On Universal Shortest Paths

Lara Turner () and Horst W. Hamacher ()
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Lara Turner: Technical University of Kaiserslautern
Horst W. Hamacher: Technical University of Kaiserslautern

A chapter in Operations Research Proceedings 2010, 2011, pp 313-318 from Springer

Abstract: Abstract The universal combinatorial optimization problem (Univ-COP) generalizes classical and new objective functions for combinatorial problems given by a ground set, a set of feasible solutions and costs assigned to the elements in the ground set. The corresponding universal objective function is of the sum type and associates additional multiplicative weights with the ordered cost coefficients of a feasible solution such that sum, bottleneck or balanced objectives can, for instance, be modeled. For the special case of shortest paths, we give two alternative definitions for the corresponding universal shortest path problem denoted Univ-SPP, one based on a sequence of cardinality constrained subproblems, the other using an auxiliary construction to establish uniform length for all paths from s to t. We show that the second version can be solved as classical sum shortest path problem on graphs with specific assumptions on edge costs and path lengths. In general, however, the problem is NP-hard. Integer programming formulations are proposed.

Keywords: Short Path; Feasible Solution; Mixed Integer Linear Programming; Combinatorial Optimization Problem; Short Path Problem (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-642-20009-0_50

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DOI: 10.1007/978-3-642-20009-0_50

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