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International Conference on VNS 2018 | Presentation
1. Studying the impact of perturbation methods
on the efficiency of GVNS for the ATSP
6th International Conference on Variable Neighborhood
Search
Christos Papalitsas*1
, Theodore Andronikos1
, Panayiotis Karakostas2
1
Department of Informatics
Ionian University
2
Department of Applied Informatics
University of Macedonia
4. An overview
• We study the impact of different perturbation methods.
• We apply our experiments on the asymmetric TSP.
• We use the General Variable Neighborhood Search (GVNS)
scheme.
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5. The Travelling Salesman Problem
• TSP is the problem of finding the shortest Hamiltonian cycle.
• NP-hard.
• Symmetric TSP, Asymmetric TSP, Multiple TSP.
• Numerous applications in many different areas (Logistics,
Artificial Intelligence, Machine Learning, Software Technology
etc).
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7. Elements of our GVNS schemes (1/2)
• Neighborhood structures
• 1-0 Relocate. This move removes node i from its current position
in the route and re-inserts it after a selected node b.
• 2-Opt. The 2-Opt move breaks two arcs in the current solution and
reconnects them in a different way.
• 1-1 Exchange. This move swaps two nodes in the current route.
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8. Elements of our GVNS schemes (2/2)
• Diversification methods
• Intensified Shake.
• Quantum-inspired Shake.
• Random restart Shake.
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9. Intensified Shake
Algorithm 1 Shake_1
procedure Shake_1(S, kmax)
l = random_integer(1, lmax)
for k ← 1, kmax do
select case(l)
case(1)
S′
← 1-0 Relocate(S)
case(2)
S′
← 2-Opt(S)
case(3)
S′
← 1-1 Exchange(S)
end select
end for
return S′
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10. Quantum-inspired Shake
Algorithm 2 Shake_2
procedure Shake_2(S, n)
NQubits ← QuantumRegister(n)
Compute the components based to the qubits.
Save the n components in the vector QCompVector.
Matching each element in the QCompVector with a node in S.
Descending sorting on QCompVector produces S′
.
Recalculate the cost of the new S′
.
return S′
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11. Random Restart
Algorithm 3 Shake_3
procedure Shake_3(S, n)
for i ← 1, n do
S′
← Suffle (S)
if The random selected position has not already been assigned.
then
Put node i in the selected position.
Mark the selected position as assigned.
end if
end for
return S′
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12. Our GVNS Scheme | pipe VND (1/2)
Algorithm 4 pipe-VND
procedure pVND(N, lmax)
l = 1
while l <= lmax do
select case(l)
case(1) : S′
← 1-0 Relocate(S)
case(2) : S′
← 2-Opt(S)
case(3) : S′
← 1-1 Exchange(S)
end select
if f(S′
) < f(S) then
S ← S′
else
l = l + 1
end if
end while
return S
end procedure=0
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13. Our GVNS Scheme | GVNS Scheme (2/2)
Algorithm 5 GVNS_1
procedure GVNS_1(S, kmax, max_time)
while time ≤ max_time do
S∗
= Shake_1(S, kmax)
S′
= pVND(S∗
)
if f(S′
) < f(S) then
S ← S′
end if
end while
return S
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15. Computational Results
• The presented methods were implemented in Fortran.
• Experiments ran on a Windows 10 PC with intel core i7-6700 CPU
at 2.6 GHz and 16GB RAM.
• The compilation was done using intel Fortran 64 XE with option
/O3.
• Maximum execution limit set at 60 and 120 seconds.
• Benchmarks ran on Best Improvement as well as on First
Improvement.
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19. Summary
• A comparative analysis on the impact of different perturbation
methods was introduced.
• Same perturbation methods on different size and class of
problems seems to be improved on Best Improvement.
• Future work:
• An exhausted comparative analysis on other TSP classes
(symmetric TSP, national TSP)
• A statistical analysis test via statistical models (ex. ANOVA etc.)
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20. References
A performance study on multi improvement neighborhood
search strategy.
Electronic Notes in Discrete Mathematics.
P. Hansen, N. Mladenović, R. Todosijević, and S. Hanafi.
Variable neighborhood search: basics and variants.
EURO Journal on Computational Optimization, 5(3):423–454, 2017.
N. Mladenovic and P. Hansen.
Variable neighborhood search.
Computers & Operations Research, 24(11):1097–1100, 1997.
C. Papalitsas, P. Karakostas, and K. Kastampolidou.
A quantum inspired gvns: Some preliminary results.
In P. Vlamos, editor, GeNeDis 2016, pages 281–289, Cham, 2017.
Springer International Publishing.
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