Abstract
This paper deals with robust optimization and network flows. Several robust variants of integer flow problems are considered. They assume uncertainty of network arc capacities as well as of arc unit costs (where applicable). Uncertainty is expressed by discrete scenarios. Since the considered variants of the maximum flow problem are easy to solve, the paper is mostly concerned with NP-hard variants of the minimum-cost flow problem, thus proposing an approximate algorithm for their solution. The accuracy of the proposed algorithm is verified by experiments.
Highlights
Network flows [1,2,3] are an important modelling paradigm used in optimization
Rather than recycling the old solutions, we describe a different approximate algorithm, which is based on relaxation and rounding
Thereby, only integer flows have been taken into account
Summary
Network flows [1,2,3] are an important modelling paradigm used in optimization. Models based on networks and flows are encountered in various areas of operation research, e.g. resource assignment, transportation, traffic regulation, and others. Two most common types of network flow problems are the maximum flow problem and the minimum-cost flow problem. An instance of a network flow problem is specified by exact values of its parameters, such as arc capacities or arc unit costs. In real-life situations, those values are often hard to specify since they may depend on some unforeseen circumstances or may be too volatile for accurate measurement. We experience uncertainty in the problem formulation. Ignoring uncertainty is not recommended since it can lead to low-quality or even infeasible solutions
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
