# Solving Single Vehicle Pickup and Delivery Problems with Time Windows and Capacity Constraints using Nested Monte-Carlo Search

### Stefan Edelkamp, Max Gath

#### Abstract

Transporting goods by courier and express services increases the service quality through short transit times and satisfies individual demands of customers. Determining the optimal route for a vehicle to satisfy transport requests while minimizing the total cost refers to the Single Vehicle Pickup and Delivery Problem. Beside time and distance objectives, in real world operations it is mandatory to consider further constraints such as time windows and the capacity of the vehicle. This paper presents a novel approach to solve Single Vehicle Pickup and Delivery Problems with time windows and capacity constraints by applying Nested Monte-Carlo Search (NMCS). NMCS is a randomized exploration technique which has successfully solved complex combinatorial search problems. To evaluate the approach, we apply benchmarks instances with up to 400 cities which have to be visited. The effects of varying the number of iterations and the search level are investigated. The results reveal, that the algorithm computes state-of-the-art solutions and is competitive with other approaches.

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#### Paper Citation

#### in Harvard Style

Edelkamp S. and Gath M. (2014). **Solving Single Vehicle Pickup and Delivery Problems with Time Windows and Capacity Constraints using Nested Monte-Carlo Search** . In *Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,* ISBN 978-989-758-015-4, pages 22-33. DOI: 10.5220/0004722300220033

#### in Bibtex Style

@conference{icaart14,

author={Stefan Edelkamp and Max Gath},

title={Solving Single Vehicle Pickup and Delivery Problems with Time Windows and Capacity Constraints using Nested Monte-Carlo Search},

booktitle={Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},

year={2014},

pages={22-33},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004722300220033},

isbn={978-989-758-015-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,

TI - Solving Single Vehicle Pickup and Delivery Problems with Time Windows and Capacity Constraints using Nested Monte-Carlo Search

SN - 978-989-758-015-4

AU - Edelkamp S.

AU - Gath M.

PY - 2014

SP - 22

EP - 33

DO - 10.5220/0004722300220033