Abstract
Capacitated Vehicle Routing Problem (CVRP) is the well-known combinatorial optimization problem remaining NP-hard even in the Euclidean spaces of fixed dimension. Thirty years ago, in their celebrated paper, M. Haimovich and A. Rinnoy Kan proposed the first PTAS for the Planar Single Depot CVRP based on their Iterated Tour Partition heuristic. For decades, this result was extended by many authors to numerous useful modifications of the problem taking into account multiple depots, pick up and delivery options, time window restrictions, etc. But, to the best of our knowledge, almost none of these results go beyond the Euclidean plane. In this paper, we try to bridge this gap and propose an EPTAS for the Euclidean CVRP for any fixed dimension.
Keywords
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- 1.
A PTAS with time complexity \(f(1/\varepsilon )p(n)\) for some polynomial p.
- 2.
Not necessarily distinct.
- 3.
e.g. for \(\rho =O((\log \log n)^{1/d})\).
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This research was supported by Russian Science Foundation, project no. 14-11-00109.
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Khachay, M., Dubinin, R. (2016). PTAS for the Euclidean Capacitated Vehicle Routing Problem in \(R^d\) . In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds) Discrete Optimization and Operations Research. DOOR 2016. Lecture Notes in Computer Science(), vol 9869. Springer, Cham. https://doi.org/10.1007/978-3-319-44914-2_16
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