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A local search heuristic for the Multi-Commodity \(k\)-splittable Maximum Flow Problem

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Abstract

The Multi-Commodity \(k\)-splittable Maximum Flow Problem consists of maximizing the amount of flow routed through a network such that each commodity uses at most \(k\) paths and such that edge capacities are satisfied. The problem is \(\mathcal NP \)-hard and has application in a.o. telecommunications. In this paper, a local search heuristic for solving the problem is proposed. The heuristic is an iterative shortest path procedure on a reduced graph combined with a local search procedure to modify certain path flows and prioritize the different commodities. The heuristic is tested on benchmark instances from the literature and solves 83 % of the instances to optimality. For the remaining instances, the heuristic finds good solution values which on average are 1.04 % from the optimal. The heuristic solves all instances in less than a second. Compared to other heuristics, the proposed heuristic again shows superior performance with respect to solution quality.

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Gamst, M. A local search heuristic for the Multi-Commodity \(k\)-splittable Maximum Flow Problem. Optim Lett 8, 919–937 (2014). https://doi.org/10.1007/s11590-013-0622-9

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