Switching Between Metamodeling Frameworks for Efficient Multi-Objective Optimization

Evaluating computationally expensive objective and constraint functions is one of the main challenges faced when solving real-world optimization problems. For handling such problems, it is common to use a metamodeling approach. A metamodel is initially formed using a few exact solution evaluations and then optimized the metamodel to find a few infill solutions. The in-fill solutions are then evaluated exactly and another metamodel is formed. This procedure is continued in a progressive manner until all allocated budget of solutions are evaluated. In multi-objective optimization, there are several ways to build and utilize metamodeling approaches. Authors have previously proposed a taxonomy of different metamodeling approaches for multi-objective optimization and provided a comparative study highlighting the advantages and disadvantages of them. In this paper, we argue that it is more efficient to use different metamodeling approaches at different stages of the optimization process and then propose several manual switching strategies between the metamodeling methods. We also introduce a trust region based method to achieve a better convergence behavior. We use the well-known Kriging approach as the core metamodeling method in this study. Our results show the efficacy of the proposed approach on challenging multi-objective optimization problems using a limited budget of high-fidelity evaluations.

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

[2]  Kalyanmoy Deb,et al.  High dimensional model representation for solving expensive multi-objective optimization problems , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[3]  John E. Dennis,et al.  Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems , 1998, SIAM J. Optim..

[4]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[5]  Layne T. Watson,et al.  Efficient global optimization algorithm assisted by multiple surrogate techniques , 2012, Journal of Global Optimization.

[6]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[7]  Kalyanmoy Deb,et al.  A Taxonomy for Metamodeling Frameworks for Evolutionary Multiobjective Optimization , 2019, IEEE Transactions on Evolutionary Computation.

[8]  Daniel Friedrich,et al.  Multi-objective optimisation using surrogate models for the design of VPSA systems , 2015, Comput. Chem. Eng..

[9]  Carlos A. Coello Coello,et al.  A Review of Techniques for Handling Expensive Functions in Evolutionary Multi-Objective Optimization , 2010 .

[10]  Kalyanmoy Deb,et al.  A Generative Kriging Surrogate Model for Constrained and Unconstrained Multi-objective Optimization , 2016, GECCO.

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

[12]  Andrzej P. Wierzbicki,et al.  The Use of Reference Objectives in Multiobjective Optimization , 1979 .

[13]  Kalyanmoy Deb,et al.  Classifying Metamodeling Methods for Evolutionary Multi-objective Optimization: First Results , 2017, EMO.

[14]  Tapabrata Ray,et al.  Multi-Objective Optimization With Multiple Spatially Distributed Surrogates , 2016 .

[15]  Shigeru Obayashi,et al.  Kriging Surrogate Model Enhanced by Coordinate Transformation of Design Space Based on Eigenvalue Decomposition , 2015, EMO.

[16]  Jorge Nocedal,et al.  Knitro: An Integrated Package for Nonlinear Optimization , 2006 .

[17]  Donald R. Jones,et al.  A Taxonomy of Global Optimization Methods Based on Response Surfaces , 2001, J. Glob. Optim..

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

[19]  Fabio Schoen,et al.  Global optimization of expensive black box problems with a known lower bound , 2013, J. Glob. Optim..

[20]  Szu Hui Ng,et al.  G-STAR: A new Kriging-based trust region method for global optimization , 2016, 2016 Winter Simulation Conference (WSC).

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

[22]  Kalyanmoy Deb,et al.  Metamodeling for multimodal selection functions in evolutionary multi-objective optimization , 2017, GECCO.

[23]  Kalyanmoy Deb,et al.  Hybrid evolutionary multi-objective optimization and analysis of machining operations , 2012 .

[24]  ChengXiang Zhai,et al.  Exploration-exploitation tradeoff in interactive relevance feedback , 2010, CIKM '10.

[25]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .