求解农产品供应链网络设计问题的混合粒子群算法

Hybrid Particle Swarm Algorithms for Solving Design Problems of Agri-food Supply Chain Network

为求解以混合整数规划(MIP)模型表征的农产品供应链网络(Agri-food Supply Chain Network,ASCN)优化设计问题,提出了基于混合粒子群算法(Particle Swarm Algorithm,PSA)的优化方法。分别将单邻域搜索和简化变邻域搜索作为局部搜索技术嵌入PSA中构建了两种混合PSAs。由混合PSA搜索MIP中二元决策变量,随后由LINGO求解MIP导出的线性规划问题并获取解。以陕西苹果产业集群的ASCN设计及其修改案例为例,验证了基于混合PSA优化方法的有效性。案例计算结果对比表明,增加局部搜索可显著增强PSA全局寻优能力,且简化变邻域搜索在改善PSA全局搜索能力上优于单邻域搜索。

The competition between modern agri-businesses is not only the competition between production enterprises but also the competition in the agri-food supply chain network （ASCN） including the production enterprises. To enhance competitiveness of ASCN, their strategic decision of optimal design is crucial. The optimal design of ASCN is effective to improve operational efficiency of ASCN and reduce operational cost. Traditionally, the design of ASCN is oriented to the core enterprise. However, in this paper we are concerned with the design of ASCN associated with the agricultural cluster. The traditional design of ASCN focuses on the logistic network design or production facility location. In fact, the integration of logistic network design and production facility location will lead to better performance of ASCNs. In the research, a mixed-integer programming （MIP） model for ASCN design problem is presented. In the MIP model, the logistic network design, production facility location, and capacity decision are considered. A hybrid particle swarm algorithm （HPSA） based approach is proposed to solve ASCN design problems formulated by MIP model. In the first part, the ASCN design problem is stated in detail. The parameters and variables of the MIP model for ASCN design problem are explained. Lastly, the MIP model is given, and the optimization objective and constrains are stated and expounded. In the MIP model, minimization of the total cost including production cost and transportation cost is selected as the optimization objective. In the second part, the main idea of the proposed HPSA based approach is explained. In addition, the HPSA is utilized to search and determine optimal binary decision variables of MIP. The LINGO is adapted to solve the linear programming problem derived from MIP＇s binary variables and obtain the final solution. After a brief introduction to binary PSA （ BPSA ）, two HPSAs are developed by incorporating two local search methods into the BPSA in order to improve the global optimization ability of BPSA. One HPSA is the HPSAsNs that is created by BPSA embedded into a single neighborhood search （SNS） and another HPSA is HPSARvNs that is formed by BPSA embedded into a reduced variable neighborhood search （RVNS）. At last, the implementation procedure of the optimization approach through LINGO and VC ＋ ＋ 6. 0 is described. In the third part, the basic case （ case 1 ） of ASCN design for Shangxi apple cluster is firstly introduced. In the MIP model of case 1, there are 100 continuous decision variables and 15 binary decision variables. Based on case 1, another two cases are generated using Matlab to further test the efficiency and effectiveness of the HPSA approach. In case 2 there are 1877 continuous decision variables and 30 binary decision variables. In case 3 there are 5007 continuous decision variables and 60 binary decision variables. The solution quality, computation time and convergence curves of BPSA, HPSAsNs and HPSARvNS against three cases are provided and compared. Case studies for optimal design of ASCN within Shangxi apple cluster illustrate the effectiveness of the HPSA based approach. In summary, the proposed HPSA based approach is effective and efficient for the ASCN design problem. The case study shows that the local search methods SNS and RVNS are able to dramatically enhance PSA＇s global optimization ability by embedding them into BPSA. The comparative computational results for two HPSAs indicate that RVNS is superior to SNS with respect to improving PSA＇s global optimization ability.