Visualization of a statistical approximation of the Pareto front

A bi-objective optimization problem is considered assuming that the objective functions can be non-convex expensive black-box type functions. A statistical model based visualization method is proposed to aid a decision maker in selecting an appropriate trade-off between objectives in case of scarce available information.

[1]  Kaisa Miettinen,et al.  Survey of methods to visualize alternatives in multiple criteria decision making problems , 2012, OR Spectrum.

[2]  Anatoly Zhigljavsky,et al.  Branch and probability bound methods in multi-objective optimization , 2014, Optimization Letters.

[3]  Roman G. Strongin,et al.  Introduction to Global Optimization Exploiting Space-Filling Curves , 2013 .

[4]  Antanas Zilinskas,et al.  Data analysis and visualisation for robust multi-criteria process optimisation , 2006, Comput. Chem. Eng..

[5]  Y. D. Sergeyev,et al.  Global Optimization with Non-Convex Constraints - Sequential and Parallel Algorithms (Nonconvex Optimization and its Applications Volume 45) (Nonconvex Optimization and Its Applications) , 2000 .

[6]  Antanas Zilinskas.  On the worst-case optimal multi-objective global optimization , 2013, Optim. Lett..

[7]  A. ilinskas,et al.  One-Dimensional global optimization for observations with noise , 2005 .

[8]  Ignacy Kaliszewski,et al.  A theorem on nonconvex functions and its application to vector optimization , 1995 .

[9]  Yaroslav D. Sergeyev,et al.  Acceleration of Univariate Global Optimization Algorithms Working with Lipschitz Functions and Lipschitz First Derivatives , 2013, SIAM J. Optim..

[10]  Antanas Zilinskas,et al.  A one-step worst-case optimal algorithm for bi-objective univariate optimization , 2014, Optim. Lett..

[11]  Antanas Zilinskas,et al.  A statistical model-based algorithm for ‘black-box’ multi-objective optimisation , 2014, Int. J. Syst. Sci..

[12]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[13]  Anatoly Zhigljavsky,et al.  Branch and probability bound methods for global optimization , 1990 .

[14]  Julius Zilinskas,et al.  Globally-biased Disimpl algorithm for expensive global optimization , 2014, Journal of Global Optimization.

[15]  Eric S. Fraga,et al.  Visualization of multi-objective decisions for the optimal design of a pressure swing adsorption system , 2015 .