A HYBRID ALGORITHM FOR THE UNCERTAIN INVERSE p-MEDIAN LOCATION PROBLEM

In this paper, we investigate the inverse p-median location  problem with variable edge lengths and variable vertex weights on networks in which the vertex weights and modification costs are the independent uncertain variables. We propose a  model for the uncertain inverse p-median location problem  with tail value at risk objective. Then, we show that  it  is NP-hard. Therefore,  a hybrid particle swarm optimization  algorithm is presented  to obtain   the approximate optimal solution of the proposed model. The algorithm contains expected value simulation and tail value at risk simulation

The Inverse 1-Median Problem on Tree Networks with Variable Real Edge Lengths

Location problems exist in the real world and they mainly deal with finding optimal locations for facilities in a network, such as net servers, hospitals, and shopping centers. The inverse location problem is also often met in practice and has been intensively investigated in the literature. As a typical inverse location problem, the inverse 1-median problem on tree networks with variable real edge lengths is discussed in this paper, which is to modify the edge lengths at minimum total cost such that a given vertex becomes a 1-median of the tree network with respect to the new edge lengths. First, this problem is shown to be solvable in linear time with variable nonnegative edge lengths. For the case when negative edge lengths are allowable, the NP-hardness is proved under Hamming distance, and strongly polynomial time algorithms are presented under l1 and l∞ norms, respectively

A MODIFIED PARTICLE SWARM OPTIMIZATION ALGORITHM FOR GENERAL INVERSE ORDERED p-MEDIAN LOCATION PROBLEM ON NETWORKS

This paper is concerned with a general inverse ordered p-median location problem on network where the task is to change (increase or decrease) the edge lengths and vertex weights at minimum cost subject to given modification bounds such that a given set of p vertices becomes an optimal solution of the location problem, i.e., an ordered p-median under the new edge lengths and vertex weights. A modified particle swarm optimization algorithm is designed to solve the problem under the cost functions related to the sum-type Hamming, bottleneck-type Hamming distances and the recti-linear and Chebyshev norms. By computational experiments, the high efficiency of the proposed algorithm is illustrated

The inverse 1-median problem on a cycle

AbstractLet the graph G=(V,E) be a cycle with n+1 vertices, non-negative vertex weights and positive edge lengths. The inverse 1-median problem on a cycle consists in changing the vertex weights at minimum cost so that a prespecified vertex becomes the 1-median. All cost coefficients for increasing or decreasing the weights are assumed to be 1. We show that this problem can be formulated as a linear program with bounded variables and a special structure of the constraint matrix: the columns of the linear program can be partitioned into two classes in which they are monotonically decreasing. This allows one to solve the problem in O(n2) time