Optimization Of Water Distribution Network Design Via Differential Evolution Algorithm

The water supply systems, as one of the most important fundamentalinfrastructure, should be required huge investment for construction. As a vital of watersupply systems, water distribution networks (WDNS) represent the largest assetaccounting for the total construction investment. It is great economic benefit andpractical significance to optimize the WDNS on the premise that the safety andreliability of water supply can be guaranteed. However, due to the problem involvedin water distribution networks optimization belong to a class of highly nonlinear,constrained, multi-modal combinatorial discrete problem, a large variety ofcomputational algorithms have been devised for the task in recent years.Due to differential evolution algorithm (DE) having a simple mechanism as wellas the characteristic of parallel computation ability, global optimization ability, robustof convergence, DE is applied to the WDNS. The innovation research works are asfollows:1. Due to the traditional mutation strategy of differential evolution algorithmcan’t reach a good tradeoff between robustness in global convergence and the searchefficiency. The differential evolution algorithm leads to many problems, such as thelow search efficiency and the premature convergence. Based on analysis ofperformance of the mutation strategies, a new mutation strategy with tournamentselection rule, that taking the best individual vector from the random individualvectors as the base vector, is proposed in this paper. Finally, the improved differentialevolution algorithm is tested on four benchmark functions. The simulation resultsshow that comparing with the traditional mutation strategy, the improved schemebased on tournament selection rule can resolve the contradiction between robustnessin global convergence and the search efficiency.2. Due to the mutation strategy based on tournament selection rule of DE can’t stillreach a good balance between the global search and the local search facing to WDNS.And the operators are constants, the differential evolution algorithm leads topremature convergence and low precision in solving high dimensions complexproblems. Based on analysis of performance of the optimization strategies, a hybridmutation strategy is proposed in this paper. The scheme attempts to balance theexploration and exploitation abilities, In this way, emphasis is laid on the globalsearch at the beginning, which results in maintaining the diversity of population; Later, contribution from the local search increases in order to converge to the optimal faster.Meanwhile, the random normal scaling factor F and the time-varying crossoverprobability factor CR are used synchronously to improve the performance of DE.Finally, the modified differential evolution algorithm is tested on benchmark functions.The simulation results show that the modified algorithm can effectively avoid thepremature convergence, as well as modified the global convergence ability and thesearch precision remarkably.3. Aiming to the shortage of traditional penalty function method in dealing withthe complex constraints of WDNS，the paper present a self-adaptive penalty functionto resolve the problem. The method can adjust the penalty factor adaptively accordingto the solutions founded in last iteration so that DE can search purposeful withinfeasible region, and make up the weakness of modified DE’S self-adaptive ability aswell. For the convenience of comparison, we have applied to the modified algorithmto well-known case studies: two-loop networks and the Hanoi networks，which bothoccur frequently in the related literature. The simulation results show Modified DEcan converge to the best engineering investment with lowest computation cost.In this paper, Due to the computation complexity of the optimization design ofWDNS，DE leads to premature convergence and the low search efficiency. Animproved scheme is presented from the standpoint of mutation strategy and operatorsto improve the search ability of DE. Achieve the economic goal of WDNS on thepremise of meeting the engineering requirements...