Adaptive Switching Strategy for Metamodeling Based Multi-objective Optimization : Part II , Simultaneous and Combined Frameworks

Most practical optimization problems are comprised of multiple conflicting objectives and constraints which involve time-consuming simulations. Construction of metamodels from a few high-fidelity solutions and then an optimization of metamodels to find infill solutions in an iterative manner stay as common metamodeling based optimization strategies. The authors have previously proposed a taxonomy of 10 different metamodeling frameworks, each of which metamodels objectives and constraints independently or in an aggregate manner. Of 10 frameworks, five proposed a generative approach in which a single Paretooptimal solution is found at a time and other five frameworks were proposed to find multiple Pareto-optimal solutions simultaneously. In Part I, we have proposed an adaptive switching based metamodeling (G-ASM) method involving generative frameworks only. Motivated by the success of G-ASM on 18 different two to five-objective problems, we develop a simultaneous ASM or (SASM) method by switching among five simultaneous frameworks in successive epochs. Of the five frameworks, M3-2 and M42 frameworks are discussed for the first time here. On the same 18 problems, S-ASM performs better than the individual simultaneous frameworks alone. Then, a more efficient switching strategy (GS-ASM) involving all 10 frameworks is developed and is found to outperform both G-ASM and S-ASM. Finally, GSASM is compared with three other recently proposed multiobjective metamodeling methods and superior performance of GS-ASM is observed. Keywords—Surrogate model, Metamodel, Evolutionary multiobjective optimization, Kriging, Taxonomy.

[1]  Deyi Xue,et al.  A multi-surrogate approximation method for metamodeling , 2011, Engineering with Computers.

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

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

[4]  Tapabrata Ray,et al.  Multiple surrogate assisted multiobjective optimization using improved pre-selection , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[5]  Swagatam Das,et al.  Automatic Clustering Using an Improved Differential Evolution Algorithm , 2007 .

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

[7]  Ye Tian,et al.  A Classification-Based Surrogate-Assisted Evolutionary Algorithm for Expensive Many-Objective Optimization , 2019, IEEE Transactions on Evolutionary Computation.

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

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

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

[11]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints , 2014, IEEE Transactions on Evolutionary Computation.

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

[13]  Kalyanmoy Deb,et al.  Trust-region based algorithms with low-budget for multi-objective optimization , 2018, GECCO.

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

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

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

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