Multi-objective optimal design of water distribution systems using a decomposition approach

Recently, the size and complexity of water distribution systems are increased, and the systems need to satisfy higher standard of water supply because of urbanization. A greater number of pipes and loops are contained within water distribution systems, and hydraulic facilities, such as pumps, valves and tanks, are contained in the water distribution systems. In addition, various of design criteria, such as reliability of system, energy consumption, water quality, are needed for water distribution system design with construction cost, and therefore, advanced design techniques considering problem characteristics of water distribution system design are required. To improve the efficiency of the water distribution system design, decomposition approaches as engineering technique can be used with current optimization algorithms. Kessler et al. [1] introduced a graph theory based optimization technique. Sonak and Bhave [2] applied graph theory with mathematical optimization technique for water distribution system design. Kadu et al. [3] integrated graph theory with the Genetic Algorithms for optimal cost design of water distribution system. Zheng et al. [4] decomposed the system by graph theory and determined the optimal design by a metaheuristic algorithm. Zheng et al. [5] applied a decomposition approach for water distribution system design with multi-source, and Zheng and Zecchin [6] proposed a friction slope method for the optimal cost design of a multi-source water distribution system. Lee et al. [7] newly proposed a water distribution system decomposition method using source tracing based technique to overcome disadvantages of the slope based (graph based) approaches. However, in Lee et al. [7], the single-objective optimal design for water distribution systems was considered. Therefore, in this study, the source tracing based water distribution system decomposition technique proposed by Lee et al. [7] is modified to apply for the multi-objective optimal design of water distribution systems. Optimal design method of the water distribution system proposed in this study consists of the following four steps: 1) network decomposition by source tracing; 2) multi-objective optimal design for sub-networks; 3) network integration and initial pareto solution generation; 4) multi-objective optimal design for whole network. The proposed method is tested by carrying out the multi-objective optimal design of sample water distribution systems, and the results are compared with multi-objective optimal designs derived from previously used optimization algorithms. The results show that, the source tracing based water distribution system decomposition approach efficiently considers topological characteristics, network connectivity, and hydraulic characteristics of water distribution system, and therefore, the multi-objective design solutions by proposed method are outstanding. This implies that, finding solutions to real engineering problems using an optimization algorithm requires a more efficient approach by considering the characteristics of the given problem. In addition, the source tracing based decomposition approach proposed in this study can be easily combined with various optimization algorithms to improve water distribution system design efficiency.