A two-phase surrogate approach for high-dimensional constrained discrete multi-objective optimization

This paper presents a two-phase surrogate approach for high-dimensional constrained discrete multi-objective optimization. In Phase I, the algorithm searches for a feasible point using surrogates for the constraints and objectives. In Phase I iterations, the algorithm identifies the infeasible points that are nondominated according to three criteria: number of constraint violations, maximum constraint violation, and sum of squares of constraint violations. Moreover, the function evaluation point is chosen from a large number of trial points in the neighborhood of a current nondominated point according to the predicted values of the above criteria. In Phase II, the algorithm searches for Pareto optimal solutions using surrogates for the objectives and constraints. In Phase II iterations, the function evaluation point is chosen from trial points that are predicted to be feasible and nondominated in the neighborhood of a current nondominated point using distance criteria in the objective and decision spaces. The algorithm is implemented using RBF surrogates and tested on the Mazda benchmark problem that has 222 discrete variables, 54 constraints and 2 objectives. The proposed method found feasible points much more quickly and obtained much better sets of nondominated objective vectors than an NSGA-II implementation given a budget of only 3330 simulations.

[1]  Juliane Müller,et al.  SOCEMO: Surrogate Optimization of Computationally Expensive Multiobjective Problems , 2017, INFORMS J. Comput..

[2]  Tea Tusar,et al.  GP-DEMO: Differential Evolution for Multiobjective Optimization based on Gaussian Process models , 2015, Eur. J. Oper. Res..

[3]  Andy J. Keane,et al.  Engineering Design via Surrogate Modelling - A Practical Guide , 2008 .

[4]  Jonathan A. Wright,et al.  Constrained, mixed-integer and multi-objective optimisation of building designs by NSGA-II with fitness approximation , 2015, Appl. Soft Comput..

[5]  Peter A. N. Bosman,et al.  Convolutional neural network surrogate-assisted GOMEA , 2019, GECCO.

[6]  R. Regis.  Constrained optimization by radial basis function interpolation for high-dimensional expensive black-box problems with infeasible initial points , 2014 .

[7]  Tom Dhaene,et al.  A constrained multi-objective surrogate-based optimization algorithm , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[8]  Rommel G. Regis,et al.  High-Dimensional Constrained Discrete Multi-objective Optimization Using Surrogates , 2020, International Conference on Machine Learning, Optimization, and Data Science.

[9]  Pramudita Satria Palar,et al.  Framework for Robust Optimization Combining Surrogate Model, Memetic Algorithm, and Uncertainty Quantification , 2016, ICSI.

[10]  Akira Oyama,et al.  Simultaneous structure design optimization of multiple car models using the K computer , 2017, 2017 IEEE Symposium Series on Computational Intelligence (SSCI).

[11]  Taimoor Akhtar,et al.  Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection , 2016, J. Glob. Optim..

[12]  Julien Bect,et al.  A Bayesian approach to constrained single- and multi-objective optimization , 2015, Journal of Global Optimization.

[13]  Ruck Thawonmas,et al.  Evolutionary algorithm using surrogate assisted model for simultaneous design optimization benchmark problem of multiple car structures , 2018, GECCO.

[14]  Thomas Bäck,et al.  Self-adjusting parameter control for surrogate-assisted constrained optimization under limited budgets , 2017, Appl. Soft Comput..

[15]  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.

[16]  Thomas Bartz-Beielstein,et al.  Model-based methods for continuous and discrete global optimization , 2017, Appl. Soft Comput..

[17]  Rommel G. Regis,et al.  Multi-objective constrained black-box optimization using radial basis function surrogates , 2016, J. Comput. Sci..

[18]  Akira Oyama,et al.  Benchmarking multiobjective evolutionary algorithms and constraint handling techniques on a real-world car structure design optimization benchmark problem , 2018, GECCO.

[19]  Tapabrata Ray,et al.  A Multiple Surrogate Assisted Decomposition-Based Evolutionary Algorithm for Expensive Multi/Many-Objective Optimization , 2019, IEEE Transactions on Evolutionary Computation.

[20]  Akira Oyama,et al.  Proposal of benchmark problem based on real-world car structure design optimization , 2018, GECCO.

[21]  Thomas Bäck,et al.  Preference-based multiobjective optimization using truncated expected hypervolume improvement , 2016, 2016 12th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD).