Parallel Cooperative Evolutionary Local Search

for the Heterogeneous Vehicle Routing Problem

EU/MEeting – 3/4 June 2010

P. Lacomme, C. Prodhon

Université de Clermont-Ferrand II, LIMOS, FranceUniversité de Technologie de Troyes, LOSI, France

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Parallel metaheuristics

Technical choices

Parallel Cooperative Evolutionary Local Search

Heterogeneous Vehicle Routing Problem

Experimentations

Sommaire

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Parallel metaheuristics

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Some publicationsParallel GRASP with path-relinking for job shop scheduling R.M. Aiex, S. Binato, and M.G.C. ResendeParallel Computing, 29:393-430, 2003.

Uma investigação experimental da distribuição de probabilidade de tempo de soluçãoem heurísticas GRASP e sua aplicação na análise de implementações paralelas R.M. AiexPhD thesis, Department of Computer Science, Catholic University of Rio de Janeiro, Rio deJaneiro, Brazil, 2002.

Parallelization strategies for the metaheuristic GRASP A.C.F. AlvimMaster's thesis, Department of Computer Science, Catholic University of Rio de Janeiro, Rio deJaneiro, RJ 22453-900 Brazil, April 1998.

Load balancing in the parallelization of the metaheuristic GRASP A.C.F. Alvim and C.C. RibeiroTechnical report, Department of Computer Science, Catholic University of Rio de Janeiro, Rio de Janeiro,

RJ22453-900 Brazil, 1998.

Parallel strategies for GRASP with path-relinking R.M. Aiex and M.G.C. ResendeTechnical report, Internet and Network Systems Research Center, AT&T Labs Research, Florham Park, NJ,

2003.

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Comments

Parallel Tabou Parallel Grasp Parallel Genetic algorithm etc…

No parallel metaheuristic provides the best published results

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Technical choices

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Technical choices (1/2)

Threads programming

Take advantages of multi-cores

Manual management of common resources

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Technical choices (2/2)

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Parallel Cooperative Evolutionary Local

Search

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Classical optimization scheme

Determine a QDRS

A quasi-direct representation of solution (QDRS)

A solution S.

Improved solution S’fA quasi-direct

representation of solution (QDRS)

Heuristics dedicated to the

problem

A solution S.

f

A quasi-direct representation of solution (QDRS)

Initial set of QDRS

Initialization of the framework

Diversification Process

Local Search(LS)

f

Improvement of solution Framework iterations

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Routing problem : 2 solution spaces

Split

Concat

metaheuristic search space A routing solution

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Proposition

Solution

Random Sampling

Evolutionary Local Search

np GRASP iterations

Greedy randomized heuristic

Local Search

Solution S

Mutation on hubs

Solution Solution Solution

Mutation

Local Search

Solution

Mutation

Local Search

Solution

Mutation

Local Search

Solution

ni ELS iterations

nc children-solutions

S replaced by best child in case of improvement

Selection

n ELS parallel

Synchronization of the n ELS

Restart with the best commun solution from the n ELS

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ExampleS0 : 10 324

Best sur 10 : 10 075

Best sur 10 : 9 633

Best sur 10 : 9 607

Best sur 10 : 9 545

Best sur 10 : 9 546

Best sur 10 : 9 884

Best sur 10 : 9 606

Best sur 10 : 9 536

Best sur 10 : 9 630

Best sur 10 : 9 636

Best sur 10 : 9 764

Best sur 10 : 9 696

Best sur 10 : 9 687

Best sur 10 : 9 618

Best sur 10 : 9 608

Best sur 10 : 9 759

Best sur 10 : 9 592

Best sur 10 : 9 592

Best sur 10 : 9 393

Best sur 10 : 9 287

Processeur 1 Processeur 2 Processeur 3 Processeur 4

Pour chaque processeur, on garde les 10 meilleurs

Les 4 meilleures solutions : 9287 (processeur 4), 9330 (P4), 9336 (P4), ??? (P??)

Best sur 10 : 9 881

Best sur 10 : 9 515

Best sur 10 : 9 390

Best sur 10 : 9 389

Best sur 10 : 9 386

Processeur 1Depart depuis:

9287Depart depuis:

9330

Best sur 10 : 9 881

Best sur 10 : 9 515

Best sur 10 : 9 390

Best sur 10 : 9 389

Best sur 10 : 9 386

Etc... Etc...

Depart depuis: 9336

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Numerical tests VFMP … HVRP

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HVRP (1/3)

VRP + heterogeneous fleet of vehicles A depot : node 0 n nodes (clients)

dj demands on node j

Cij cost from node i to j

Fleet of K vehicle types For each type K of vehicles nk vehicles For each type K of vehicles Qk vehicle capacity

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Published Results– HVRP

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New instances

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Presentation (1/5)

http://www.isima.fr/~lacomme/students.html

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Presentation (2/5)

96 French districts

From 20 to 300 nodes Non euclidien distances 8 vehicles types

4 subset of instances < 100 nodes DLP_HVRP_1 From 100 to 150 nodes DLP_HVRP_2 From 150 to 200 nodes DLP_HVRP_3 + 200 nodes DLP_HVRP_4

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Auvergne….

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Aube…

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Nightmare instances

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GRASPxELS solutions (2/2)

Solutions from 5 to 35 trips

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Machine de test

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Machine (1/2)

Windows Server 2003

8 processors

1 processor 4 cores

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Machine (2/2)

4 threads communication time = nul 8 threads slowdown factor = 2 16 threads slowdown factor = 4 32 threads slowdown factor = 8

BUS

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Numerical Results

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Small instances (1/3)

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Small instances (2/3)

Comparative study between total time and best time

0

100

200

300

400

500

600

700

800

900

1000

1P 2P 4P 8P 16P

Best time

Total time

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Small instances (3/3)

% of best solutions

0

10

20

30

40

50

60

70

80

90

100

1P 2P 4P 8P 16P

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Medium Scale Instances (1/2)

Comparative study between the total time and the best time

0

100

200

300

400

500

600

700

800

900

1000

1P 2P 4P 8P 16P

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Medium Scale Instances (2/2)

% of best solutions

0

10

20

30

40

50

60

70

80

90

100

1P 2P 4P 8P 16P

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Concluding remarks

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Conclusion

Significant impact of hardware

Parallel metaheuristic proves its capacity to provide high quality results

Increase convergence rate

Increase solution quality