  


The Quadratic Shortest Path Problem: Complexity, Approximability, and Solution Methods
Borzou Rostami(borzou.rostamimath.tudortmund.de) Abstract: We consider the problem of finding a shortest path in a directed graph with a quadratic objective function (the QSPP). We show that the QSPP cannot be approximated unless P=NP. For the case of a convex objective function, an napproximation algorithm is presented, where n is the number of nodes in the graph, and APXhardness is shown. Furthermore, we prove that even if only adjacent arcs play a part in the quadratic objective function, the problem still cannot be approximated unless P=NP. In order to solve the problem we first propose a mixed integer programming formulation, and then devise an efficient exact BranchandBound algorithm for the general QSPP, where lower bounds are computed by considering a reformulation scheme that is solvable through a number of minimum cost flow problems. In our computational experiments we solve to optimality different classes of instances with up to 1000 nodes. Keywords: Shortest path problem; Quadratic 01 optimization; Computational complexity, Branch and Bound Category 1: Combinatorial Optimization Category 2: Integer Programming ((Mixed) Integer Linear Programming ) Citation: Download: [PDF] Entry Submitted: 02/24/2016 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  