Multi-objective optimisation of water distribution systems design using metaheuristics

The design of a water distribution system (WDS) involves finding an acceptable trade-off between cost minimisation and the maximisation of numerous system benefits, such as hydraulic reliability and surplus capacity. The primary design problem involves cost-effective specification of a pipe network layout and pipe sizes (which are typically available in a discrete set of commercial diameters) in order to satisfy expected consumer water demands within required pressure limits. The problem may be extended to consider the design of additional WDS components, such as reservoirs, tanks, pumps and valves. Practical designs must also cater for the uncertainty of demand, the requirement of surplus capacity for future growth, and the hydraulic reliability of the system under different demand and potential failure conditions. A detailed literature review of exact and approximate approaches towards single-objective (minimum cost) WDS design optimisation is provided. Essential topics which have to be included in any modern WDS design paradigm (such as demand estimation, reliability quantification, tank design and pipe layout) are discussed. A number of formative concepts in multi-objective evolutionary optimisation are also reviewed (including a generic problem formulation, performance evaluation measures, comparative testing strategies, and suitable classes of metaheuristics). The two central themes of this dissertation are conducting multi-objective WDS design optimisation using metaheuristics, and a critical examination of surrogate measures used to quantify WDS reliability. The aim in the first theme is to compare numerous modern metaheuristics, including several multi-objective evolutionary algorithms, an estimation of distribution algorithm and a recent hyperheuristic named AMALGAM (an evolutionary framework for the simultaneous incorporation of multiple metaheuristics applied here for the first time to a real-world problem), in order to determine which approach is most capable with respect to WDS design optimisation. Several novel metaheuristics are developed, as well as a number of new variants of existing algorithms, so that a total of twenty-three algorithms were compared. Testing with respect to eight small-to-large-sized WDS benchmarks from the literature reveals that the four top-performing algorithms are mutually non-dominated with respect to the various performance metrics. These algorithms are NSGA-II, TAMALGAMJndu, TAMALGAMndu and AMALGAMSndp (the last three being novel variants of AMALGAM). However, when these four algorithms are applied to the design of a very large real-world benchmark, the AMALGAM paradigm outperforms NSGA-II convincingly, with AMALGAMSndp exhibiting the best performance overall. As part of this study, a novel multi-objective greedy algorithm is developed by combining several heuristic design methods from the literature in order to mimic the design strategy of a human engineer. This algorithm functions as a powerful local search. However, it is shown that such an algorithm cannot compete with modern metaheuristics, which employ advanced strategies in order to uncover better solutions with less computational effort. The second central theme involves the comparison of several popular WDS reliability surrogate measures (namely the Resilience Index, Network Resilience, Flow Entropy, and a novel mixed surrogate measure) in terms of their ability to produce designs that are robust against pipe failure and water demand variation. This is the first systematic study on a number of WDS benchmarks in which regression analysis is used to compare reliability surrogate measures with probabilistic reliability typically derived via simulation, and failure reliability calculated by considering all single-pipe failure events, with both reliability types quantified by means of average demand satisfaction. Although no single measure consistently outperforms the others, it is shown that using the Resilience Index and Network Resilience yields designs that achieve a better positive correlation with both probabilistic and failure reliability, and while the Mixed Surrogate measure shows some promise, using Flow Entropy on its own as a quantifier of reliability should be avoided. Network Resilience is identified as being a superior predictor of failure reliability, and also having the desirable property of supplying designs with fewer and less severe size discontinuities between adjacent pipes. For this reason, it is recommended as the surrogate measure of choice for practical application towards design in the WDS industry. AMALGAMSndp is also applied to the design of a real South African WDS design case study in Gauteng Province, achieving savings of millions of Rands as well as significant reliability improvements on a preliminary engineered design by a consulting engineering firm.