关键词: 双目标设施选址模型, ε-约束法, 负效应, 废弃物分类回收

Abstract: Facility location problem is a classic area of research in the field of optimization and has been one of the hotspots that many researchers have continued to focus on for decades. Recently, the location of facilities related to urban public services has received more attention from academics. Urban public service facilities are essential for the normal operation of a city, but some of them have negative effects on the surrounding environment when they are in operation. Typical cases are waste disposal centers, also known as neighbourhood avoidance public facilities, where the location issues are often more complex. Proper selection of urban waste disposal facilities can help improve the quality of life for the general public, timely recycle valuable renewable resources and effectively reduce the severe impact of waste on the environment.
Against this background, we consider a three-echelon recycling network consisting of collection points, disposal centers, and recycling centers. Each collection point generates different types of waste, which are disposed in the disposal centers, and then transported to the recycling centers for incineration or recycling. We first consider the capacity limitation, the nearest distance between disposal centers, the requirements for waste sorting and recycling, as well as the environmental negative effects of disposal facilities, and then we construct a bi-objective mixed integer programming model with the objective of minimizing the total cost and total negative effects in order to determine the location of waste disposal centers, and the allocation of recycling networks. By constructing and solving the model, it is ultimately necessary to answer: (1)the location and capacity planning of the disposal centers; (2)the demand allocation from collection points to disposal centers, and from disposal centers to recycling centers; (3)the transportation planning from disposal centers to recycling centers.
Furthermore, to solve this model, based on the classical ε-constraint method, an improved ε-constraint method is designed by incorporating the optimization sequence strategy considering greedy rules (improved Strategy 1), and the cycle parameter strategy (improved Strategy 2) to obtain the Pareto frontier. Strategy 1 specifies the optimization order of the objective function under greedy rules, which makes use of the information on the slack variables and remaining variables generated during the solution process of CPLEX solver. The weights of each remaining variable are changed, forcing the constrained objective function to be optimized in a specific order based on the weight sizes of the remaining variables. Strategy 2 sets relevant parameters in the loop that can omit the number of cycles, which can effectively reduce redundant iterations and save computational time and space. After these adjustments, the improved ε-constraint method can be effectively applied to multi-objective programming models of larger magnitudes, avoiding the computational complexity of the classical ε-constraint method, while ensuring that a more accurate set of Pareto frontier solutions is eventually obtained. Subsequently, extensive data experiments are designed to verify the effectiveness of the algorithm and model. The results show that: (1)The model proposed in this paper can effectively improve the problem of the unreasonable layout of disposal centers; it can also reasonably reduce the number of waste disposal centers and balance the distance between them and the collection points. (2)Compared with the classical ε-constraint method, the improved ε-constraint method can obtain a large number of Pareto solutions with good quality and uniform distribution, avoiding the shortcomings of the classical ε-constraint method; it can also effectively reduce the number of iterations and save computational time, which is more suitable for solving large-scale problems.
Finally, the improved ε-constraint method is applied to the real scenario of waste sorting and recycling in Xi’an. The results show that the proposed model may effectively improve the layout planning of disposal centers, and provide strategy selection and support for the implementation of such facilities.

Key words: bi-objective facility location model, ε-constraint method, negative effects, waste sorting and recycling