The Multi-Objective Optimization of Low-Impact Development Facilities in Shallow Mountainous Areas Using Genetic Algorithms

From the perspective of whole-area sponge city construction, it is important to scientifically determine the layout plan of LID facilities for controlling urban rainfall and flooding problems, given the topographical features and rainfall runoff characteristics of shallow urban mountainous areas. Current research on the optimization of low-impact development facilities is limited to the central urban area level, with insufficient research on shallow urban mountainous areas, and there is great uncertainty in the layout of LID facilities when multiple objectives are considered. Therefore, this paper applied a genetic algorithm (NSGA-II) to optimize the layout scheme of LID facilities. Multiple objectives of the peak runoff abatement rate, cost, and land area were selected as the optimization objectives, and the optimized results were ranked using the EWM-TOPSIS and VCWM-TOPSIS methods. The 2nd Hebei Provincial Garden Flower Expo (Qinhuangdao) Park was used as the research object for the optimization design. The results showed that, under the premise of water safety, the lowest cost priority was given to the LID facility with a 15.49% share, 99.43% peak runoff reduction rate, and a cost of CNY 1.215 × 107; the lowest area priority was given to the LID facility with a 15.25% share, 99.42% peak runoff reduction rate, and a cost of CNY 1.267 × 107. The EWM-TOPSIS method was also used to obtain the best optimized solution with 16.18% LID facilities, 99.64% peak runoff abatement rate, and a cost of CNY 1.26 × 107, and the worst optimized solution with 12.55% LID facilities, 97.91% peak runoff abatement rate, and a cost of CNY 1.061 × 107. The decision results under different decision-maker preferences were obtained by the VCWM-TOPSIS method. This study showed that the combination of a genetic algorithm and TOPSIS can optimize the layout of LID facilities in shallow mountainous areas more scientifically and efficiently compared to the actual construction plan for building a sponge city.