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Valparaíso, Chile November 13, 2012. Applying a Hybrid Approach to an Asymmetric Heterogeneous Vehicle Routing Problem. José Cáceres Cruz Daniel Riera Angel A. Juan {jcaceresc, ajuanp, drierat}@uoc.edu Department of Computer Science IN3 - Open University of Catalonia, Barcelona, SPAIN.

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Valparaíso, Chile

November 13, 2012

Applying a Hybrid Approach to an Asymmetric Heterogeneous Vehicle Routing Problem

José Cáceres CruzDaniel RieraAngel A. Juan

{jcaceresc, ajuanp, drierat}@uoc.edu

Department of Computer Science

IN3 - Open University of Catalonia, Barcelona, SPAIN

Roman Buil

  • [email protected]

    Department of Telecommunications and Systems Engineering

    Universitat Autònoma de Barcelona, Bellaterra, Spain

http://dpcs.uoc.edu


0. Agenda

Introduction.

UrbanTransportation: Real Case.

Related Works.

Solving CVRP: SR-GCWS.

OurApproachforthe AHVRP.

Design of Experiments.

ComputationalResults.

Conclusions.

FutureWork.

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1. Introduction: Motivation

  • The Urban Transportation (big cities) has special considerations like Traffic lights, Direction of streets, etc.

  • Food Delivery and Postal Companies: They need to delivery in a short period of time, using different types of vehicles for different types of vehicles.

  • Increase use of ICTs for transfer of information on real time.

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1. Introduction: The AHVRP

  • The AHVRP is a well-known NP-hard problem:

    • A set of customers’ demands must be supplied by a fleet of vehicles.

    • The fleet of vehicles is fixed and heterogeneous.

    • Resources are available from a depot.

    • Moving a vehicle from one node i to another j has associated costsc(i, j) that is different cost from j to i (Asymmetric Cost Matrix).

    • Several constraints must be considered: maximum load capacity per vehicle, service times, route length, etc.

Customers (demand)

edge in a route

Depot

(resources)

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2. Urban Transportation: Real Case (1/2).

  • A food distribution company needs to distribute several boxes of food in a short time windows in Barcelona.

  • Clients are relative close however the traffic and direction of streets could make of this a hard task.

  • Objective: Minimizing the total distance!

  • Considering next restrictions:

    • Heterogeneous Fixed Fleet of Vehicles,

    • Asymmetric Cost Matrix,

    • Maximum Route Length,

    • Service Times.

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2. Urban Transportation: Real Case (2/2).

  • Research Objective: To promote the knowledge transfer to SME.

  • Research community is interested in real applications!

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3. Related Works

  • Asymmetric Cost Matrix studies:

Nagata, Y. (2007). Edge assembly crossover for the capacitated vehicle routing problem. In Cotta, C. and van Hemert, J. I., editors, Evolutionary Computation in Combinatorial Optimization, 7th European Conference, EvoCOP, Lecture Notes in Computer Science,

pages 142–153, Valencia. Springer.

Toth, P., Vigo, D., 1999. A heuristic algorithm for the symmetric and asymmetric vehicle routing problems with backhauls. European Journal of Operational Research 113: 528-543.

  • Heterogeneous Fleet studies:

Li F, Golden B, and Wasil E (2007). A record-to-record travel algorithm for solving the heterogeneous fleet vehicle routing problem. Computers and Operations Research 34(9): 2734-2742.

Baldacci, R., Battarra, M., Vigo, D. 2008. Routing a Heterogeneous Fleet of Vehicles. In The Vehicle Routinh Problem: Latest Advances and New Challenges. B. Golden, S. Raghavan and E. E. Wasil, Sringer: 3-27.

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4. Solving AHVRP: SR-GCWS-CS (1/3)

Start

  • Our CVRP approach is based on the Clarke and Wright’s savings (CWS) algorithm (Clarke & Wright 1964).

  • CWS algorithm:

    • For each pair of nodes i and j, calculate the savings, s(i, j), associated to the edge connecting them, where:

      s(i, j) = c(0, i) + c(0, j) – c(i, j)

    • Construct a list of edges, sorting the edges according to their associated savings

    • Construct an initial feasible solution by routing a vehicle to each client node

    • Select the first edge in the savings list and, if no constraint is violated, merge the routes that it connects

    • Repeat step 4 until the savings list is empty

savings(i, j)

Savings list

Initial solution

Select first edge

& Merge

List empty?

  • This parallel version of the CWS heuristic usually provides ‘acceptable solutions’ (average gap between 5% and 10%), especially for small and medium-size problems

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Juan, A.; Faulin, J.; Jorba, J.; Riera, D.; Masip; D.; Barrios, B. (2011): “On the Use of Monte Carlo Simulation, Cache and Splitting Techniques to Improve the Clarke and Wright Savings Heuristics”. Journal of the Operational Research Society, Vol. 62, pp. 1085-1097.

End

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4. Solving CVRP: SR-GCWS-CS (2/3)

  • CWS the first edge (the one with the most savings) is the one selected.

  • SR-GCWS introduces randomness in this process by using a quasi-geometric statistical distribution  edges with more savings will be more likely to be selected at each step, but all edges in the list are potentially eligible.

  • Notice: Each time SR-GCWS is run, a random feasible solution is obtained. By construction, chances are that this solution outperforms the CWS one  hundreds of ‘good’ solutions can be obtained after some seconds/minutes.

Good results with

0.10 < α < 0.20

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4. Solving AHVRP: SR-GCWS-CS (3/3)

Improvement #1: Hash Table

  • Adding ‘memory’ to our algorithm with a hash table:

    • A hash table is used to save, for each generated route, the best-known sequence of nodes (this will be used to improve new solutions)

    • ‘Fast’ method that provides small improvements on the average

Adding a Vehicle Assignment procedure.

Adding a Asymmetric Cost and Edge direction in the construction of routes.

Caceres, J., Lourenço, H., Juan, A., Grasas, A., Roca, M., Colome, R. 2012. Aplicación de un Algoritmo Híbrido para la Resolución de un Problema de Enrutamiento de Vehículos Heterogéneos en una Empresa de Distribución. In Proceddings of MAEB, 767-773. February 8-10. Albacete, Spain.

Rodríguez, A., Ruiz, R. 2012. A study on the effect of the asymmetry on real capacitated vehicle routing problems. Computers & Operations Research 39(9): 2142–2151.

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5. Our Approach for the AHVRP

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6. Design of Experiments (1/2)

  • The inspiration of this study is a real food distribution company located in Barcelona, Spain. Daily, they distribute food for around of 50 customers. Their orders arrive in the morning and the vehicles must to deliver them after noon.

  • They currently use four or five vehicles for their daily distribution. They manage a small fleet of two types:

  • The routes must have a Maximum Length of 180 minutes in order to respect the defined time window.

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6. Design of Experiments (2/2)

  • They provided the information of the demands and location of clients in previous seven distribution days:

  • The service times for each client follows a triangular distribution with min = 1, max = 12 and mode = 3.

  • For each instance, a single run with a total maximum time of 500 seconds was employed for executing the Java algorithm.

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7. Computational Results (1/2)

  • Using their information, we estimated new routes reducing the number of used vehicles:

  • However, we also estimate the routes using the whole fleet:

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7. Computational Results (2/2)

Approximated routing planning of the company forcing to use 4 vehicles for instance B.

Designed routes in the proposed solution for instance B.

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8. Conclusions

  • We have presented a hybrid approach for solving the AHVRP with service times and routes length restrictions.

  • This approach combines MCS and the SR-GCWS algorithm with a Local Search technique.

  • A set of real set of instances have been used in order to test the performance of our approach. This experience has allowed supporting a food distribution company in order to:

    • realize the current situation with quantitative methods;

    • improve their routing planning with a simple approach.

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9. Future Work

  • Including other constraints: Balanced Load of Routes and also Open Routes.

  • Considering other representations of savings for the Asymmetric costs.

  • Considering other heterogeneous vehicle assignment procedures.

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Valparaíso, Chile

November 13, 2012

Thanks for your attention!

Applying a Hybrid Approach to an Asymmetric Heterogeneous Vehicle Routing Problem

José Cáceres CruzDaniel RieraAngel A. Juan

{jcaceresc, ajuanp, drierat}@uoc.edu

Department of Computer Science

IN3 - Open University of Catalonia, Barcelona, SPAIN

Roman Buil

  • [email protected]

    Department of Telecommunications and Systems Engineering

    Universitat Autònoma de Barcelona, Bellaterra, Spain

http://dpcs.uoc.edu


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