Abstract:
The operation of urban water supply network has an important impact on social and economic development and people’s produc‐tion and life.To ensure the safe and stable operation of urban water supply network,it is necessary to study methods to reduce the failure rate of the network.In the design of urban pipe network,it is necessary to consider not only the economic indicators such as the total cost of the pipe network,but also the reliability indicators such as the failure rate of the pipe network.With the increase in the total cost,the failure rate shows a downward trend.On the contrary,with the reduction of the total cost,the failure rate shows an upward trend.Obviously,total costs and failure rates are a pair of conflicting objectives.This paper adopts the decomposition-based multi-objective evolutionary algorithm(MOEA/D) to deal with the multi-objective optimization problem.MOEA/D can obtain a set of mutually non-dominated solutions in one run,which is called Pareto solution.To balance the diversity and convergence of the Pareto solutions,this paper proposes an adaptive MOEA/D algorithm with two-stage strategy and niche guidance strategy,named MOEA/D-TPN.In the MOEA/D-TPN,the evolution pro‐cess is divided into two stages.In the first stage,the algorithm uses the ideal point z
*as the reference point,and in the second stage,the al‐gorithm uses the peak point z
nadas the reference point,so it can better solve the multi-objective optimization problems with convex or concave shapes.At the same time,the algorithm designs a niche guidance strategy to select different mating individuals,so as to enhance the diversi‐ty of the final obtained approximate Pareto front.The performance of the proposed MOEA/D-TPN algorithm is verified by six benchmark test‐ing problems and urban water supply network optimization problems.The simulation results show that MOEA/D-TPN algorithm can deal with complex multi-objective optimization problems,and the obtained solutions can balance the total cost and failure rate,providing a feasible reference scheme for the engineering design of urban water supply network.