Many optimization models to determine cost-effectiveness and obtain the least-cost system designs for water distribution networks have been developed. An algorithm used for solving an optimization model, such as the branch-and-bound or enumeration method, has deficiencies that may include efficiency problems and local optimal solution problems. A heuristic approach, with a bounded implicit enumeration (BIE) algorithm was developed in this study to improve searching efficiency. The heuristic approach first treats the system as a sub-system so that the sub-system's solution must spread widely at the solution space. Then, the optimal sub-system solution is found by a BIE algorithm. On the basis of the optimal solution for the initial system, one larger than and one smaller than its commercial diameter is used to form a new system design. Finally, an optimal solution is determined by using the BIE algorithm until the same solution is found. In this study, five water distribution network designs were used to illustrate the performance of this approach. The results show that a heuristic approach is more efficient than the BIE alone. The efficiency becomes more obvious when the system becomes larger. Comparing the three case studies, the heuristic approach along with the BIE algorithm finds global optimal solution more efficiently. (C) 1997 IAWQ. Published by Elsevier Science Ltd.
