Applications of Machine Learning in Solving Vehicle Routing Problem

Report
Applications of Machine
Learning in Solving Vehicle
Routing Problem
RESEARCH TOPICS / Jussi Rasku
Postgraduate seminar
March 3rd 2011
Introduction
No Silver Bullet [1]
The “No Free Lunch” Theorem [2,3,4]
The Ugly Duckling Theorem [5]
[1] Brooks, F.P. (1986). "No Silver Bullet — Essence and Accident in Software Engineering". Proceedings of the IFIP Tenth World
Computing Conference: 1069–1076.
[2] Wolpert, D.H., Macready, W.G. (1995), No Free Lunch Theorems for Search, Technical Report SFI-TR-95-02-010 (Santa Fe
Institute).
[3] Wolpert, D.H., Macready, W.G. (1997), "No Free Lunch Theorems for Optimization," IEEE Transactions on Evolutionary
Computation 1, 67.
[4] Wolpert, D.H. (1996), "“The Lack of A Priori Distinctions between Learning Algorithms," Neural Computation, pp. 1341-1390.
[5] Watanabe, Satosi (1969) (page scan). Knowing and Guessing: A Quantitative Study of Inference and Information. New York:
Wiley. pp. 376–377.
Contents
• Background
• About the Researcher and Thesis
• Vehicle Routing Problem
• Machine Learning
• 5-Phase Research Plan
• Conclusions and Questions
Applications of Machine Learning in Solving Vehicle Routing Problem
Background
About the Researcher
•
•
•
•
Jussi Rasku, DI, M.Sc. (Tech.)
Background in software industry (2001-2008)
•
2001-2002 Windows application development.
•
2002-2008 Machine vision quality control software
development.
Working at University of Jyväskylä since 2/2009 –
in the Research Group on Computational Logistics
Postgraduate studies
•
Started 7/2010
•
Supervised by Tommi Kärkkäinen, Sami Äyrämö
About the Thesis
•
•
•
Topic of my thesis is “Applications of Machine
Learning in Solving Vehicle Routing Problem”
Aim is to discover ways to use intelligent methods
of Machine Learning (ML) in solving Vehicle
Routing Problems (VRP).
Thesis format will be collection of papers
•
First paper to be submitted before summer 2011.
•
Second paper by the end of the year 2011.
•
2 more papers 2012-2014.
•
PhD, winter 2014.
The Vehicle Routing Problem
Depot
Customer
Route
Vehicle Routing Problem Variants
• VRP with time windows (VRPTW)
• Fleet size and mix VRP (FSMVRP)
• Open VRP (OVRP)
• Multi-depot VRP (MDVRP)
• Periodic VRP (PVRP)
• VRP with backhauls (VRPB)
• Pickup and delivery problem (PDP)
• Dynamic VRP (DVRP)
• VRP with stochastic demands (VRPSD)
...And combinations of these like MDVRPTWSD
VRP Solving
•
VRP Solving (recognized issues)
• Many different kind of problem variants to model
and solve.
• In literature there are variety of specialized solving
methods for different VRP types.
• Limited generalization ability and robustness of
known solving methods.
• It is not always clear which algorithms are best for
given problem → Human expertise is needed.
Machine Learning
• Machine Learning
– Allows computers to evolve behaviors based on
previously seen data.
– Can be used as expert systems that remove the
human element to create fully automated
systems.
– Methods that allow us to build computer
programs that improve their performance at some
task through experience.
Automating VRP solving
XXVRPXX
expert translates to
MODEL
SOLVER
SOLUTION
Intelligent methods automate this
Machine learning allows exploiting the special
structure of the problem. Better results are achieved
by using suitable solution methods.
Applications of Machine Learning in Solving Vehicle Routing Problem
Research Plan
Research Plan Outline
• Adapting ML methods in VRP solving is
done in 5 steps:
•
•
•
•
Phase 1: Feature extraction for VRP
Phase 2: Classification of VRP instances
Phase 3: Algorithm parameter prediction
Phase 4: Automatic selection of solving
methods
• Phase 5: Machine Learning Hyperheuristic
Phase 1 : Features for VRP
• How to describe the special structure of…
• … VRP instance
• … VRP solution
• … VRP solving methods
• Features are needed for determining similarity (for
clustering, classification, prediction)
• Existing feature extractors for VRP are charted
• Adapting existing feature extraction methods from other
fields like,
• Graph similarity from graph theory
• Molecule similarity from computational chemistry and
biochemistry
• Clusterability from mathematical analysis
Phase 1: Article
Article: "Feature Descriptors for Rich Vehicle Routing
Problems“
• Submitted Q2/2011 to “Mathematical Methods
of Operations Research”, Springer.
Phase 2 : Classification of Instances
• Recognition of types using max π(R0) -formulation.
• Methods that are specifically tuned to efficiently solve
class prototype case are used to test hypothesis that
solver can benefit from VRP case classification.
• Perhaps unforeseen connections of different VRP types
can be found (explorative analysis)
Classification allows exploiting the special structure of
the problem. Better results are achieved by using
suitable solution methods.
Phase 2 : Classification Process
CASE 1
CASE 1
CASE
CASE 1
CLASSIFIER
CATEGORY 1
PROTOTYPE
Solving
methods
CASE 1
CASE 1
SOLUTION
CATEGORY 2
CASE 1
CASE 3
Phase 2 : Publishing Results
• Can be used to prove the usability of
descriptors of the phase 1.
• Or, the results can be published as separate
paper.
• There could also be separate publication
that verifies the manual taxonomy of VRP’s
found in literature with statistical methods
and clustering.
Phase 3: Parameter Prediction
• Heuristic VRP algorithms have parameters that
adjust their behaviour.
• But what are the right values?
• Machine Learning methods can predict them
from previously seen cases.
• Data Mining, Bayesian learning, Neural Networks etc.
PREDICTION ALGORITHM
(x,y,z) = r(p)
x, y, z
CASE
Problem p
Solving
Methods
f(x,y,z,p)
SOLUTION
Phase 3: Challenges
• Are the features of the Phase 1 usable for prediction?
• We have to collect an knowledge database of problems
we know how to solve and matching parameter values
for those problem instances.
• We need tools to find the right parameter values
when there is lots of time and expertise present.
• To produce enough learning data we need tools for
distributed and batch solving and automation
(Genetic Algorithms and/or Grid Search)
• To test the prediction we need good test heuristic.
Clustering insertion heuristic developed by research
group could be good candidate.
Phase 3: Research
• I’m hoping to do part of the research aboard as
visiting researcher during summer 2011.
• IIASA / YSSP (already applied) with emphasis on
• Problem modeling
• Data warehouse / knowledge base
• Distributed computing
• LION (will contact ASAP) with emphasis on
• Intelligent optimization
• Reactive search
• Tuning metaheuristics
Phase 3: Articles
• “An Adaptive VRP Construction Heuristic Based on
Clustering and Statistical Prediction“
• Submitted Q4/2011 to “Computers & Operations
Research”, Elsevier (Call for Papers “Hierarchical
Optimization and its Application in Engineering”).
• "An Framework for Adaptive Algorithms for Rich
Vehicle Routing Problems Based on Statistical
Prediction“
• Submitted Q2/2012 to "Mathematical Methods of
Operations Research“, Springer.
Phase 4: Algorithm Selection
Building heuristics
2-phase heuristics
Local search heuristics
Metaheuristics
TS
GRASP
VNS
Cross
SA
Eject
CLI
λ-IC
ChI
PA
Or-opt
k-opt
FI
GA
SA
Exch
NN
ACO
Reloc
CkT
GENIEject ChI
CLI
R
Exch
I1
I1
TBB
RFCS
GAP
MA
LNS
SS
HYPERHEURISTIC
?
MODEL
?
?
?
SOLVER
?
?
?
SOLUTION
CLP
Applications of Machine Learning in Solving Vehicle Routing Problem
Phase 5: Bringing it all together
Phase 5: The Hyperheuristic
• Brings the previous research together by introducing
an Machine Learning based Hyperheuristic for
Vehicle Routing Problems.
• Contains following features:
• Knowledge database for Vehicle Routing Problems,
instances, best known solutions and solving trajectories.
• Problem instance analysis and classification.
• Adaptive selection of solving methods.
• Reactive adjusting of solving method parameters.
• Hyperheuristic definition acts as the “glue” that connects
articles forming my thesis.
Conclusions
• From previous TRANS-OPT project we have a solid
modeling framework for Rich Vehicle Routing
Problems.
• By using my prior knowledge in statistics, machine
learning and soft computing new advances in
automating solving vehicle routing problems can be
made.
• Using intelligent methods should improve
Robustness in VRP solving. This has been identified
as an ongoing challenge in the VRP research field.
Addressing this issue is the contribution of my thesis.
Thank you for your attention
I hope something similar to silver bullets, free
lunches or ugly ducklings are found along the way.
Any questions or comments?

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