Hybrid model for water distribution design

Various heuristic and deterministic algorithms have been developed in the past two decades for solving optimization problems and applied to the design of water distribution systems. Nevertheless, there is still some uncertainty about finding a generally trustworthy method that can consistently find solutions which are really close to the global optimum of this problem. The paper proposes a combined harmony search (HS) and linear programming (LP) method for solving water distribution system design problems. It was investigated that the proposed method provides results that are more stable in terms of closeness to a global minimum. The HS method is used in the outer loop of the proposed algorithm and is intended to be used to search for the optimal possibility how to decompose a complex looped network in a branched network, the design of which would be equivalent to the original network. LP is then used in an inner loop to solve each of the branched networks produced by HS and provide a minimum-cost design. After evaluating a high number of possible branched networks (by LP, which alone is suitable only for solving this type of network and is nested in an HS objective function), an optimal solution could be found for the original looped network. The proposed method was tested on two benchmark least-cost design problems and compared with other methods; the results suggest that it consistently provides better solutions than when the heuristic methods tested are set to solve this task alone.