摘要
多设施Weber问题(multi-source Weber problem,MWP)是设施选址中的重要模型之一,而Cooper算法是求解MWP最为常用的数值方法.Cooper算法包含选址步和分配步,两步交替进行直至达到局部最优解.本文对Cooper算法的选址步和分配步分别引入改进策略,提出改进Cooper算法:选址步中将Weiszfeld算法和adaptive Barzilai-Borwein(ABB)算法结合,提出收敛速度更快的ABB—Weiszfeld算法求解选址子问题;分配步中提出贪婪簇分割策略来处理退化设施,由此进一步提出具有更好性质的贪婪混合策略.数值实验表明本文提出的改进策略有效地提高了Cooper算法的计算效率,改进算法有着更好的数值表现.
The multi-source Weber problem (MWP) is a very important model in facility location and Cooper algorithm is the most well-used method to solve MWP. Cooper algorithm con- sists of two steps: location step and allocation step. By doing such two steps alternately, the local optimal solution can be obtained. In this paper, we propose a modified Cooper algorithm by introducing improved strategy for both steps. For location step, we combine the Weiszfeld method with the adaptive Barzilai-Borwein (ABB) method to propose ABB- Weiszfeld method, which has a faster convergence rate in solving location subproblems. For allocation step~ we propose a greedy cluster splitting strategy to deal with out-of-use fa- cilities, and then we propose a mixed greedy strategy which has better properties. Some preliminary numerical experiments are reported which have shown that the proposed strate- gies improve the computational efficiency of Cooper algorithm and thus result in a modified algorithm which has better performance.
作者
蒋建林
潘蕴文
Jiang Jianlin;Pan Yunwen(Nanjing University of Aeronautics and Astronautics,College of Science,Nanjing 210016,China)
出处
《计算数学》
CSCD
北大核心
2018年第4期470-484,共15页
Mathematica Numerica Sinica
基金
国家自然科学基金(11571169)