Choice function based hyper-heuristics for multi-objective optimization

Hyper-heuristics are emerging methodologies that perform a search over the space of heuristics to solve difficult computational optimization problems. There are two main types of hyper-heuristics: selective and generative hyper-heuristics. An online selective hyper-heuristic framework manages a set of low level heuristics and aims to choose the best one at any given time using a performance measure for each low level heuristic. In this study, we propose a selective hyper-heuristic choice function based to solve multi-objective optimization problems. This hyper-heuristic controls and combines the strengths of three well-known multi-objective evolutionary algorithms (NSGAII, SPEA2, and MOGA) as the low level heuristics. The choice function heuristic selection method uses a scheme which ranks four performance measurements. All-Moves is employed as an acceptance strategy, meaning that we accept the output of each low level heuristic whether it improves the quality of the solution or not. Our proposed approached compared to the three low level heuristics when used in isolations and two multi-objective hyper-heuristics; a random hyper-heuristics and an adaptive multi-method search namely (AMALGAM). The experimental results demonstrate the effectiveness of the hyper-heuristic approach over the WFG test suite, a common benchmark for multi-objective optimization.

[1]  David W. Corne,et al.  Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy , 2000, Evolutionary Computation.

[2]  Antonio J. Nebro,et al.  A Study of the Parallelization of the Multi-Objective Metaheuristic MOEA/D , 2010, LION.

[3]  Graham Kendall,et al.  Hyper-Heuristics: An Emerging Direction in Modern Search Technology , 2003, Handbook of Metaheuristics.

[4]  Kalyanmoy Deb,et al.  Controlled Elitist Non-dominated Sorting Genetic Algorithms for Better Convergence , 2001, EMO.

[5]  Edmund K. Burke,et al.  Hybridizations within a graph-based hyper-heuristic framework for university timetabling problems , 2009, J. Oper. Res. Soc..

[6]  Michel Gendreau,et al.  Handbook of Metaheuristics , 2010 .

[7]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[8]  Tong Heng Lee,et al.  Evolutionary Algorithms for Multi-Objective Optimization: Performance Assessments and Comparisons , 2004, Artificial Intelligence Review.

[9]  Hugo Terashima-Marín,et al.  Approximating Multi-Objective Hyper-Heuristics for Solving 2D Irregular Cutting Stock Problems , 2010, MICAI.

[10]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[11]  Ender Özcan,et al.  Constructing Constrained-Version of Magic Squares Using Selection Hyper-heuristics , 2014, Comput. J..

[12]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[13]  D. N. Raad,et al.  Multiobjective Optimization for Water Distribution System Design Using a Hyperheuristic , 2010 .

[14]  Bruce A. Robinson,et al.  Comment on paper “Multi-strategy ensemble evolutionary algorithm for dynamic multi-objective optimization” by Wang and Li , 2010, Memetic Comput..

[15]  Edmund K. Burke,et al.  Examination timetabling using late acceptance hyper-heuristics , 2009, 2009 IEEE Congress on Evolutionary Computation.

[16]  Graham Kendall,et al.  A new model and a hyper-heuristic approach for two-dimensional shelf space allocation , 2013, 4OR.

[17]  Sanja Petrovic,et al.  An Introduction to Multiobjective Metaheuristics for Scheduling and Timetabling , 2004, Metaheuristics for Multiobjective Optimisation.

[18]  Carlos A. Coello Coello,et al.  Solving Multiobjective Optimization Problems Using an Artificial Immune System , 2005, Genetic Programming and Evolvable Machines.

[19]  Amer Farhan Rafique.  Multiobjective hyper heuristic scheme for system design and optimization , 2012 .

[20]  Kent McClymont,et al.  Markov chain hyper-heuristic (MCHH): an online selective hyper-heuristic for multi-objective continuous problems , 2011, GECCO '11.

[21]  Edmund K. Burke,et al.  A Reinforcement Learning - Great-Deluge Hyper-Heuristic for Examination Timetabling , 2010, Int. J. Appl. Metaheuristic Comput..

[22]  Michel Gendreau,et al.  Hyper-heuristics: a survey of the state of the art , 2013, J. Oper. Res. Soc..

[23]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[24]  Hui Li,et al.  An Adaptive Evolutionary Multi-Objective Approach Based on Simulated Annealing , 2011, Evolutionary Computation.

[25]  Eckart Zitzler,et al.  Evolutionary algorithms for multiobjective optimization: methods and applications , 1999 .

[26]  C. Coello,et al.  Multiobjective optimization using a micro-genetic algorithm , 2001 .

[27]  Graham Kendall,et al.  Scheduling English Football Fixtures over the Holiday Period Using Hyper-heuristics , 2010, PPSN.

[28]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

[29]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[30]  Graham Kendall,et al.  Exploring Hyper-heuristic Methodologies with Genetic Programming , 2009 .

[31]  E. Soubeiga,et al.  Multi-Objective Hyper-Heuristic Approaches for Space Allocation and Timetabling , 2005 .

[32]  J. van Leeuwen,et al.  Evolutionary Multi-Criterion Optimization , 2003, Lecture Notes in Computer Science.

[33]  David A. Van Veldhuizen,et al.  Evolutionary Computation and Convergence to a Pareto Front , 1998 .

[34]  Sanja Petrovic,et al.  Case-based selection of initialisation heuristics for metaheuristic examination timetabling , 2007, Expert Syst. Appl..

[35]  Andy J. Keane,et al.  Multi-Objective Optimization Using Surrogates , 2010 .

[36]  Michael G.H. Bell,et al.  Optimisation of a fuzzy logic traffic signal controller by a multiobjective genetic algorithm , 1998 .

[37]  Kent McClymont,et al.  A general multi-objective hyper-heuristic for water distribution network design with discolouration risk , 2013 .

[38]  Bin Li,et al.  Multi-strategy ensemble evolutionary algorithm for dynamic multi-objective optimization , 2010, Memetic Comput..

[39]  Graham Kendall,et al.  Monte Carlo hyper-heuristics for examination timetabling , 2012, Ann. Oper. Res..

[40]  Jésica de Armas,et al.  Hyperheuristic encoding scheme for multi-objective guillotine cutting problems , 2011, GECCO '11.

[41]  Peter J. Fleming,et al.  Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I. A unified formulation , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[42]  Sanja Petrovic,et al.  A Multiobjective Optimisation Technique for Exam Timetabling Based on Trajectories , 2002, PATAT.

[43]  Sanja Petrovic,et al.  A mixture experiments multi-objective hyper-heuristic , 2013, J. Oper. Res. Soc..

[44]  Xin Yao,et al.  Performance Scaling of Multi-objective Evolutionary Algorithms , 2003, EMO.

[45]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[46]  Edmund K. Burke,et al.  The late acceptance Hill-Climbing heuristic , 2017, Eur. J. Oper. Res..

[47]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

[48]  C. Reeves.  Modern heuristic techniques for combinatorial problems , 1993 .

[49]  Graham Kendall,et al.  An Investigation of a Tabu-Search-Based Hyper-Heuristic for Examination Timetabling , 2005 .

[50]  David B. Fogel,et al.  Evolutionary algorithms in theory and practice , 1997, Complex.

[51]  Jing J. Liang,et al.  Problem Definitions for Performance Assessment of Multi-objective Optimization Algorithms , 2007 .

[52]  Gara Miranda,et al.  Hyperheuristics for a Dynamic-Mapped Multi-Objective Island-Based Model , 2009, IWANN.

[53]  Mauro Birattari,et al.  Swarm Intelligence , 2012, Lecture Notes in Computer Science.

[54]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[55]  E. Burke,et al.  A Late Acceptance Strategy in Hill-Climbing for Exam Timetabling Problems , 2008 .

[56]  H. Haario,et al.  An adaptive Metropolis algorithm , 2001 .

[57]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[58]  Lucas Bradstreet,et al.  Use of the WFG Toolkit and PISA for Comparison of MOEAs , 2007, 2007 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making.

[59]  Landa Silva,et al.  Metaheuristic and Multiobjective Approaches for Space Allocation , 2003 .

[60]  D. E. Goldberg,et al.  Simple Genetic Algorithms and the Minimal, Deceptive Problem , 1987 .

[61]  H. Kita,et al.  Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[62]  Ender Özcan,et al.  A comprehensive analysis of hyper-heuristics , 2008, Intell. Data Anal..

[63]  Jürgen Branke,et al.  Memory enhanced evolutionary algorithms for changing optimization problems , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[64]  Silvia Curteanu,et al.  Multi-objective optimization of a stacked neural network using an evolutionary hyper-heuristic , 2012, Appl. Soft Comput..

[65]  Graham Kendall,et al.  A multi-objective hyper-heuristic based on choice function , 2014, Expert Syst. Appl..

[66]  Qing Li,et al.  Multiobjective optimization for crash safety design of vehicles using stepwise regression model , 2008 .

[67]  Xavier Gandibleux,et al.  1984-2004 - 20 Years of Multiobjective Metaheuristics. But What About the Solution of Combinatorial Problems with Multiple Objectives? , 2005, EMO.

[68]  Kay Chen Tan,et al.  A Multiobjective Memetic Algorithm Based on Particle Swarm Optimization , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[69]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[70]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

[71]  Hillol Kargupta,et al.  Signal-to-noise, Crosstalk, and Long Range Problem Difficulty in Genetic Algorithms , 1995, ICGA.

[72]  G. Dueck.  New optimization heuristics , 1993 .

[73]  Xavier Gandibleux,et al.  Hyperheuristic as Component of a Multi-Objective MetaHeuristic , 2009 .

[74]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[75]  Graham K. Rand,et al.  Operational Research Society , 2013 .

[76]  Worthy N. Martin,et al.  Foundations of Genetic Algorithms 6 (Foga-6) , 2001 .

[77]  Graham Kendall,et al.  Hyperheuristics: A Tool for Rapid Prototyping in Scheduling and Optimisation , 2002, EvoWorkshops.

[78]  Graham Kendall,et al.  A Hyperheuristic Approach to Scheduling a Sales Summit , 2000, PATAT.

[79]  David E. Goldberg,et al.  Genetic Algorithm Difficulty and the Modality of Fitness Landscapes , 1994, FOGA.

[80]  Tomoyuki Hiroyasu,et al.  LCGA: Local Cultivation Genetic Algorithm For Multi-objective Optimization Problems , 2002, GECCO.

[81]  Graham Kendall,et al.  Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques , 2013 .

[82]  Amelia C. Regan,et al.  A surrogate-based multiobjective metaheuristic and network degradation simulation model for robust toll pricing , 2014 .

[83]  Nang Saing Moon Kham,et al.  Hyper heuristic based on great deluge and its variants for exam timetabling problem , 2012, ArXiv.

[84]  Gary B. Lamont,et al.  Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art , 2000, Evolutionary Computation.

[85]  Barry McCollum,et al.  Dynamic Job Scheduling on the Grid Environment Using the Great Deluge Algorithm , 2007, PaCT.

[86]  Sanja Petrovic,et al.  Calibrating continuous multi-objective heuristics using mixture experiments , 2012, J. Heuristics.

[87]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[88]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[89]  Ender Özcan,et al.  An Experimental Study on Hyper-heuristics and Exam Timetabling , 2006, PATAT.

[90]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.

[91]  M. P. Gupta,et al.  Software module clustering using a hyper-heuristic based multi-objective genetic algorithm , 2013, 2013 3rd IEEE International Advance Computing Conference (IACC).

[92]  Ender Özcan,et al.  A Hyper-Heuristic Based on Random Gradient, Greedy and Dominance , 2011, ISCIS.

[93]  Xuesong Zhang,et al.  On the use of multi‐algorithm, genetically adaptive multi‐objective method for multi‐site calibration of the SWAT model , 2010 .

[94]  Toshihide Ibaraki,et al.  Metaheuristics : progress as real problem solvers , 2005 .

[95]  Andrzej Jaszkiewicz.  Comparison of local search-based metaheuristics on the multiple objective knapsack problem , 2001 .

[96]  L. Darrell Whitley,et al.  Fundamental Principles of Deception in Genetic Search , 1990, FOGA.

[97]  Graham Kendall,et al.  Channel assignment in cellular communication using a great deluge hyper-heuristic , 2004, Proceedings. 2004 12th IEEE International Conference on Networks (ICON 2004) (IEEE Cat. No.04EX955).

[98]  Lawrence Davis,et al.  Genetic Algorithms and Simulated Annealing , 1987 .

[99]  P. Cowling,et al.  CHOICE FUNCTION AND RANDOM HYPERHEURISTICS , 2002 .

[100]  Jésica de Armas,et al.  Hyperheuristic codification for the multi-objective 2D Guillotine Strip Packing Problem , 2010, IEEE Congress on Evolutionary Computation.

[101]  Jasper A Vrugt,et al.  Improved evolutionary optimization from genetically adaptive multimethod search , 2007, Proceedings of the National Academy of Sciences.

[102]  Tong Heng Lee,et al.  Evolutionary Algorithms for Multi-Objective Optimization: Performance Assessments and Comparisons , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[103]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

[104]  Sanja Petrovic,et al.  A time-predefined local search approach to exam timetabling problems , 2004 .