The Theory And Algorithms For Several Types Of Continuous Location Models

Facility location problem is a hot topic in Operational Research and Cybernetics in recent years,and it is widely used in the field of life,economics,management and so on.The research content is to find the optimal location for one or more service facilities,thus we could achieve an optimal objective function by using the selected facilities to serve the customers.The introduction of Chapter 1 presents the background current situation of research field.Chapter 2 reviews three kinds of continuous location problems: single-source Weber problem,Min-Max problem and Multi-source Weber problem.Chapter 3 considers the robust facility location model for Weber problem and Min-Max problem,then proposes a distributed method based on improved probability distribution set.Robust method is a commonly used method to solve uncertain facility location problem.Traditional robust facility location is somewhat conservative due to excessive attention to the worst case.In order to overcome this drawback,the method in this paper does not focus on the worst case,but focuses on the worst distribution by constructing a distribution set of the robust optimization model.We construct a new probability distribution set of the robust optimization model based on the semi-positive covariance matrix of the random vector.Chapter 4 uses the modified robust method to solve uncertain Weber problem and Min-Max problem.Based on the new probability distribution set of the robust optimization model proposed in Chapter 3,the distributionally robust optimization model is transformed into a semi-definite programming problem by means of the dual transformation,the equivalent transformation of model and conditions.Compare the method in this paper with the Min-Max Regret method,and numerical experiments are reported which have shown that the modified robust method is superior to the minmax-regret method.Chapter 5 considers the Cooper algorithm for Multi-source Weber problem in determined case.Cooper algorithm consists 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 theWeiszfeld 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 facilities,and then we propose a mixed greedy strategy which has better properties.Some preliminary numerical experiments are reported which have shown that the proposed strategies improve the computational efficiency of Cooper algorithm and thus result in a modified algorithm which has better performance.Finally,we summarize the whole paper and point out some possible research direction in the future.