presentation at OR in the digital era - ICT challenges conference at 2017

1. Initialization methods for the TSP with Time Windows
using qGVNS
*Christos Papalitsas1 Panayiotis Karakostas2 Konstantinos
Giannakis1 Angelo Sifaleras2 Theodore Andronikos1
1Department of Informatics
Ionian University
2Department of Applied Informatics
University of Macedonia
OR in the digital era - ICT challenges, 2017
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2. Preview of our study
Meta-heuristic procedures
Variable Neighborhood Search
qGVNS
TSP,TSP with Time Windows
Experimental results
Conclusion - Future Work
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3. Meta-heuristics
Meta-heuristic methods An overview
Meta-heuristics: optimization frameworks which can be modified
properly in order to produce heuristic approaches for hard
optimization problems.
Ideal for problems with missing or incomplete information, or with
limited computing capacity.
They do not guarantee a global optimal solution for each category of
problems.
By searching into a large set of feasible solutions, the meta-heuristic
procedures can often find good solutions with less computational
effort.
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4. Meta-heuristics
VNS Variable Neighborhood Search (1/2)
VNS is a meta-heuristic method for solving a set of combinatorial
problems and global optimization problems.
This strategy is driven by three principles:
1 a local minimum for a neighborhood structure cannot be a local
minimum to a different neighborhood structure
2 a global minimum is a local minimum for all possible structures of the
neighborhood, and
3 a local minimum is closely related to the total minimum for many
classes of problems.
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5. Meta-heuristics
VNS Variable Neighborhood Search (2/2)
The systematic neighborhood change try to find an optimal (or a
close-to-optimal) solution.
VNS heuristic consists of three parts:
1 A shaking procedure, used to escape local optimal solutions.
2 Improvement phase: exploration of neighborhood structures through
different local search moves. Systematic neighborhood change to reach
an optimal (or a close-to-optimal) solution.
3 The neighborhood change, where the following neighborhood structure
is determined.
an approval or rejection criterion is also applied on the last solution
found.
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6. Our approach
qGVNS (1/4) An overview
The quantum-inspired GVNS (qGVNS) consists of:
A VND local search.
1 the 1-shift local search operator: solutions obtained by nodes
repositioning in tour.
A quantum inspired shaking procedure.
Neighborhood change step.
The main difference between qGVNS and classic GVNS is in the
diversification (shaking) phase.
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7. Our approach
qGVNS (2/4)
Local Search used in qGVNS is 1-shift procedure.
A violated node is a node that has been visited after its expiration
time.
Two sets arise:
the violated nodes (nodes that were visited after their due time) and
the non-violated nodes.
We separate the main neighborhood in two new sub-neighborhoods.
It is important to define the ordering.
1 Move backwards violated nodes
2 Move forward not violated nodes
3 Move backwards not violated nodes
4 Move forward violated nodes
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8. Our approach
qGVNS (3/4) Quantum inspired perturbation
Perturbation phase adopts quantum computation principles.
Step 1: shaking begins: a quantum register generates the necessary
qubits.
Step 2: The generated qubits produce the corresponding components.
(These components will be equal or higher than the number of the
nodes in the tour)
Step 3: The algorithm chooses serially the components, and put them
in a 1 x n vector.
Step 4: Each one will be matched to each node of our current
solution. Note, that components can be 0 ≤ C ≤ 1
Step 5: sorting the first vector will affect the node’s order in the
solution vector.
This is the route occurring after the shaking move, driving our exploration
effort in another search space.
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9. Our approach
qGVNS (4/4) qGVNS Pseudocode
Data: an initial solution
Result: an optimized solution
Initialization of the feasibility distance matrix
begin
X < − Nearest Neighbor heuristic;
repeat
X’ < − Quantum-Perturbation(X)
X” < − VND(X’)
if X” is better than X’ then
X < − X”
end
until optimal solution is found or time limit is met;
end
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10. The problem: TSP-TW
TSP
Numerous applications in many different areas (Logistics, Artificial
Intelligence, Machine Learning, Software Technology etc).
Symmetric TSP, Asymmetric TSP, Multiple TSP.
TSP is the problem of finding the shortest Hamiltonian cycle.
NP-hard.
Significant in various fields, such as operational research and
theoretical computer science.
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11. The problem: TSP-TW
TSP Formulation
An undirected graph G = (V, E), if symmetrical.
A directed graph G = (V, A), if asymmetric.
The set V = {1,2,3, ..., n} is the set of vertices.
A = {(i, j): i, j ∈V, i < j} is the set of the edges.
By n we denote a number of cities (nodes).
A cost matrix C = (ci,j ) defined on E.
The total number of possible paths is equal to (n-1)!/2.
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12. The problem: TSP-TW
TSP-TW TSP with Time-Windows
TSP-TW is a variant of the TSP
Cities (or customers) should be visited in a certain period (or
“window”).
It limits the search tree because all TSP solutions are not necessarily
TSP-TW solutions.
In TSP, any permutation of cities is a feasible solution, in TSP-TW
even the search of feasible solutions is difficult.
NP-hard
Given a depot, a set of customers, the service time (i.e., the time that
should be spent on client) and a time window (i.e., the start and the
expiration time), the TSP-TW problem refers to finding a shortest
path, which starts and ends at a given depot.
Each customer has been only visited once before its expiry date!
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13. The problem: TSP-TW
TSP-TW TSP with Time-Windows
The agent is allowed to reach the customer before its ready time, but
must wait.
Obviously, there are paths that do not allow the agent to respect the
deadlines of all customers. We call these paths infeasible paths.
TSP-TW can be formulated as a TSP, satisfying all timing
constraints and minimizing the total distance traveled.
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14. Computational Results
Experimental results (1/2)
Proposed qGVNS was implemented in Java.
Applied on 10 randomly selected benchmark TSP-TW instances from
various datasets.
Stopping criteria:
1 a feasible solution
2 720-second limit
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15. Computational Results
Experimental results (2/2)
Table: Experimental Results.
Name N Max Window Length Solution Cost Best Solution
n20w120.001 20 120 354.03 16.75
n20w120.002 20 120 320.21 21.80
n20w120.003 20 120 370.42 21.55
n20w120.004 20 120 381.60 20.20
n20w180.001 20 180 449.25 71.85
n20w180.002 20 180 397.07 81.70
n40w160.001 40 160 500.19 58.35
n40w160.002 40 160 538.27 57.75
n40w200.001 40 200 484.07 99.70
n40w200.002 40 200 491.49 101.40
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16. Conclusion
Conclusion
Constructive phase qGVNS for solving the TSP-TW has been
introduced.
qGVNS seems to be able to provide a feasible solution by solving the
constructive meta-heuristic proposed to this research work for all
selected instances.
We presented our methodology through experimental results for small
dimension benchmark problems.
Our method seems promising since was retrieved a feasible solution
for each benchmark. Feasibility for TSP with Time Windows is also a
NP-Hard problem.
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17. Conclusion
Future work
1 Extended comparative study between classic GVNS and qGVNS
applied on TSP-TW.
2 Apply different neighborhood structures and neighborhood change
moves.
3 Extend this constructive meta-heuristic to Optimization phase
meta-heuristic for the TSP with Time Windows.
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18. Appendix References
For Further Reading I
Mladenovic, N., Hansen, P.: Variable neighborhood search.
Computers Operations Research 24(11), 10971100 (1997). DOI
10.1016/s0305-0548(97)00031-2
Papalitsas, Ch., Karakostas, P., Kastampolidou, K.,: A Quantum
Inspired GVNS: Some preliminary results. In Advances in
Experimental Medicine and Biology of the Workshop on Natural,
Unconventional, and Bio-inspired Algorithms and Computation
Methods.(GeNeDis 2016), 20-23 October,Sparta,Greece (2016)
Papalitsas, Ch., Giannakis, K., Andronikos, Th., Theotokis, D.,
Sifaleras, A.: Initialization methods for the tsp with time windows
using variable neighborhood search. In:IEEE Proc. of the 6th
International Conference on Information, Intelligence, Systems and
Applications (IISA 2015), 6-8 July, Corfu, Greece (2015)
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19. Appendix References
Any Questions?
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