Modeling Rich and Dynamic Vehicle Routing Problems in Heuristiclab
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Leveraging Machine Learning to Solve the Vehicle Routing Problem with Time Windows Julie Poullet
Leveraging Machine Learning to Solve the Vehicle Routing Problem with Time Windows by Julie Poullet M.Eng, Ecole Polytechnique (2018) Submitted to the Sloan School of Management in partial fulfillment of the requirements for the degree of Master of Science in Operations Research at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2020 ○c Massachusetts Institute of Technology 2020. All rights reserved. Author...................................................................... Sloan School of Management April 30th, 2020 Certified by. Matthias Winkenbach Research Scientist Thesis Supervisor Accepted by................................................................. Patrick Jaillet Dugald C. Jackson Professor, Department of Electrical Engineering and Computer Science Co-director, Operations Research Center 2 Leveraging Machine Learning to Solve the Vehicle Routing Problem with Time Windows by Julie Poullet Submitted to the Sloan School of Management on April 30th, 2020, in partial fulfillment of the requirements for the degree of Master of Science in Operations Research Abstract The Vehicle Routing Problem with Time Windows (VRPTW) has been widely studied in the Operations Research (OR) literature given its increasingly widespread applications, rang- ing from school bus scheduling to packages delivery. In the last decades, and in large part due to the surge in e-commerce and shortened promised lead times, the scale of the highly constrained VRPTW instances encountered in real-world applications has significantly in- creased. Simultaneously, various Machine Learning (ML) methods have been developed to tackle combinatorial problems and to leverage complex data structure, but little research has been done on applying these techniques to the VRPTW. In light of this research gap, our thesis develops a process to solve large-scale VRPTW without classical OR routing by proposing a two-stage algorithm. -
Reinforcement Learning for Solving the Vehicle Routing Problem
Industrial and Systems Engineering Reinforcement Learning for Solving the Vehicle Routing Problem Mohammadreza Nazari1, Afshin Oroojlooy1, Lawrence V. Snyder1, and Martin Taka´cˇ1 1Lehigh University ISE Technical Report 19T-002 Reinforcement Learning for Solving the Vehicle Routing Problem Mohammadreza Nazari Afshin Oroojlooy Lawrence V. Snyder Martin Takácˇ Department of Industrial and Systems Engineering Lehigh University, Bethlehem, PA 18015 {mon314,afo214,lvs2,takac}@lehigh.edu Abstract We present an end-to-end framework for solving the Vehicle Routing Problem (VRP) using reinforcement learning. In this approach, we train a single policy model that finds near-optimal solutions for a broad range of problem instances of similar size, only by observing the reward signals and following feasibility rules. We consider a parameterized stochastic policy, and by applying a policy gradient algorithm to optimize its parameters, the trained model produces the solution as a sequence of consecutive actions in real time, without the need to re-train for every new problem instance. On capacitated VRP, our approach outperforms classical heuristics and Google’s OR-Tools on medium-sized instances in solution quality with comparable computation time (after training). We demonstrate how our approach can handle problems with split delivery and explore the effect of such deliveries on the solution quality. Our proposed framework can be applied to other variants of the VRP such as the stochastic VRP, and has the potential to be applied more generally to combinatorial optimization problems. 1 Introduction The Vehicle Routing Problem (VRP) is a combinatorial optimization problem that has been studied in applied mathematics and computer science for decades. -
Metaheuristics ``In the Large''
Metaheuristics “In the Large” Jerry Swan∗, Steven Adriaensen, Alexander E. I. Brownlee, Kevin Hammond, Colin G. Johnson, Ahmed Kheiri, Faustyna Krawiec, J. J. Merelo, Leandro L. Minku, Ender Ozcan,¨ Gisele L. Pappa, Pablo Garc´ıa-S´anchez, Kenneth S¨orensen, Stefan Voß, Markus Wagner, David R. White Abstract Following decades of sustained improvement, metaheuristics are one of the great success stories of optimization research. However, in order for research in metaheuristics to avoid fragmentation and a lack of reproducibility, there is a pressing need for stronger scientific and computational infrastructure to sup- port the development, analysis and comparison of new approaches. To this end, we present the vision and progress of the “Metaheuristics ‘In the Large’ ” project. The conceptual uderpinnings of the project are: truly extensible algo- rithm templates that support reuse without modification, white box problem descriptions that provide generic support for the injection of domain specific knowledge, and remotely accessible frameworks, components and problems that will enhance reproducibility and accelerate the field’s progress. We ar- gue that, via principled choice of infrastructure support, the field can pur- sue a higher level of scientific enquiry. We describe our vision and report on progress, showing how the adoption of common protocols for all metaheuris- tics can help liberate the potential of the field, easing the exploration of the design space of metaheuristics. Keywords: Evolutionary Computation, Operational Research, Heuristic design, Heuristic methods, Architecture, Frameworks, Interoperability 1. Introduction arXiv:2011.09821v4 [cs.NE] 3 Jun 2021 Optimization problems have myriad real world applications [42] and have motivated a wealth of research since before the advent of the digital computer [25]. -
Particle Swarm Optimization
PARTICLE SWARM OPTIMIZATION Thesis Submitted to The School of Engineering of the UNIVERSITY OF DAYTON In Partial Fulfillment of the Requirements for The Degree of Master of Science in Electrical Engineering By SaiPrasanth Devarakonda UNIVERSITY OF DAYTON Dayton, Ohio May, 2012 PARTICLE SWARM OPTIMIZATION Name: Devarakonda, SaiPrasanth APPROVED BY: Raul Ordonez, Ph.D. John Loomis, Ph.D. Advisor Committee Chairman Committee Member Associate Professor Associate Professor Electrical & Computer Engineering Electrical & Computer Engineering Robert Penno, Ph.D. Committee Member Associate Professor Electrical & Computer Engineering John G. Weber, Ph.D. Tony E. Saliba, Ph.D. Associate Dean Dean, School of Engineering School of Engineering & Wilke Distinguished Professor ii ABSTRACT PARTICLE SWARM OPTIMIZATION Name: Devarakonda, SaiPrasanth University of Dayton Advisor: Dr. Raul Ordonez The particle swarm algorithm is a computational method to optimize a problem iteratively. As the neighborhood determines the sufficiency and frequency of information flow, the static and dynamic neighborhoods are discussed. The characteristics of the different methods for the selection of the algorithm for a particular problem are summarized. The performance of particle swarm optimization with dynamic neighborhood is investigated by three different methods. In the present work two more benchmark functions are tested using the algorithm. Conclusions are drawn by testing the different benchmark functions that reflect the performance of the PSO with dynamic neighborhood. And all the benchmark functions are analyzed by both Synchronous and Asynchronous PSO algorithms. iii This thesis is dedicated to my grandmother Jogi Lakshmi Narasamma. iv ACKNOWLEDGMENTS I would like to thank my advisor Dr.Raul Ordonez for being my mentor, guide and personally supporting during my graduate studies and while carrying out the thesis work and offering me excellent ideas. -
Metaheuristic Optimization Frameworks: a Survey and Benchmarking
Soft Comput DOI 10.1007/s00500-011-0754-8 ORIGINAL PAPER Metaheuristic optimization frameworks: a survey and benchmarking Jose´ Antonio Parejo • Antonio Ruiz-Corte´s • Sebastia´n Lozano • Pablo Fernandez Ó Springer-Verlag 2011 Abstract This paper performs an unprecedented com- and affordable time and cost. However, heuristics are parative study of Metaheuristic optimization frameworks. usually based on specific characteristics of the problem at As criteria for comparison a set of 271 features grouped in hand, which makes their design and development a com- 30 characteristics and 6 areas has been selected. These plex task. In order to solve this drawback, metaheuristics features include the different metaheuristic techniques appear as a significant advance (Glover 1977); they are covered, mechanisms for solution encoding, constraint problem-agnostic algorithms that can be adapted to incor- handling, neighborhood specification, hybridization, par- porate the problem-specific knowledge. Metaheuristics allel and distributed computation, software engineering have been remarkably developed in recent decades (Voß best practices, documentation and user interface, etc. A 2001), becoming popular and being applied to many metric has been defined for each feature so that the scores problems in diverse areas (Glover and Kochenberger 2002; obtained by a framework are averaged within each group of Back et al. 1997). However, when new are considered, features, leading to a final average score for each frame- metaheuristics should be implemented and tested, implying work. Out of 33 frameworks ten have been selected from costs and risks. the literature using well-defined filtering criteria, and the As a solution, object-oriented paradigm has become a results of the comparison are analyzed with the aim of successful mechanism used to ease the burden of applica- identifying improvement areas and gaps in specific tion development and particularly, on adapting a given frameworks and the whole set. -
Parameter Meta-Optimization of Metaheuristic Optimization Algorithms
Fachhochschul-Masterstudiengang SOFTWARE ENGINEERING 4232 Hagenberg, Austria Parameter Meta-Optimization of Metaheuristic Optimization Algorithms Diplomarbeit zur Erlangung des akademischen Grades Master of Science in Engineering Eingereicht von Christoph Neumüller, BSc Begutachter: Prof. (FH) DI Dr. Stefan Wagner September 2011 Erklärung Hiermit erkläre ich an Eides statt, dass ich die vorliegende Arbeit selbstständig und ohne fremde Hilfe verfasst, andere als die angegebenen Quellen und Hilfsmit- tel nicht benutzt und die aus anderen Quellen entnommenen Stellen als solche gekennzeichnet habe. Hagenberg, am 4. September 2011 Christoph Neumüller, BSc. ii Contents Erklärung ii Abstract 1 Kurzfassung 2 1 Introduction 3 1.1 Motivation and Goal . .3 1.2 Structure and Content . .4 2 Theoretical Foundations 5 2.1 Metaheuristic Optimization . .5 2.1.1 Trajectory-Based Metaheuristics . .6 2.1.2 Population-Based Metaheuristics . .7 2.1.3 Optimization Problems . 11 2.1.4 Operators . 13 2.2 Parameter Optimization . 17 2.2.1 Parameter Control . 18 2.2.2 Parameter Tuning . 18 2.3 Related Work in Meta-Optimization . 19 3 Technical Foundations 22 3.1 HeuristicLab . 22 3.1.1 Key Concepts . 22 3.1.2 Algorithm Model . 23 3.2 HeuristicLab Hive . 25 3.2.1 Components . 26 4 Requirements 29 5 Implementation 31 5.1 Solution Encoding . 31 5.1.1 Parameter Trees in HeuristicLab . 31 5.1.2 Parameter Configuration Trees . 33 iii Contents iv 5.1.3 Search Ranges . 36 5.1.4 Symbolic Expression Grammars . 37 5.2 Fitness Function . 39 5.2.1 Handling of Infeasible Solutions . 41 5.3 Operators . 41 5.3.1 Solution Creator . -
A Pointer Neural Network for the Vehicle Routing Problem with Task
Information Technology and Control 2020/2/49 237 ITC 2/49 A Pointer Neural Network for the Vehicle Routing Problem with Task Priority and Limited Resources Information Technology and Control Received 2019/11/13 Accepted after revision 2020/03/22 Vol. 49 / No. 2 / 2020 pp. 237-248 DOI 10.5755/j01.itc.49.2.24613 http://dx.doi.org/10.5755/j01.itc.49.2.24613 HOW TO CITE: Ma, H., Sheng, Y., Xia, W. (2020). A Pointer Neural Network for the Vehicle Routing Problem with Task Priority and Limited Resources. Information Technology and Control, 49(1), 237-248. https://doi.org/10.5755/j01.itc.49.2.24613 A Pointer Neural Network for the Vehicle Routing Problem with Task Priority and Limited Resources Huawei Ma, Yuxiang Sheng, Wei Xia School of Management, Hefei University of Technology, Hefei 230000, P.R. China, e-mails: [email protected], [email protected], [email protected] Corresponding author: [email protected] The vehicle routing problem with task priority and limited resources (VRPTPLR) is a generalized version of the vehicle routing problem (VRP) with multiple task priorities and insufficient vehicle capacities. The objec- tive of this problem is to maximize the total benefits. Compared to the traditional mathematical analysis meth- ods, the pointer neural network proposed in this paper continuously learns the mapping relationship between input nodes and output decision schemes based on the actual distribution conditions. In addition, a global at- tention mechanism is adopted in the neural network to improve the convergence rate and results. To verify the effectiveness of the method, we model the VRPTPLR and compare the results with those of genetic algorithm and differential evolution algorithm. -
Rapid and Flexible User-Defined Low-Level Hybridization for Metaheuristics Algorithm in Software Framework
Journal of Software Engineering and Applications, 2012, 5, 873-882 873 http://dx.doi.org/10.4236/jsea.2012.511102 Published Online November 2012 (http://www.SciRP.org/journal/jsea) Rapid and Flexible User-Defined Low-Level Hybridization for Metaheuristics Algorithm in Software Framework S. Masrom*, Siti Z. Z. Abidin, N. Omar Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Shah Alam, Malaysia. Email: *[email protected], [email protected], [email protected] Received September 23rd, 2012; revised October 21st, 2012; accepted October 30th, 2012 ABSTRACT The metaheuristics algorithm is increasingly important in solving many kinds of real-life optimization problems but the implementation involves programming difficulties. As a result, many researchers have relied on software framework to accelerate the development life cycle. However, the available software frameworks were mostly designed for rapid de- velopment rather than flexible programming. Therefore, in order to extend software functions, this approach involves modifying software libraries which requires the programmers to have in-depth understanding about the internal working structure of software and the programming language. Besides, it has restricted programmers for implementing flexible user-defined low-level hybridization. This paper presents the concepts and formal definition of metaheuristics and its low-level hybridization. In addition, the weaknesses of current programming approaches supported by available soft- ware frameworks for metaheuristics are discussed. Responding to the deficiencies, this paper introduces a rapid and flexible software framework with scripting language environment. This approach is more flexible for programmers to create a variety of user-defined low-level hybridization rather than bounded with built-in metaheuristics strategy in software libraries. -
Integrating Heuristiclab with Compilers and Interpreters for Non-Functional Code Optimization
Integrating HeuristicLab with Compilers and Interpreters for Non-Functional Code Optimization Daniel Dorfmeister Oliver Krauss Software Competence Center Hagenberg Johannes Kepler University Linz Hagenberg, Austria Linz, Austria [email protected] University of Applied Sciences Upper Austria Hagenberg, Austria [email protected] ABSTRACT 1 INTRODUCTION Modern compilers and interpreters provide code optimizations dur- Genetic Compiler Optimization Environment (GCE) [5, 6] integrates ing compile and run time, simplifying the development process for genetic improvement (GI) [9, 10] with execution environments, i.e., the developer and resulting in optimized software. These optimiza- the Truffle interpreter [23] and Graal compiler [13]. Truffle is a tions are often based on formal proof, or alternatively stochastic language prototyping and interpreter framework that interprets optimizations have recovery paths as backup. The Genetic Compiler abstract syntax trees (ASTs). Truffle already provides implementa- Optimization Environment (GCE) uses a novel approach, which tions of multiple programming languages such as Python, Ruby, utilizes genetic improvement to optimize the run-time performance JavaScript and C. Truffle languages are compiled, optimized and of code with stochastic machine learning techniques. executed via the Graal compiler directly in the JVM. Thus, GCE In this paper, we propose an architecture to integrate GCE, which provides an option to generate, modify and evaluate code directly directly integrates with low-level interpreters and compilers, with at the interpreter and compiler level and enables research in that HeuristicLab, a high-level optimization framework that features a area. wide range of heuristic and evolutionary algorithms, and a graph- HeuristicLab [20–22] is an optimization framework that provides ical user interface to control and monitor the machine learning a multitude of meta-heuristic algorithms, research problems from process. -
Arxiv:2102.10012V1 [Cs.LG] 19 Feb 2021 Vehicle Routing; Machine Learning; Data Driven Methods; Uncertainties
Analytics and Machine Learning in Vehicle Routing Research Ruibin Baia and Xinan Chena and Zhi-Long Chenb and Tianxiang Cuia and Shuhui Gongc and Wentao Hea and Xiaoping Jiangd and Huan Jina and Jiahuan Jina and Graham Kendalle,f and Jiawei Lia and Zheng Lua and Jianfeng Rena and Paul Wengg,h and Ning Xuei and Huayan Zhanga a School of Computer Science, University of Nottingham Ningbo China, Ningbo, China. b Robert H. Smith School of Business, University of Maryland, MD 20742, USA. c China University of Geosciences, Beijing, China. d National University of Defence Technology, Hefei, China e School of Computer Science, University of Nottingham, UK. f School of Computer Science, University of Nottingham Malaysia, Malaysia g UM-SJTU Joint Institute, Shanghai Jiao Tong University, Shanghai, China. h Department of Automation, Shanghai Jiao Tong University, Shanghai, China. i Faculty of Medicine and Health Sciences, University of Nottingham, UK. ARTICLE HISTORY Compiled February 22, 2021 ABSTRACT The Vehicle Routing Problem (VRP) is one of the most intensively studied com- binatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in real-world VRP applications, Machine Learning (ML) methods have been used in combination with analytical approaches to enhance problem formulations and algorithmic performance across different problem solving scenarios. However, the relevant papers are scattered in several traditional research fields with very differ- ent, sometimes confusing, terminologies. This paper presents a first, comprehensive review of hybrid methods that combine analytical techniques with ML tools in ad- dressing VRP problems. Specifically, we review the emerging research streams on ML-assisted VRP modelling and ML-assisted VRP optimisation. -
Vehicle Routing Problem with Stochastic Demands Using the Cross-Entropy Method
Annals of Operations Research 134, 153–181, 2005 c 2005 Springer Science + Business Media, Inc. Manufactured in The Netherlands. Solving the Vehicle Routing Problem with Stochastic Demands using the Cross-Entropy Method KRISHNA CHEPURI [email protected] Decision Analysis & Portfolio Management, J&J PRD, Titusvile, NJ 08560 TITO HOMEM-DE-MELLO ∗ [email protected] Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208 Received January 2003; Revised August 2003; Accepted January 2004 Abstract. An alternate formulation of the classical vehicle routing problem with stochastic demands (VRPSD)isconsidered. We propose a new heuristic method to solve the problem, based on the Cross-Entropy method. In order to better estimate the objective function at each point in the domain, we incorporate Monte Carlo sampling. This creates many practical issues, especially the decision as to when to draw new samples and how many samples to use. We also develop a framework for obtaining exact solutions and tight lower bounds for the problem under various conditions, which include specific families of demand distributions. This is used to assess the performance of the algorithm. Finally, numerical results are presented for various problem instances to illustrate the ideas. Keywords: vehicle routing problem, stochastic optimization, cross-entropy method 1. Stochastic vehicle routing The classical vehicle routing problem (VRP)isdefined on a graph G = (V, A), where V ={v0,v1,...,vn} is a set of vertices and A ={(vi ,vj ): i, j ∈{0,...,n},vi ,vj ∈ V } is the arc set. A matrix L = (Li, j ) can be defined on A, where the coefficient Li, j defines the distance between nodes vi and v j and is proportional to the cost of travelling the corresponding arc. -
Heuristiclab References
Facts HeuristicLab provides a feature rich software environment for heuristic optimization researchers and practitioners. It is based on a generic and flexible model layer and offers a graphical algorithm designer that enables the user to cre- ate, apply, and analyze heuristic optimization methods. A powerful experimenter allows HeuristicLab users to design and perform parameter tests even in parallel. The results of these tests can be stored and analyzed easily in several configurable charts. HeuristicLab is available under the GPL license and is currently used in education, research, and in- dev.heuristiclab.com dustry projects. System Requirements REFERENCES HEURISTICLAB >> Microsoft Windows XP / Vista / 7 / 8 >> Microsoft .NET Framework 4.0 (full version) A Paradigm-Independent and Extensible Environment for Download Heuristic Optimization >> http://dev.heuristiclab.com Contact Heuristic and Evolutionary Algorithms Laboratory (HEAL) University of Applied Sciences Upper Austria Softwarepark 11, 4232 Hagenberg, Austria Phone: +43 7236 3888 2030 KAROSSERIE & KABINENBAU GMBH Web: http://heal.heuristiclab.com E-Mail: [email protected] KAROSSERIE & KABINENBAU GMBH KAROSSERIE & KABINENBAU GMBH FH OÖ Forschungs & Entwicklungs GmbH • Franz-Fritsch-Str. 11/Top 3 4600 Wels/Austria • Telefonnummer: +43 (0)7242 44808-43 Fax: +43 (0)7242 44808-77 • E-Mail: [email protected] • www.fh-ooe.at Features HeuristicLab >> Rich User Experience The development of HeuristicLab started in 2002, when a Algorithm developers can use a number of included well- A comfortable and feature rich graphical group of researchers in the heuristic optimization domain de- known metaheuristics, a large library of operators, a graphical user interface enables non-program- cided to build a software system for exploring new research algorithm designer and an experiment designer to create and mers to use and apply HeuristicLab.