Hyper-heuristics and Cross-domain Optimisation Gabriela Ochoa Computing Science and Mathematics, School of Natural Sciences University of Stirling, Stirling, Scotland
Outline 1. Hyper-heuristics (for optimisation) Search and optimisation in practice o The need for automation o Motivation, definition, origins, classification o 2. Case studies The HyFlex framework and the cross-domain challenge o Hyper-heuristics for the course timetabling problem o 3. Discussion Contributions/ Collaborations DAASE o Research vision o Gabriela Ochoa, goc@cs.stir.ac.uk
Search and optimisation in practice Many challenging applications in science and industry can be formulated as optimisation problems! Problem Model Real-world • Problem representation problem • Constraints • A fitness function Formulation, Modelling Optimisation/Search Algorithm Problem • Exact methods • Approximate (heuristic) methods Model Solution to the Model Algorithm • Feasible candidate solution • Optimal (or good enough) value of Selection/ the objective function Design Solution Gabriela Ochoa, goc@cs.stir.ac.uk
Algorithm selection, configuration and tuning Holy-Grail: Finding the most suitable optimisation/search algorithm and its correct setting for solving a given problem Algorithm Algorithm Parameter selection configuration tuning Can we automate these processes? Gabriela Ochoa, goc@cs.stir.ac.uk
Autonomous/adaptive (self-*) search approaches • Incorporate ideas from machine learning and statistics Static (Offline) Configuration Dynamic (Online) Control • Algorithm selection • Adaptive operator selection • Algorithm portfolios • Parameter control • Algorithm configuration • Reactive search • Parameter tuning • Adaptive memetic algorithms • Hyper-heuristics • Hyper-heuristics Gabriela Ochoa, goc@cs.stir.ac.uk
Hyper-heuristics: Motivation vs. Decision support systems that are off the Doesn’t peg vs. Taylor made The General Solver exist…. Work well on different Significant scope for future research problems How general we could make hyper-heuristics ? These situations exist ( no free lunch theorem) More General Thanks to Prof. E. K. Burke Problem Specific Solvers and Dr. Rong Qu, For this an the next Slide Gabriela Ochoa, goc@cs.stir.ac.uk
What is a hyper-heuristic? ‘ standard’ search heuristic Operates upon potential Solutions Gabriela Ochoa, goc@cs.stir.ac.uk
Hyper-heuristics : “ Operate on a search space of heuristics ” hyper-heuristic ‘ standard’ search heuristic Operates upon Operates upon heuristics Operates upon potential Solutions potential Solutions Gabriela Ochoa, goc@cs.stir.ac.uk
Classification of hyper-heuristics ( nature of the search space ) Hyper- heuristics Heuristic Heuristic Selection generation Construction Improvement Construction Improvement heuristics heuristics heuristics heuristics Fixed, human-designed low level Heuristic components heuristics Gabriela Ochoa, goc@cs.stir.ac.uk
Case Study 1: Selection (dynamic) hyper-heuristics • The HyFlex software framework • The vehicle routing problem Joint work with: E. K. The Cross- domain ‘Decathlon’ competition • Burke, M. Hyde, T. Curtois, J. Walker M. Gendreau , J. A Vazquez-Rodriguez, Gabriela Ochoa, goc@cs.stir.ac.uk
The concept of HyFlex Hyper-heuristics Problem Domains (general-purpose) (problem-specific ) Pers. AdapHH Sched. VNS-TW VRP HyFlex Others ... Others Software Interface ... Gabriela Ochoa, goc@cs.stir.ac.uk
Vehicle routing domain Mutational Local Ruin & Crossover Search Recreate Two-opt [4] Simple hill- Time-based Combine routes Or-opt [5] climbers radial ruin[6] Two-opt* [2] based on Longest Combine: Shift [1] mutational Location-based orders routes Interchange [1] heuristics radial ruin[6] according to length GENI [3] [1] M. W. P. Savelsbergh. The vehicle routing problem with time windows: Minimizing route duration. INFORMS Journal on Computing, 4(2):146-154, 1992. [2] J-Y. Potvin and J-M. Rousseau. An exchange heuristic for routing problems with time windows. The Journal of the Operational Research Society, 1995. [3] M. Gendreau, A. Hertz, and G. Laporte. A new insertion and postoptimization procedures for the traveling salesman problem. Operations Research, 1992. [4] O. Braysy and M. Gendreau. Vehicle routing problem with time windows, part i: Route construction and local search algorithms. Transportation Science, 2005. [5] I. Or. Traveling salesman-type combinatorial problems and their relation to the logistics of regional blood banking. PhD thesis, Northwestern [6] G. Schrimpf, J. Schneider, H. Stamm-Wilbrandt, and G. Dueck. Record breaking optimization results using the ruin and recreate principle. Journal of Computational Physics, 2000. Gabriela Ochoa, goc@cs.stir.ac.uk
The Competition Reg. participants : 43 (23 countries), Competition entries : 20 (14 countries) Page visits (since May 2011) : Total visits: 5,470, Total page views: 10,929 UK (3) U. Exeter, Poland (1) U. Warwick Canada (2) Poznan U. U. Napier U.de Montreal Czech Republic (1) P. de Montreal Czech Technical U. Prague 3,627 326 Austria (1) Belgium (2) Vienna U. of T. China (2) U. d'Angers 948 Dalian U.of T. U. Libre de Italy (1) Hong Kong P.U U. of Udine Bruxelles Tunisia (1) Taiwan (1) Higher I. of National Taiwan U. Management Colombia (1) 89 164 U. Nacional de New Zealand Colmbia (1) Australia Victoria U. of (1) 179 Wellington Chile (2) U. New U. de Santiago South Wales de Chile Gabriela Ochoa, goc@cs.stir.ac.uk
Results – Top 5: Formula 1 score 200 180 160 140 120 AdapHH VNS-TW 100 ML PHUNTER 80 EPH 60 40 20 0 Total Max-SAT Bin Packing P. Sched. Flow Shop TSP VRP Gabriela Ochoa, goc@cs.stir.ac.uk
Case Study 2: Hyper-heuristics for the Course Timetabling Problem The course timetabling problem • • Search operators • Results Joint work with Jorge A. Soria (PhD Student, University of Leon, Mexico) Jerry Swan, Edmund K. Burke Gabriela Ochoa, goc@cs.stir.ac.uk
Course timetabling problem Representation : set of integers representing indexes Assigns subjects to individual students Events (courses • E = {e 1 , e 2 ,…, e n } of subjects) Time periods • T = {t 1 , t 2 …, t s } Places • P = {p 1 , p 2 …, p s } (classrooms) Fitness function : Students • A = {a 1 , a 2 …, a s } Assignment • quadruple (e,t,p,S) S subset A Timetabling • complete set of n assignments, solution that satisfies the constraints Instances : real-world, ITC 2002, 2007 Gabriela Ochoa, goc@cs.stir.ac.uk
The pool of operators Simple Random Perturbation (SRP) QUESTION : Given K search operators Best Single Perturbation (BSP) • How to select (on the fly) the operator Statistical Dynamic Perturbation (SDP) to be applied next, considering the Double Dynamic Perturbation (DDP) history of their performance? • Swap (SWP) Measuring performance Assigning Two Points Perturbation (2PP) credit Selecting the operator: Fitness Move to Less Conflict (MLC) Improvement + Extreme Credit + Adaptive Pursuit Burke-Abdhulla (BA) Conant-Pablos (LSA) Gabriela Ochoa, goc@cs.stir.ac.uk
Competitive results and 3 new best-known solutions! Gabriela Ochoa, goc@cs.stir.ac.uk
Frequency of selection of the operators, HHRand 200 x iterations Gabriela Ochoa, goc@cs.stir.ac.uk
Frequency of selection of the operators, HHExAP Gabriela Ochoa, goc@cs.stir.ac.uk
Contributions/Collaborations with DAASE partners Good algorithms are Hybrid and Dynamic! • Adaptive approaches can beat state-of-the-art domain specific algorithms • They are more robust and general New metrics for impact/ New credit assignment mechanisms • Multiobjective impact/credit • Considering noisy/costly evaluations: • Online learning: concept drift, ensembles:Adaptive mechanisms from filter theory (multinomial tracking) New problems • SBSE Domains: Requirements, Testing , Improving and Repair • Industrial applications (DAASE industrial partners) Gabriela Ochoa, goc@cs.stir.ac.uk
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