Applications of MachineLearning in Solving Vehicle

Routing ProblemRESEARCH TOPICS / Jussi Rasku

Postgraduate seminarMarch 3rd 2011

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.

Introduction

Contents• Background

• About the Researcher and Thesis• Vehicle Routing Problem• Machine Learning

• 5-Phase Research Plan• Conclusions and Questions

BackgroundApplications of Machine Learning in Solving Vehicle Routing Problem

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 ProblemDepot

CustomerRoute

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– 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.

Machine Learning

XXVRPXX

SOLVER SOLUTIONMODEL

expert translates to

Intelligent methods automate this

Automating VRP solving

Machine learning allows exploiting the special structure of the problem. Better results are achieved by using suitable solution methods.

Research PlanApplications of Machine Learning in Solving Vehicle Routing Problem

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.

CLASSIFIER

CATEGORY 1

Phase 2 : Classification ProcessCASE 1CASE 1CASE

PROTOTYPE

Solvingmethods SOLUTION

CASE 1CASE 1

CASE 1

CATEGORY 2

CASE 1CASE 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.

SolvingMethodsf(x,y,z,p)

SOLUTIONCASEProblem p

PREDICTION ALGORITHM(x,y,z) = r(p)

x, y, z

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

NN Exch

R

CkTReloc

GENIλ-IC

Cross

Ejectk-opt

CLIFI

Or-optI1

GAPCLP

TBBRFCS

PA

Building heuristics

Local search heuristics

2-phase heuristics

ChI

GRASP

SA

TS

VNS

ACO

MA

GA

SS

Metaheuristics

SOLUTIONMODEL

?HYPERHEURISTIC

GA

LNS

CLISA

Exch

Eject ChI I1

??

?

? ? ?SOLVER

Phase 5: Bringing it all togetherApplications of Machine Learning in Solving Vehicle Routing Problem

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.

I hope something similar to silver bullets, free lunches or ugly ducklings are found along the way.

Any questions or comments?

Thank you for your attention