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Applications of Machine Learning in Solving Vehicle Routing Problem RESEARCH TOPICS / Jussi Rasku Postgraduate seminar March 3 rd 2011

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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

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Contents Background About the Researcher and Thesis Vehicle Routing Problem Machine Learning 5-Phase Research Plan Conclusions and Questions

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Background Applications of Machine Learning in Solving Vehicle Routing Problem

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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

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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.

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The Vehicle Routing Problem Depot Customer Route

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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

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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.

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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

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XXVRPXX SOLVER SOLUTION MODEL 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.

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Research Plan Applications of Machine Learning in Solving Vehicle Routing Problem

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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

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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

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Phase 1: Article Article: "Feature Descriptors for Rich Vehicle Routing Problems“ Submitted Q2/2011 to “Mathematical Methods of Operations Research”, Springer.

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Phase 2 : Classification of Instances Recognition of types using max π(R 0 ) - 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.

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CLASSIFIER CATEGORY 1 Phase 2 : Classification Process CASE 1 CASE PROTOTYPE Solving methods SOLUTION CASE 1 CATEGORY 2 CASE 1 CASE 3

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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.

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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. Solving Methods f(x,y,z,p) SOLUTION CASE Problem p PREDICTION ALGORITHM (x,y,z) = r(p) x, y, z

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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.

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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

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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.

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Phase 4: Algorithm Selection NN Exch R CkT Reloc GENI λ-IC Cross Eject k-opt CLI FI Or-opt I1 GAP CLP TBB RFCS PA Building heuristics Local search heuristics 2-phase heuristics ChI GRASP SA TS VNS ACO MA GA SS Metaheuristics SOLUTION MODEL ? HYPERHEURISTIC GA LNS CLI SA Exch Eject ChI I1 ? ? ? ? ? ? SOLVER

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

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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.

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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.

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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

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Linked Research Topics Applications of Machine Learning in Solving Vehicle Routing Problem

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Prune Groups (1/2) Shortest path calculation can be speeded up up to three million times by preprocessing the road network. Current Shortest Path calculation speedup methods do one way contraction preprocessing. Very fast shortest path queries on static road networks. Not suitable for dynamic road networks or for heterogeneous fleet.

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Prune Groups (2/2) Storing the preprocessing steps the preprocessing can be done locally. Aim is to find efficient speed up technique for dynamic road network.

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Multidimensional clustering (1/3) What means that VRP customers are close to each other? Euclidian distance Shortest path along road network Time windows Capacities / Incompabilities Special requirements

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Multidimensional clustering (2/3) Instead of this: We cluster this: x y t y … and even higher dimensional clustering → Dimension reduction (PCA etc.) → Using clustering to improve algorithm performance → Using clustering in selecting active algorithms

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Multidimensional clustering (3/3) Large Problem Partitioning Necessary for tackling large cases. Using Fuzzy Clustering to split large problems. Swapping nodes between subproblems using fuzzy membership value. R-tree and other methods.

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