## Route relaxations on GPU for vehicle routing problems.(English)Zbl 1394.90542

Summary: State-space relaxation (SSR) is an approach often used to compute by dynamic programming (DP) effective bounds for many combinatorial optimization problems. Currently, the most effective exact approaches for solving many vehicle routing problems (VRPs) are DP algorithms making use of SSR for computing their bounding components. In particular, most of these make use of the $$q$$-route and $$ng$$-route relaxations. The bounding procedures based on these relaxations provide good quality bounds but they are often time consuming to compute, even for moderate size instances. In this paper, we investigate the use of GPU computing for solving $$q$$-route and $$ng$$-route relaxations. The results prove that the proposed GPU implementations are able to achieve remarkable computing time reductions, up to 40 times with respect to the sequential versions.

### MSC:

 90C35 Programming involving graphs or networks 90B06 Transportation, logistics and supply chain management 90C39 Dynamic programming 90C60 Abstract computational complexity for mathematical programming problems

### Software:

Cvrplib; VRPLIB; CUDA; CVRPSP; VRP
Full Text:

### References:

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