A case study of algorithm selection for the traveling thief problem

Many real-world problems are composed of several interacting components. In order to facilitate research on such interactions, the Traveling Thief Problem (TTP) was created in 2013 as the combination of two well-understood combinatorial optimization problems. With this article, we contribute in four ways. First, we create a comprehensive dataset that comprises the performance data of 21 TTP algorithms on the full original set of 9720 TTP instances. Second, we define 55 characteristics for all TPP instances that can be used to select the best algorithm on a per-instance basis. Third, we use these algorithms and features to construct the first algorithm portfolios for TTP, clearly outperforming the single best algorithm. Finally, we study which algorithms contribute most to this portfolio.

[1]  Kevin Leyton-Brown,et al.  Algorithm runtime prediction: Methods & evaluation , 2012, Artif. Intell..

[2]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

[3]  Yuri Malitsky,et al.  Algorithm Portfolios Based on Cost-Sensitive Hierarchical Clustering , 2013, IJCAI.

[4]  Kevin Leyton-Brown,et al.  SATzilla: Portfolio-based Algorithm Selection for SAT , 2008, J. Artif. Intell. Res..

[5]  Mohamed El Yafrani,et al.  Population-based vs. Single-solution Heuristics for the Travelling Thief Problem , 2016, GECCO.

[6]  Lars Kottho,et al.  Algorithm Selection for Combinatorial Search Problems: A survey , 2012 .

[7]  George B. Dantzig,et al.  The Truck Dispatching Problem , 1959 .

[8]  Toby Walsh,et al.  Handbook of satisfiability , 2009 .

[9]  Ricardo Vilalta,et al.  A Perspective View and Survey of Meta-Learning , 2002, Artificial Intelligence Review.

[10]  Markus Wagner,et al.  Fast Heuristics for the Multiple Traveling Thieves Problem , 2016, GECCO.

[11]  Kevin Leyton-Brown,et al.  Sequential Model-Based Optimization for General Algorithm Configuration , 2011, LION.

[12]  Luca Pulina,et al.  A multi-engine approach to answer-set programming* , 2013, Theory and Practice of Logic Programming.

[13]  Ricardo Vilalta,et al.  Metalearning - Applications to Data Mining , 2008, Cognitive Technologies.

[14]  Kate Smith-Miles,et al.  Towards objective measures of algorithm performance across instance space , 2014, Comput. Oper. Res..

[15]  Roberto Montemanni,et al.  Ant colony optimization for real-world vehicle routing problems , 2007, Swarm Intelligence.

[16]  Gilbert Laporte,et al.  The vehicle routing problem: An overview of exact and approximate algorithms , 1992 .

[17]  S. Martello,et al.  Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem , 1999 .

[18]  F. Pfenning.  Theory and Practice of Logic Programming , 2014 .

[19]  Talal Rahwan,et al.  Using the Shapley Value to Analyze Algorithm Portfolios , 2016, AAAI.

[20]  Xiaodong Li,et al.  Improving Efficiency of Heuristics for the Large Scale Traveling Thief Problem , 2014, SEAL.

[21]  Kevin Leyton-Brown,et al.  Algorithm Runtime Prediction: Methods and Evaluation (Extended Abstract) , 2015, IJCAI.

[22]  Kate Smith-Miles,et al.  Cross-disciplinary perspectives on meta-learning for algorithm selection , 2009, CSUR.

[23]  Raymond Chiong,et al.  Why Is Optimization Difficult? , 2009, Nature-Inspired Algorithms for Optimisation.

[24]  Andrea Lodi,et al.  MIPLIB 2010 , 2011, Math. Program. Comput..

[25]  Markus Wagner,et al.  Analyzing the Effects of Instance Features and Algorithm Parameters for Max–Min Ant System and the Traveling Salesperson Problem , 2015, Front. Robot. AI.

[26]  Yuri Malitsky,et al.  ISAC - Instance-Specific Algorithm Configuration , 2010, ECAI.

[27]  Zbigniew Michalewicz,et al.  How to solve it - modern heuristics: second, revised and extended edition, Second Edition , 2004 .

[28]  Marius Thomas Lindauer,et al.  AutoFolio: An Automatically Configured Algorithm Selector , 2015, J. Artif. Intell. Res..

[29]  Tad Hogg,et al.  An Economics Approach to Hard Computational Problems , 1997, Science.

[30]  Michael Wooldridge,et al.  Computational Aspects of Cooperative Game Theory (Synthesis Lectures on Artificial Inetlligence and Machine Learning) , 2011 .

[31]  Zbigniew Michalewicz,et al.  A comprehensive benchmark set and heuristics for the traveling thief problem , 2014, GECCO.

[32]  F. Hutter,et al.  Hydra-MIP : Automated Algorithm Configuration and Selection for Mixed Integer Programming , 2011 .

[33]  Markus Wagner,et al.  Parameter Prediction Based on Features of Evolved Instances for Ant Colony Optimization and the Traveling Salesperson Problem , 2014, PPSN.

[34]  Joaquin Vanschoren,et al.  Fast Algorithm Selection Using Learning Curves , 2015, IDA.

[35]  Bernd Bischl,et al.  A feature-based comparison of local search and the christofides algorithm for the travelling salesperson problem , 2013, FOGA XII '13.

[36]  Marius Thomas Lindauer,et al.  aspeed: Solver scheduling via answer set programming 1 , 2014, Theory and Practice of Logic Programming.

[37]  Günter Rudolph,et al.  Multiobjective optimization for interwoven systems , 2017 .

[38]  Yuri Malitsky,et al.  Algorithm Selection and Scheduling , 2011, CP.

[39]  Michèle Sebag,et al.  Algorithm Selection as a Collaborative Filtering Problem , 2013 .

[40]  Markus Wagner,et al.  Approximate Approaches to the Traveling Thief Problem , 2015, GECCO.

[41]  Markus Wagner,et al.  Stealing Items More Efficiently with Ants: A Swarm Intelligence Approach to the Travelling Thief Problem , 2016, ANTS Conference.

[42]  Adam Wierzbicki,et al.  Socially inspired algorithms for the travelling thief problem , 2014, GECCO.

[43]  Bernd Bischl,et al.  ASlib: A benchmark library for algorithm selection , 2015, Artif. Intell..

[44]  Patrick R. McMullen,et al.  Ant colony optimization techniques for the vehicle routing problem , 2004, Adv. Eng. Informatics.

[45]  Forschungsinstitut für Diskrete.  Chained Lin-Kernighan for Large Traveling Salesman Problems , 2003 .

[46]  Markus Wagner,et al.  Ant colony optimisation and the traveling salesperson problem: hardness, features and parameter settings , 2013, GECCO '13 Companion.

[47]  Zbigniew Michalewicz,et al.  The travelling thief problem: The first step in the transition from theoretical problems to realistic problems , 2013, 2013 IEEE Congress on Evolutionary Computation.

[48]  Michael Wooldridge,et al.  Computational Aspects of Cooperative Game Theory , 2011, KES-AMSTA.

[49]  Bernd Bischl,et al.  Local Search and the Traveling Salesman Problem: A Feature-Based Characterization of Problem Hardness , 2012, LION.

[50]  Thomas Stützle,et al.  MAX-MIN Ant System , 2000, Future Gener. Comput. Syst..

[51]  Zbigniew Michalewicz.  Ubiquity symposium: Evolutionary computation and the processes of life: the emperor is naked: evolutionary algorithms for real-world applications , 2012, UBIQ.

[52]  Zbigniew Michalewicz,et al.  Evolutionary computation for multicomponent problems: opportunities and future directions , 2016, Optimization in Industry.

[53]  Xiaodong Li,et al.  On investigation of interdependence between sub-problems of the Travelling Thief Problem , 2016, Soft Comput..

[54]  Lars Kotthoff,et al.  Algorithm Selection for Combinatorial Search Problems: A Survey , 2012, AI Mag..

[55]  R. Geoff Dromey,et al.  An algorithm for the selection problem , 1986, Softw. Pract. Exp..

[56]  Marius Thomas Lindauer,et al.  claspfolio 2: Advances in Algorithm Selection for Answer Set Programming , 2014, Theory and Practice of Logic Programming.

[57]  Sergey Polyakovskiy,et al.  Packing While Traveling: Mixed Integer Programming for a Class of Nonlinear Knapsack Problems , 2015, CPAIOR.

[58]  Bernd Bischl,et al.  A novel feature-based approach to characterize algorithm performance for the traveling salesperson problem , 2012, Annals of Mathematics and Artificial Intelligence.

[59]  Erik Ostermann.  How To Solve It Modern Heuristics , 2016 .

[60]  John E. Beasley,et al.  OR-Library: Distributing Test Problems by Electronic Mail , 1990 .

[61]  Kevin Leyton-Brown,et al.  Evaluating Component Solver Contributions to Portfolio-Based Algorithm Selectors , 2012, SAT.

[62]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.

[63]  Yoav Shoham,et al.  Learning the Empirical Hardness of Optimization Problems: The Case of Combinatorial Auctions , 2002, CP.

[64]  Alfred Endres,et al.  The Economic Approach , 2012 .

[65]  Kalyanmoy Deb,et al.  Solving the Bi-objective Traveling Thief Problem with Multi-objective Evolutionary Algorithms , 2017, EMO.