Hybrid Optimisation Algorithms for Two-Objective Design of Water Distribution Systems

Multi-objective design or extended design of Water Distribution Systems (WDSs) has received more attention in recent years. It is of particular interest for obtaining the trade-offs between cost and hydraulic benefit to support the decision-making process. The design problem is usually formulated as a multi-objective optimisation problem, featuring a huge search space associated with a great number of constraints. Multi-objective evolutionary algorithms (MOEAs) are popular tools for addressing this kind of problem because they are capable of approximating the Pareto-optimal front effectively in a single run. However, these methods are often held by the “No Free Lunch” theorem (Wolpert and Macready 1997) that there is no guarantee that they can perform well on a wide range of cases. To overcome this drawback, many hybrid optimisation methods have been proposed to take advantage of multiple search mechanisms which can synergistically facilitate optimisation. In this thesis, a novel hybrid algorithm, called Genetically Adaptive Leaping Algorithm for approXimation and diversitY (GALAXY), is proposed. It is a dedicated optimiser for solving the discrete two-objective design or extended design of WDSs, minimising the total cost and maximising the network resilience, which is a surrogate indicator of hydraulic benefit. GALAXY is developed using the general framework of MOEAs with substantial improvements and modifications tailored for WDS design. It features a generational framework, a hybrid use of the traditional Pareto-dominance and the epsilon-dominance concepts, an integer coding scheme, and six search operators organised in a high-level teamwork hybrid paradigm. In addition, several important strategies are implemented within GALAXY, including the genetically adaptive strategy, the global information sharing strategy, the duplicates handling strategy and the hybrid replacement strategy. One great advantage of GALAXY over other state-of-the-art MOEAs lies in the fact that it eliminates all the individual parameters of search operators, thus providing an effective and efficient tool to researchers and practitioners alike for dealing with real-world cases. To verify the capability of GALAXY, an archive of benchmark problems of WDS design collected from the literature is first established, ranging from small to large cases. GALAXY has been applied to solve these benchmark design problems and its achievements in terms of both ultimate and dynamic performances are compared with those obtained by two state-of-the-art hybrid algorithms and two baseline MOEAs. GALAXY generally outperforms these MOEAs according to various numerical indicators and a graphical comparison tool. For the largest problem considered in this thesis, GALAXY does not perform as well as its competitors due to the limited computational budget in terms of number of function evaluations. All the algorithms have also been applied to solve the challenging Anytown rehabilitation problem, which considers both the design and operation of a system from the extended period simulation perspective. The performance of each algorithm is sensitive to the quality of the initial population and the random seed used. GALAXY and the Pareto-dominance based MOEAs are superior to the epsilon-dominance based methods; however, there is a tie between GALAXY and the Pareto-dominance based approaches. At the end, a summary of this thesis is provided and relevant conclusions are drawn. Recommendations for future research work are also made