Bi-objective decision making in global optimization based on statistical models

Antanas Žilinskas1, James M. Calvin2
1Institute of Data Science and Digital Technologies, Vilnius University, Vilnius, Lithuania
2Department of Computer Science, New Jersey Institute of Technology, Newark, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Calvin, J.: Probability models in global optimization. Informatica 27(2), 323–334 (2016)

Calvin, J., Žilinskas, A.: A one-dimensional P-algorithm with convergence rate $$o(n^{-3+\delta })$$ for smooth functions. J. Optim. Theory Appl. 106, 297–307 (2000)

Emmerich, M., Yang, K., Deutz, A., Wang, H., Fonseca, C.: A multicriteria generalization of Bayesian global optimization. In: Pardalos, P.M., Zhigljavsky, A., Žilinskas, J. (eds.) Advances in Stochastic and Deterministic Global Optimization, pp. 229–242. Springer, Berlin (2016)

Gimbutas, A., Žilinskas, A.: An algorithm of simplicial Lipschitz optimization with the bi-criteria selection of simplices for the bi-section. J. Global Optim. (2018). https://doi.org/10.1007/s10898-017-0550-9

Huang, D., Allen, T., Notz, W., Miller, R.: Sequential kriging optimization using multiple-fidelity evaluations. Struct. Multidiscip. Optim. 32, 369–382 (2006)

Jones, D.: A taxonomy of global optimization methods based on response surfaces. J. Glob. Optim. 21, 345–383 (2001)

Kleijnen, J., van Beers, W., van Nieuwenhuyse, I.: Expected improvement in efficient global optimization through bootstrapped kriging. J. Glob. Optim. 54, 59–73 (2012)

Knowles, J.: ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Trans. Evolut. Comput. 10(1), 50–66 (2006)

Knowles, J., Corne, D., Reynolds, A.: Noisy multiobjective optimization on a budget of 250 evaluations. In: Ehrgott, M., et al. (eds.) Lecture Notes in Computer Science, vol. 5467, pp. 36–50. Springer (2009)

Kushner, H.: A versatile stochastic model of a function of unknown and time-varying form. J. Math. Anal. Appl. 5, 150–167 (1962)

Mockus, J.: On Bayes methods for seeking an extremum. Avtomatika i Vychislitelnaja Technika 3, 53–62 (1972). in Russian

Pepelyshev, A.: Fixed-domain asymtotics of the maximum likelihood estiomator and the gaussian process approach for deterministic models. Stat. Methodol. 8(4), 356–362 (2011)

Picheny, V.: Multiobjective optimization using gaussian process emulators via stepwise uncertainty reduction. Stat. Comput. 25, 1265–1280 (2015)

Sasena, M.: Dissertation: Flexibility and Efficiency Enhancements for Constrained Global Design Optimization with Kriging Approximations. Michigan University (2002)

Strongin, R.: Information method of global minimization in the presence of noise. Eng. Cybern. 6, 118–126 (1969). in Russian

Strongin, R.G., Sergeyev, Y.D.: Global Optimization with Non-convex Constraints: Sequential and Parallel Algorithms. Kluwer Academic Publishers, Dordrecht (2000)

Zhigljavsky, A., Žilinskas, A.: Stochastic Global Optimization. Springer, Berlin (2008)

Žilinskas, A.: One-step Bayesian method for the search of the optimum of one-variable functions. Cybernetics 1, 139–144 (1975). in Russian

Žilinskas, A.: Axiomatic characterization of a global optimization algorithm and investigation of its search strategies. Oper. Res. Lett. 4, 35–39 (1985)

Žilinskas, A.: A statistical model-based algorithm for black-box multi-objective optimisation. Int. J. Syst. Sci. 45(1), 82–92 (2014)

Žilinskas, A.: Global search as a sequence of rational decisions under uncertainty. In: AIP Conference Proceedings, vol. 1776, No. 020001, pp. 1–8 (2016)

Žilinskas, A., Zhigljavsky, A.: Stochastic global optimization: a review on the occasion of 25 years of Informatica. Informatica 27(2), 229–256 (2016)

Žilinskas, A., Žilinskas, J.: A hybrid global optimization algorithm for non-linear least squares regression. J. Glob. Optim. 56, 265–277 (2013)