Embedding linear programming in multi objective genetic algorithms for reducing the size of the search space with application to leakage minimization in water distribution networks

This paper shows how embedding a local search algorithm, such as the iterated linear programming (LP), in the multi-objective genetic algorithms (MOGAs) can lead to a reduction in the search space and then to the improvement of the computational efficiency of the MOGAs. In fact, when the optimization problem features both continuous real variables and discrete integer variables, the search space can be subdivided into two sub-spaces, related to the two kinds of variables respectively. The problem can then be structured in such a way that MOGAs can be used for the search within the sub-space of the discrete integer variables. For each solution proposed by the MOGAs, the iterated LP can be used for the search within the sub-space of the continuous real variables. An example of this hybrid algorithm is provided herein as far as water distribution networks are concerned. In particular, the problem of the optimal location of control valves for leakage attenuation is considered. In this framework, the MOGA NSGAII is used to search for the optimal valve locations and for the identification of the isolation valves which have to be closed in the network in order to improve the effectiveness of the control valves whereas the iterated linear programming is used to search for the optimal settings of the control valves. The application to two case studies clearly proves the reduction in the MOGA search space size to render the hybrid algorithm more efficient than the MOGA without iterated linear programming embedded.