Set Covering Location Research On The Model And Algorithm Of Two-level Shopping Center With Capacity Constraints

With the development of urban economy and commerce,shopping malls have replaced department stores to become the main form of urban retail commerce.Different levels of shopping centers have different service radius and complementary functions,which constitute the urban retail commercial system.The location of shopping center has a direct impact on retail sales and return on investment,which is an important decisionmaking problem that urban business planning departments and commercial investors need to consider.First of all,in order to meet the different levels of consumption needs of all consumers within the service radius,this paper draws lessons from the hierarchical maximum coverage location model,gives the service radius of different levels of shopping centers,and aims to minimize the construction cost of shopping malls.in this paper,a twolevel shopping center set coverage mixed integer programming model with limited ability is constructed.According to the characteristics of the model,a genetic algorithm for chromosome matrix coding is designed.The location decision variable is encoded by 0-1coding,which is composed of G1 and G2 chromosomes,while the service allocation decision variable is coded by real number and composed of G3 chromosome matrix.Four groups of simulation examples are generated by using Python’s NetworkX library to test the algorithm performance from two aspects of algorithm convergence and algorithm efficiency,and good results are obtained.Secondly,based on the above model and considering the interests of both commercial investors and consumers,this paper minimizes the total cost of shopping center development and construction and the total transportation cost of consumers as biobjective,and gives different levels of shopping center service radius.in this paper,a biobjective two-level shopping center set coverage location model with capacity limitation is constructed.Aiming at the bi-objective set covering location problem,a chromosome archiving mechanism is designed in this paper,and the second generation fast nondominant sorting genetic algorithm of NSGA-Ⅱ(Non-dominated Sorting Genetic Algorithm Ⅱ)is improved.By comparing with the ε epsilon(Epsilon)constraint algorithm based on examples,the performance of the improved NSGA-Ⅱ algorithm is verified in terms of solution diversity,quantity,convergence and efficiency.Finally,this paper takes the eight subway lines opened in Xi’an at the end of 2020 as the transportation network,163 subway stations as demand points and shopping center alternative points,and makes a case study based on the subway network using the above two models.The case calculation results of the two-level shopping center set coverage location model based on Xi’an subway network show that according to the spatial distribution of city-level and regional-level shopping centers,4 city-level shopping centers and 11 regional-level shopping centers should be built,and the location results are visually displayed based on Arc GIS software.The Pareto optimal solution set is obtained from the case calculation result of the bi-objective two-level shopping center collection coverage location model based on Xi’an subway network,and the model parameters are further analyzed.The results show that the construction cost proportional coefficient α is positively correlated with the construction cost and the number of Pareto solutions,the capacity proportional coefficient β has no significant effect on the optimization results,and the radius proportional coefficient γ is negatively correlated with construction cost and transportation cost.It is negatively related to the number of shopping centers at city and district level.