The lower bounded inverse optimal value problem on minimum spanning tree under unit l∞ norm

We consider the lower bounded inverse optimal value problem on minimum spanning tree under unit l ∞ norm. Given an edge weighted connected undirected network G = ( V , E , w ) , a spanning tree T 0 , a lower bound vector l and a value K , we aim to find a new weight vector w ¯ respecting the lower b...

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Bibliographic Details
Published in:Journal of global optimization Vol. 79; no. 3; pp. 757 - 777
Main Authors: Zhang, Binwu, Guan, Xiucui, Pardalos, Panos M., Wang, Hui, Zhang, Qiao, Liu, Yan, Chen, Shuyi
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2021
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Graph theory
Lower bounds
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Polynomials
Real Functions
Weight
Inverse optimal value problem
Strongly polynomial time algorithm
Minimum spanning tree
norm
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:We consider the lower bounded inverse optimal value problem on minimum spanning tree under unit l ∞ norm. Given an edge weighted connected undirected network G = ( V , E , w ) , a spanning tree T 0 , a lower bound vector l and a value K , we aim to find a new weight vector w ¯ respecting the lower bound such that T 0 is a minimum spanning tree under the vector w ¯ with weight K , and the objective is to minimize the modification cost under unit l ∞ norm. We present a mathematical model of the problem. After analyzing optimality conditions of the problem, we develop a strongly polynomial time algorithm with running time O (| V || E |). Finally, we give an example to demonstrate the algorithm and present the numerical experiments.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-020-00947-3