Tuning Optimization Algorithms Under Multiple Objective Function Evaluation Budgets

Most sensitivity analysis studies of optimization algorithm control parameters are restricted to a single objective function evaluation (OFE) budget. This restriction is problematic because the optimality of control parameter values (CPVs) is dependent not only on the problem's fitness landscape, but also on the OFE budget available to explore that landscape. Therefore, the OFE budget needs to be taken into consideration when performing control parameter tuning. This paper presents a new algorithm tuning multiobjective particle swarm optimization (tMOPSO) for tuning the CPVs of stochastic optimization algorithms under a range of OFE budget constraints. Specifically, for a given problem tMOPSO aims to determine multiple groups of CPVs, each of which results in optimal performance at a different OFE budget. To achieve this, the control parameter tuning problem is formulated as a multiobjective optimization problem. Additionally, tMOPSO uses a noise-handling strategy and CPV assessment procedure, which are specialized for tuning stochastic optimization algorithms. Conducted numerical experiments provide evidence that tMOPSO is effective at tuning under multiple OFE budget constraints.

[1]  Andrew John Chipperfield,et al.  Parameter tuning versus adaptation : proof of principle study on differential evolution , 2008 .

[2]  Peter Vamplew,et al.  An efficient approach to unbounded bi-objective archives -: introducing the mak_tree algorithm , 2006, GECCO.

[3]  Raymond Ros,et al.  Real-Parameter Black-Box Optimization Benchmarking 2009: Experimental Setup , 2009 .

[4]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[5]  Antonio J. Nebro,et al.  jMetal: A Java framework for multi-objective optimization , 2011, Adv. Eng. Softw..

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

[7]  Russell C. Eberhart,et al.  Parameter Selection in Particle Swarm Optimization , 1998, Evolutionary Programming.

[8]  Nicola Beume,et al.  SMS-EMOA: Multiobjective selection based on dominated hypervolume , 2007, Eur. J. Oper. Res..

[9]  Thomas Stützle,et al.  Improvement Strategies for the F-Race Algorithm: Sampling Design and Iterative Refinement , 2007, Hybrid Metaheuristics.

[10]  Soon-Thiam Khu,et al.  An Investigation on Preference Order Ranking Scheme for Multiobjective Evolutionary Optimization , 2007, IEEE Transactions on Evolutionary Computation.

[11]  Johann Dréo,et al.  Using performance fronts for parameter setting of stochastic metaheuristics , 2009, GECCO '09.

[12]  Andrew W. Moore,et al.  The Racing Algorithm: Model Selection for Lazy Learners , 1997, Artificial Intelligence Review.

[13]  John J. Grefenstette,et al.  Optimization of Control Parameters for Genetic Algorithms , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[14]  A. E. Eiben,et al.  An MOEA-based Method to Tune EA Parameters on Multiple Objective Functions , 2010, IJCCI.

[15]  R. A. Groeneveld,et al.  Practical Nonparametric Statistics (2nd ed). , 1981 .

[16]  C. Borror Practical Nonparametric Statistics, 3rd Ed. , 2001 .

[17]  Kevin P. Murphy,et al.  An experimental investigation of model-based parameter optimisation: SPO and beyond , 2009, GECCO.

[18]  A. E. Eiben,et al.  Beating the ‘world champion’ evolutionary algorithm via REVAC tuning , 2010, IEEE Congress on Evolutionary Computation.

[19]  Simon Wessing,et al.  On the Effect of Response Transformations in Sequential Parameter Optimization , 2012, Evolutionary Computation.

[20]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

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

[22]  László Pál,et al.  A Comparison of Global Search Algorithms for Continuous Black Box Optimization , 2012, Evolutionary Computation.

[23]  Thomas Stützle,et al.  Automatic Configuration of Multi-Objective ACO Algorithms , 2010, ANTS Conference.

[24]  Thomas Stützle,et al.  A Racing Algorithm for Configuring Metaheuristics , 2002, GECCO.

[25]  M. F. Fuller,et al.  Practical Nonparametric Statistics; Nonparametric Statistical Inference , 1973 .

[26]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[27]  Shahryar Rahnamayan,et al.  Micro-differential evolution with vectorized random mutation factor , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[28]  Jorge J. Moré,et al.  Digital Object Identifier (DOI) 10.1007/s101070100263 , 2001 .

[29]  P. Suganthan,et al.  Problem Definitions and Evaluation Criteria for the CEC 2010 Competition on Constrained Real- Parameter Optimization , 2010 .

[30]  Chao Hu,et al.  A comparative study of probability estimation methods for reliability analysis , 2012 .

[31]  Hussein A. Abbass,et al.  Localization for Solving Noisy Multi-Objective Optimization Problems , 2009, Evolutionary Computation.

[32]  Zbigniew Michalewicz,et al.  Parameter control in evolutionary algorithms , 1999, IEEE Trans. Evol. Comput..

[33]  Qingfu Zhang,et al.  Expensive Multiobjective Optimization by MOEA/D With Gaussian Process Model , 2010, IEEE Transactions on Evolutionary Computation.

[34]  Thomas Stützle,et al.  Automatically Improving the Anytime Behaviour of Multiobjective Evolutionary Algorithms , 2013, EMO.

[35]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[36]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[37]  Andries Petrus Engelbrecht,et al.  The sensitivity of single objective optimization algorithm control parameter values under different computational constraints , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[38]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[39]  Thomas Bartz-Beielstein,et al.  Sequential parameter optimization , 2005, 2005 IEEE Congress on Evolutionary Computation.

[40]  M. E. H. Pedersen,et al.  Tuning & simplifying heuristical optimization , 2010 .

[41]  Andries P. Engelbrecht,et al.  Computational Intelligence: An Introduction , 2002 .

[42]  C. Coello,et al.  Improving PSO-based Multi-Objective Optimization using Crowding , Mutation and �-Dominance , 2005 .

[43]  A. E. Eiben,et al.  Efficient relevance estimation and value calibration of evolutionary algorithm parameters , 2007, 2007 IEEE Congress on Evolutionary Computation.

[44]  Joshua D. Knowles,et al.  Multiobjectivization by Decomposition of Scalar Cost Functions , 2008, PPSN.

[45]  Qingfu Zhang,et al.  Differential Evolution With Composite Trial Vector Generation Strategies and Control Parameters , 2011, IEEE Transactions on Evolutionary Computation.

[46]  Jürgen Teich,et al.  Quad-trees: A Data Structure for Storing Pareto Sets in Multiobjective Evolutionary Algorithms with Elitism , 2005, Evolutionary Multiobjective Optimization.

[47]  A. E. Eiben,et al.  Parameter Tuning of Evolutionary Algorithms: Generalist vs. Specialist , 2010, EvoApplications.

[48]  Mauro Birattari,et al.  The irace Package: Iterated Race for Automatic Algorithm , 2011 .

[49]  H. Beyer Evolutionary algorithms in noisy environments : theoretical issues and guidelines for practice , 2000 .

[50]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[51]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

[52]  Thomas Bartz-Beielstein,et al.  Design and Analysis of Optimization Algorithms Using Computational Statistics , 2004 .

[53]  Matthijs Leendert den Besten,et al.  Simple metaheuristics for scheduling: an empirical investigation into the application of iterated local search to deterministic scheduling problems with tardiness penalties , 2004 .

[54]  Yves Deville,et al.  DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization , 2012 .

[55]  Qingfu Zhang,et al.  Objective Reduction in Many-Objective Optimization: Linear and Nonlinear Algorithms , 2013, IEEE Transactions on Evolutionary Computation.

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

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

[58]  Eckart Zitzler,et al.  Objective Reduction in Evolutionary Multiobjective Optimization: Theory and Applications , 2009, Evolutionary Computation.

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

[60]  Stefan M. Wild,et al.  Benchmarking Derivative-Free Optimization Algorithms , 2009, SIAM J. Optim..

[61]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[62]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

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

[64]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[65]  Carlos A. Coello Coello,et al.  Improving PSO-Based Multi-objective Optimization Using Crowding, Mutation and epsilon-Dominance , 2005, EMO.

[66]  Anne Auger,et al.  Performance evaluation of an advanced local search evolutionary algorithm , 2005, 2005 IEEE Congress on Evolutionary Computation.

[67]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[68]  Schalk Kok,et al.  The sensitivity of multi-objective optimization algorithm performance to objective function evaluation budgets , 2013, 2013 IEEE Congress on Evolutionary Computation.

[69]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[70]  A. E. Eiben,et al.  Comparing parameter tuning methods for evolutionary algorithms , 2009, 2009 IEEE Congress on Evolutionary Computation.

[71]  Andries Petrus Engelbrecht,et al.  Quantifying ruggedness of continuous landscapes using entropy , 2009, 2009 IEEE Congress on Evolutionary Computation.

[72]  Jürgen Branke,et al.  Meta-optimization for parameter tuning with a flexible computing budget , 2012, GECCO '12.

[73]  Arthur C. Sanderson,et al.  JADE: Adaptive Differential Evolution With Optional External Archive , 2009, IEEE Transactions on Evolutionary Computation.

[74]  Thomas Stützle,et al.  Modern Continuous Optimization Algorithms for Tuning Real and Integer Algorithm Parameters , 2010, ANTS Conference.