LAUSR

In the present work, a new approach is presented for the optimization of multi-modal nonlinear programming problems with constraints or a nondifferentiable objective function. The model is applied in the optimization of water distribution networks (WDN). An algorithm is proposed to solve the problem, based on multi-swarm optimization (MSO) with multiple swarms that work corporately – a master swarm and several slave swarms – named multi-swarm corporative particle-swarm optimizer (MSC-PSO). There are discrete and continuous decision variables and the problem can be treated as a mixed discrete nonlinear programming (MDNLP) one. The combinations of the algorithm search parameters are obtained in a simple manner, allowing viable and promising solutions. A benchmark problem from the literature is studied, in which the installation costs of a WDN are to be minimized with a computational time of 50 s. The implementation of the algorithm is proven to be efficient, with reduction in pipe installation cost up to 1.08% when compared with results from the literature. The algorithm is also implemented in a primary network, installed in the town of Esperança Nova, Paraná, Brazil, with reduction of 4.28% in the total cost when compared to the current WDN in operation. The computational time for this case was 69 s.