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**Applications of Machine Learning in Solving Vehicle Routing Problem**

RESEARCH TOPICS / Jussi Rasku Postgraduate seminar March 3rd 2011 Let's get started. Professor, fellow researchers. My name is Jussi Rasku. I work in Research group on Computational Logistics. This is my first presentation here at Postgraduate Seminar in Information Technology.

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**Introduction No Silver Bullet [1] The “No Free Lunch” Theorem [2,3,4]**

The Ugly Duckling Theorem [5] What I’m going to present to you is my quest for silver bullets, free lunches and ugly ducklings. I will return to what I mean with them at the end of this presentation. [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 (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 [5] Watanabe, Satosi (1969) (page scan). Knowing and Guessing: A Quantitative Study of Inference and Information. New York: Wiley. pp. 376–377.

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**Contents Background About the Researcher and Thesis**

Vehicle Routing Problem Machine Learning 5-Phase Research Plan Conclusions and Questions Here is the outline of my presentation. In the presentation I will explain my research problems and the vision for research steps I’m going to take to answer them. But first some background…, Then we will take a look into… I hope that there will be some time for questions at the end.

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**Applications of Machine Learning in Solving Vehicle Routing Problem**

Background

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**About the Researcher Jussi Rasku, DI, M.Sc. (Tech.)**

Background in software industry ( ) Windows application development. 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 Tampere university of Technology July

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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 PhD, winter 2014.

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**The Vehicle Routing Problem**

Depot Customer Route The vehicle routing problem (VRP) is a combinatorial optimization problem seeking to service a number of customers with a fleet of vehicles. Vehicle routing problems arise from the fields of transportation, distribution and logistics. Here is an example of clients (red dots) that are to be served with a fleet of vehicles leaving and returning from the depot (green dot). Clients may have constraints like capacities, time windows or compabilities. Solving is done usually with construction and improvement heuristics. Construction heuristics build initial solutions and improvement heuristics do local search to find local optima.

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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 As you can imagine this leads to research that heavily relies on tailored modeling and solving methods.

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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. Answering these problems optimally, or near optimally, has gotten wide attention, since even small improvements in the performance of the supply chain may lead to notable financial and ecological benefits and competitive advantage. However, even the simplest cases have been proved to be NP-hard, which suggests that the problem cannot be solved exactly by examining each solution alternative. Heuristic approaches have been under extensive study during past decade, but truly intelligent heuristics and local search methods have yet not been widely studied, which calls for pioneering research in the area. Solving methods are complex and as the number of professionals working in this field is limited, increasing the intelligence and level of automation in these systems is necessary to make the VRP solving methods usable in the operational level.

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**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.

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**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.

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**Applications of Machine Learning in Solving Vehicle Routing Problem**

Research Plan

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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

15
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(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.

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**Phase 2 : Classification Process**

CASE 1 CASE 1 CASE CASE 1 CLASSIFIER CATEGORY 1 CATEGORY 2 PROTOTYPE CASE 1 CASE 1 CASE 1 CASE 3 Solving methods SOLUTION

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

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

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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 International Institute for Applied Systems Analysis (Vienna, Austria), Young Scientists Summer Program. Advanced Systems Analysis research program, which uses mathematical models and analytical techniques to investigate complex systems with a focus on an integrated, interdisciplinary approach. The institute has long been involved in developing new, more sophisticated methodologies for systems analysis so that better solutions to global problems can be found. The LION (machine Learning and Intelligent OptimizationN) laboratory at the University of Trento (Italy) fosters research and development in intelligent optimization and reactive search techniques for solving relevant problems arising in different application areas, including intelligent transportation systems, computer networks and mobility, mobile services and ubiquitous computing, social networks, clustering and pattern recognition in bio-informatics. Roberto Battiti (research program leader) Mauro Brunato Andrea Passerini

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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**

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

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**Phase 5: Bringing it all together**

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

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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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**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? Brooks argues that at the time of writing the paper there was no silver bullet to make software construction easy enough for anyone to do well. He makes a remark that in the future AI and expert systems may discounted as silver bullets. "The 'no free lunch' theorem of Wolpert and Macready,” is that "any two algorithms are equivalent when their performance is averaged across all possible problems.“ The "no free lunch" results indicate that matching algorithms to problems gives higher average performance than does applying a fixed algorithm to all. The Ugly Duckling theorem is an argument asserting that classification is impossible without some sort of bias. Sort of “eauty is in the eye of the beholder” argument. From these theorems and from previous research it seems promising that Machine Learning methodology can be used to solve some of the issues recognized in VRP research.

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**Linked Research Topics**

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

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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. Storing the preprocessing steps the preprocessing can be done locally. 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: t x y 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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