Maximum entropy based evolutionary optimization of water distribution networks under multiple operating conditions and self-adaptive search space reduction method

Previously held under moratorium from 1st December 2016 until 1st December 2021.One of the complexities in designing WDN is evaluation of network performance. The accurate network performance measures such as reliability or failure tolerance are very time consuming calculations, thus surrogate measures are used for water distribution network (WDN) design optimization. Entropy is particularly advantageous since it involves only the flow in the pipe and the demands at the nodes. This thesis developed efficient new computational methods based on the maximum entropy formalism for the optimization of water distribution systems. Thus the maximum entropy based design approach has been extended here to include multiple operation conditions. Also, the path-related properties of the flow entropy have been exploited to develop a new self-adaptive approach for solution space reduction in multiobjective evolutionary optimization of water distribution systems that resulted in a significant reduction in the number of function evaluations required to find optimal and near optimal solutions. The novelty and originality of the current research are presented next. A new penalty-free multi-objective evolutionary optimization approach for the design of WDNs has been developed. It combines genetic algorithm with least cost design and maximum entropy. The approach can handle single operating conditions (SOC) as well as multiple operating conditions (MOC) for any given network. Previously, most of the work has been done for single loading patterns and it was assumed that nodal demands are constant. In reality nodal demand vary over the time so network designed to satisfy one operating condition might not be able to satisfy other loading patterns (i.e. pressure constraints might not be meet). The model has been applied to three well known water distribution networks. The approach has also been implemented on a large real-world network in the literature. Three different methods of designing for multiple loading patterns were investigated. Extensive testing proved that MOC outperform SOC in terms of hydraulic feasibility, pipe size distribution and reliability. The approach is computationally efficient and robust. The above mentioned penalty-free approach has been extended to form a module that would improve the convergence criteria of the GA by reducing its search space. For large real-world network GA might require extremely large number of function evaluations which could lead to delayed convergence. By reducing the search space, the GA’s effectiveness and efficiency will increase as the algorithm will identify the solutions in smaller number of function evaluations. The search space reduction method presented herein is based on entropy and uses the importance of every path through network, which is an inherent property of the entropy function. The developed algorithm is dynamic, self-adaptive and does not require pre-defining the reduced sets of candidate diameters for each pipe. The method has been applied to a large network from the literature. Two cases were studied, one based on full search space and one for reduce search space (RSS) approach. Rapid stabilization was observed for the results obtained using RSS.One of the complexities in designing WDN is evaluation of network performance. The accurate network performance measures such as reliability or failure tolerance are very time consuming calculations, thus surrogate measures are used for water distribution network (WDN) design optimization. Entropy is particularly advantageous since it involves only the flow in the pipe and the demands at the nodes. This thesis developed efficient new computational methods based on the maximum entropy formalism for the optimization of water distribution systems. Thus the maximum entropy based design approach has been extended here to include multiple operation conditions. Also, the path-related properties of the flow entropy have been exploited to develop a new self-adaptive approach for solution space reduction in multiobjective evolutionary optimization of water distribution systems that resulted in a significant reduction in the number of function evaluations required to find optimal and near optimal solutions. The novelty and originality of the current research are presented next. A new penalty-free multi-objective evolutionary optimization approach for the design of WDNs has been developed. It combines genetic algorithm with least cost design and maximum entropy. The approach can handle single operating conditions (SOC) as well as multiple operating conditions (MOC) for any given network. Previously, most of the work has been done for single loading patterns and it was assumed that nodal demands are constant. In reality nodal demand vary over the time so network designed to satisfy one operating condition might not be able to satisfy other loading patterns (i.e. pressure constraints might not be meet). The model has been applied to three well known water distribution networks. The approach has also been implemented on a large real-world network in the literature. Three different methods of designing for multiple loading patterns were investigated. Extensive testing proved that MOC outperform SOC in terms of hydraulic feasibility, pipe size distribution and reliability. The approach is computationally efficient and robust. The above mentioned penalty-free approach has been extended to form a module that would improve the convergence criteria of the GA by reducing its search space. For large real-world network GA might require extremely large number of function evaluations which could lead to delayed convergence. By reducing the search space, the GA’s effectiveness and efficiency will increase as the algorithm will identify the solutions in smaller number of function evaluations. The search space reduction method presented herein is based on entropy and uses the importance of every path through network, which is an inherent property of the entropy function. The developed algorithm is dynamic, self-adaptive and does not require pre-defining the reduced sets of candidate diameters for each pipe. The method has been applied to a large network from the literature. Two cases were studied, one based on full search space and one for reduce search space (RSS) approach. Rapid stabilization was observed for the results obtained using RSS