Improving the Approximation Ratio for Capacitated Vehicle Routing

Blauth, Jannis; Traub, Vera; Vygen, Jens

doi:10.1007/978-3-030-73879-2_1

Cited by 14 publications

(21 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Essentially the same algorithm implies a (2 + (1 − 2/Q)α)-approximation for unsplittable CVRP [2]. These stood as the best known bounds until recently, when Blauth et al [10] showed that given a TSP approximation α, there is an > 0 such that there is an (α + 2 • (1 − ))-approximation algorithm for CVRP. For α = 3/2, they showed > 1/3000.…”

Section: Related Workmentioning

confidence: 96%

“…A similar approach implies a 2 + (1 − 2/Q)α)-approximation for the unsplittable variant [2]. Very recently, Blauth et al [10] improved these approximations by showing that there is an > 0 such that there is an (α +2•(1− ))approximation algorithm for unsplittable CVRP and a (α + 1 − )-approximation algorithm for unit demand CVRP and splittable CVRP. For α = 3/2, they showed > 1/3000.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Approximation Schemes for Capacitated Vehicle Routing on Graphs of Bounded Treewidth, Bounded Doubling, or Highway Dimension

Jayaprakash¹,

Salavatipour²

2021

Preprint

View full text Add to dashboard Cite

In this paper we present Approximation Schemes for Capacitated Vehicle Routing Problem (CVRP) on several classes of graphs. In CVRP, introduced by Dantzig and Ramser in 1959 [14], we are given a graph G = (V, E) with metric edges costs, a depot r ∈ V , and a vehicle of bounded capacity Q. The goal is to find minimum cost collection of tours for the vehicle that return to the depot, each visiting at most Q nodes, such that they cover all the nodes. This generalizes classic TSP and has been studied extensively. In the more general setting each node v has a demand dv and the total demand of each tour must be no more than Q. Either the demand of each node must be served by one tour (unsplittable) or can be served by multiple tour (splittable). The best known approximation algorithm for general graphs has ratio α + 2(1 − ) (for the unsplittable) and α + 1 − (for the splittable) for some fixed > 1 3000 , where α is the best approximation for TSP. Even for the case of trees, the best approximation ratio is 4/3 [5] and it has been an open question if there is an approximation scheme for this simple class of graphs. Das and Mathieu [15] presented an approximation scheme with time n log O(1/ ) n for Euclidean plane R 2 . No other approximation scheme is known for any other class of metrics (without further restrictions on Q). In this paper we make significant progress on this classic problem by presenting Quasi-Polynomial Time Approximation Schemes (QPTAS) for graphs of bounded treewidth, graphs of bounded highway dimensions, and graphs of bounded doubling dimensions. For comparison, our result implies an approximation scheme for Euclidean plane with run time n O(log 10 n/ 9 ) .

show abstract

Section: Related Workmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Approximation Schemes for Capacitated Vehicle Routing on Graphs of Bounded Treewidth, Bounded Doubling, or Highway Dimension

Jayaprakash¹,

Salavatipour²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…All kinds of vehicle routing problems include the traveling salesman problem and are therefore APX-hard. Approximation algorithms exist only for some restricted models (e.g., [11,19,8,12,37]), and they are -as of today -not suitable for practical purposes. There is a large body of work on mixed-integer programming models.…”

Section: Related Workmentioning

confidence: 99%

Vehicle Routing with Time-Dependent Travel Times: Theory, Practice, and Benchmarks

Blauth¹,

Held²,

Müller³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

We develop theoretical foundations and practical algorithms for vehicle routing with time-dependent travel times. We also provide new benchmark instances and experimental results.First, we study basic operations on piecewise linear arrival time functions. In particular, we devise a faster algorithm to compute the pointwise minimum of a set of piecewise linear functions and a monotonicity-preserving variant of the Imai-Iri algorithm to approximate an arrival time function with fewer breakpoints.Next, we show how to evaluate insertion and deletion operations in tours efficiently and update the underlying data structure faster than previously known when a tour changes. Evaluating a tour also requires a scheduling step which is non-trivial in the presence of time windows and time-dependent travel times. We show how to perform this in linear time.Based on these results, we develop a local search heuristic to solve real-world vehicle routing problems with various constraints efficiently and report experimental results on classical benchmarks. Since most of these do not have time-dependent travel times, we generate and publish new benchmark instances that are based on real-world data. This data also demonstrates the importance of considering time-dependent travel times in instances with tight time windows.

show abstract

“…On general metrics, the first constant-factor approximation algorithm for the unsplittable CVRP was the iterated tour partitioning (ITP), which was proposed and analyzed in the 1980s by Haimovich and Rinnooy Kan [HR85] and Altinkemer and Gavish [AG87]. The approximation ratio for the unsplittable CVRP was only recently improved in work by Blauth, Traub, and Vygen [BTV21], and then further by Friggstad et al [FMRS21], so that the best-to-date approximation ratio stands at roughly 3.194.…”

Section: Introductionmentioning

confidence: 99%

A Tight $(\frac{3}{2}+ε)$-Approximation for Unsplittable Capacitated Vehicle Routing on Trees

Mathieu¹,

Zhou²

2022

Preprint

View full text Add to dashboard Cite

show abstract

Improving the Approximation Ratio for Capacitated Vehicle Routing

Cited by 14 publications

References 30 publications

Approximation Schemes for Capacitated Vehicle Routing on Graphs of Bounded Treewidth, Bounded Doubling, or Highway Dimension

Approximation Schemes for Capacitated Vehicle Routing on Graphs of Bounded Treewidth, Bounded Doubling, or Highway Dimension

Vehicle Routing with Time-Dependent Travel Times: Theory, Practice, and Benchmarks

A Tight $(\frac{3}{2}+ε)$-Approximation for Unsplittable Capacitated Vehicle Routing on Trees

Contact Info

Product

Resources

About