Multi-objective multi-generation Gaussian process optimizer for design optimization

We present a multi-objective evolutionary optimization algorithm that uses Gaussian process (GP) regression-based models to select trial solutions in a multi-generation iterative procedure. In each generation, a surrogate model is constructed for each objective function with the sample data. The models are used to evaluate solutions and to select the ones with a high potential before they are evaluated on the actual system. Since the trial solutions selected by the GP models tend to have better performance than other methods that only rely on random operations, the new algorithm has much higher efficiency in exploring the parameter space. Simulations with multiple test cases show that the new algorithm has a substantially higher convergence speed and stability than NSGA-II, MOPSO, and some other more recent algorithms.

[1]  Xiaobiao Huang,et al.  Nonlinear dynamics optimization with particle swarm and genetic algorithms for SPEAR3 emittance upgrade , 2014 .

[2]  Kaisa Miettinen,et al.  A Surrogate-Assisted Reference Vector Guided Evolutionary Algorithm for Computationally Expensive Many-Objective Optimization , 2018, IEEE Transactions on Evolutionary Computation.

[3]  Nando de Freitas,et al.  A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning , 2010, ArXiv.

[4]  G. P. Liu,et al.  A novel multi-objective optimization method based on an approximation model management technique , 2008 .

[5]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[6]  Ye Tian,et al.  PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum] , 2017, IEEE Computational Intelligence Magazine.

[7]  Jianqiang Li,et al.  A novel multi-objective particle swarm optimization with multiple search strategies , 2015, Eur. J. Oper. Res..

[8]  D Robin,et al.  Global Optimization of the Magnetic Lattice Using Genetic Algoritihms , 2008 .

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

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

[11]  Hisao Ishibuchi,et al.  A Framework for Large-Scale Multiobjective Optimization Based on Problem Transformation , 2018, IEEE Transactions on Evolutionary Computation.

[12]  A. G. Zhilinskas,et al.  Single-step Bayesian search method for an extremum of functions of a single variable , 1975 .

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

[14]  Robert Ivor John,et al.  A parallel surrogate-assisted multi-objective evolutionary algorithm for computationally expensive optimization problems , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[15]  Peter Auer,et al.  Using Confidence Bounds for Exploitation-Exploration Trade-offs , 2003, J. Mach. Learn. Res..

[16]  Harold J. Kushner,et al.  A New Method of Locating the Maximum Point of an Arbitrary Multipeak Curve in the Presence of Noise , 1964 .

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

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

[19]  Jonas Mockus,et al.  On Bayesian Methods for Seeking the Extremum and their Application , 1977, IFIP Congress.

[20]  Sanaz Mostaghim,et al.  Comparison study of large-scale optimisation techniques on the LSMOP benchmark functions , 2017, 2017 IEEE Symposium Series on Computational Intelligence (SSCI).

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

[22]  Peter J. Fleming,et al.  Multiobjective optimization and multiple constraint handling with evolutionary algorithms. II. Application example , 1998, IEEE Trans. Syst. Man Cybern. Part A.

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

[24]  Konstantinos Liagkouras,et al.  An Elitist Polynomial Mutation Operator for Improved Performance of MOEAs in Computer Networks , 2013, 2013 22nd International Conference on Computer Communication and Networks (ICCCN).

[25]  Joshua D. Knowles,et al.  ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems , 2006, IEEE Transactions on Evolutionary Computation.

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

[27]  Carlos A. Coello Coello,et al.  A Study of the Parallelization of a Coevolutionary Multi-objective Evolutionary Algorithm , 2004, MICAI.

[28]  George Kourakos,et al.  Development of a multi-objective optimization algorithm using surrogate models for coastal aquifer management. , 2013 .

[29]  Andreas Adelmann,et al.  Machine Learning for Orders of Magnitude Speedup in Multi-Objective Optimization of Particle Accelerator Systems. , 2019 .

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

[31]  A. Xiao,et al.  DIRECT METHODS OF OPTIMIZATION OF STORAGE RING DYNAMIC AND MOMENTUM APERTURE , 2010 .

[32]  Lawrence J. Rybarcyk,et al.  Multi-objective particle swarm and genetic algorithm for the optimization of the LANSCE linac operation , 2014 .

[33]  Charles Sinclair,et al.  Multivariate optimization of a high brightness dc gun photoinjector , 2005 .