abstract

Most of the real world problems in water resources involve nonlinear formulations in their solution construction. Obtaining optimal solutions for large scale nonlinear optimization problems is always a challenging task. The conventional methods, such as linear programming (LP), dynamic programming (DP) and nonlinear programming (NLP) may often face problems in solving them. Recently, there has been an increasing interest in biologically motivated adaptive systems for solving real world optimization problems. The multi-member, stochastic approach followed in Evolutionary Algorithms (EA) makes them less susceptible to getting trapped at local optimal solutions, and they can search easier for global optimal solutions.

In this thesis, efficient optimization techniques based on swarm intelligence and evolutionary computation principles have been proposed for single and multi-objective optimization in water resource systems. To overcome the inherent limitations of conventional optimization techniques, meta-heuristic techniques like ant colony optimization (ACO), particle swarm optimization (PSO) and differential evolution (DE) approaches are developed for single and multi-objective optimization. These methods are then applied to few case studies in planning and operation of reservoir systems in India.

First a methodology based on ant colony optimization (ACO) principles is investigated for reservoir operation. The utility of the ACO technique for obtaining optimal solutions is explored for large scale nonlinear optimization problems, by solving a reservoir operation problem for monthly operation over a long-time horizon of 36 years. It is found that this methodology relaxes the over-year storage constraints and provides efficient operating policy that can be implemented over a long period of time. By using ACO technique for reservoir operation problems, some of the limitations of traditional nonlinear optimization methods are surmounted and thus the performance of the reservoir system is improved.

To achieve faster optimization in water resource systems, a novel technique based on swarm intelligence, namely particle swarm optimization (PSO) has been proposed. In general, PSO has distinctly faster convergence towards global optimal solutions for numerical optimization. However, it is found that the technique has the problem of getting trapped to local optima while solving real world complex problems. To overcome such drawbacks, the standard particle swarm optimization technique has been further improved by incorporating a novel elitist-mutation (EM) mechanism into the algorithm. This strategy provides proper exploration and exploitation throughout the iterations. The improvement is demonstrated by applying it to a multi-purpose single reservoir problem and also to a multi reservoir system. The results showed robust performance of the EM-PSO approach in yielding global optimal solutions.

Most of the practical problems in water resources are not only nonlinear in their formulations but are also multi-objective in nature. For multi-objective optimization, generating feasible efficient Pareto-optimal solutions is always a complicated task. In the past, many attempts with various conventional approaches were made to solve water resources problems and some of them are reported as successful. However, in using the conventional linear programming (LP) and nonlinear programming (NLP) methods, they usually involve essential approximations, especially while dealing withdiscontinuous, non-differentiable, non-convex and multi-objective functions. Most of these methods consider multiple objective functions using weighted approach or constrained approach without considering all the objectives simultaneously. Also, the conventional approaches use a point-by-point search approach, in which the outcome of these methods is a single optimal solution. So they may require a large number of simulation runs to arrive at a good Pareto optimal front. One of the major goals in multi-objective optimization is to find a set of well distributed optimal solutions along the true Pareto optimal front. The classical optimization methods often fail to attain a good and true Pareto optimal front due to accretion of the above problems. To overcome such drawbacks of the classical methods, there has recently been an increasing interest in evolutionary computation methods for solving real world multi-objective problems. In this thesis, some novel approaches for multi-objective optimization are developed based on swarm intelligence and evolutionary computation principles.

By incorporating Pareto optimality principles into particle swarm optimization algorithm, a novel approach for multi-objective optimization has been developed. To obtain efficient Pareto-frontiers, along with proper selection scheme and diversity preserving mechanisms, an efficient elitist mutation strategy is proposed. The developed elitist-mutated multi-objective particle swarm optimization (EM-MOPSO) technique is tested for various numerical test problems and engineering design problems. It is found that the EM-MOPSO algorithm resulting in improved performance over a state-of-the-art multi-objective evolutionary algorithm (MOEA). The utility of EM-MOPSO technique for water resources optimization is demonstrated through application to a case study, to obtain optimal trade-off solutions to a reservoir operation problem. Through multi-objective analysis for reservoir operation policies, it is found that the technique can offer wide range of efficient alternatives along with flexibility to the decision maker.

In general, most of the water resources optimization problems involve interdependence relations among the various decision variables. By using differential evolution (DE) scheme, which has a proven ability of effective handling of this kind of interdependence relationships, an efficient multi-objective solver, namely multi-objective differential evolution (MODE) is proposed. The single objective differential evolution algorithm is extended to multi-objective optimization by integrating various operators like, Pareto-optimality, non-dominated sorting, an efficient selection strategy, crowding distance operator for maintaining diversity, an external elite archive for storing non- dominated solutions and an effective constraint handling scheme. First, different variations of DE approaches for multi-objective optimization are evaluated through several benchmark test problems for numerical optimization. The developed MODE algorithm showed improved performance over a standard MOEA, namely non-dominated sorting genetic algorithm–II (NSGA-II). Then MODE is applied to a case study of Hirakud reservoir operation problem to derive operational tradeoffs in the reservoir system optimization. It is found that MODE is achieving robust performance in evaluation for the water resources problem, and that the interdependence relationships among the decision variables can be effectively modeled using differential evolution operators.

For optimal utilization of scarce water resources, an integrated operational model is developed for reservoir operation for irrigation of multiple crops. The model integrates the dynamics associated with the water released from a reservoir to the actual water utilized by the crops at farm level. It also takes into account the non-linear relationship of root growth, soil heterogeneity, soil moisture dynamics for multiple crops and yield response to water deficit at various growth stages of the crops. Two types of objective functions are evaluated for the model by applying to a case study of Malaprabha reservoir project. It is found that both the cropping area and economic benefits from the crops need to be accounted for in the objective function. In this connection, a multi-objective frame work is developed and solved using the MODE algorithm to derive simultaneous policies for irrigation cropping pattern and reservoir operation. It is found that the proposed frame work can provide effective and flexible policies for decision maker aiming at maximization of overall benefits from the irrigation system.

For efficient management of water resources projects, there is always a great necessity to accurately forecast the hydrologic variables. To handle uncertain behavior of hydrologic variables, soft computing based artificial neural networks (ANNs) and fuzzy inference system (FIS) models are proposed for reservoir inflow forecasting. The forecast models are developed using large scale climate inputs like indices of El-Nino Southern Oscialltion (ENSO), past information on rainfall in the catchment area and inflows into the reservoir. In this purpose, back propagation neural network (BPNN), hybrid particle swarm optimization trained neural network (PSONN) and adaptive network fuzzy inference system (ANFIS) models have been developed. The developed models are applied for forecasting inflows into the Malaprabha reservoir. The performances of these models are evaluated using standard performance measures and it is found that the hybrid PSONN model is performing better than BPNN and ANFIS models. Finally by adopting PSONN model for inflow forecasting and EMPSO technique for solving the reservoir operation model, the practical utility of the different models developed in the thesis are demonstrated through application to a real time reservoir operation problem. The developed methodologies can certainly help in better planning and operation of the scarce water resources.