On the Statistical Models-Based Multi-objective Optimization

Multi-objective optimization problems with expensive, black-box objectives are difficult to tackle. For such type of single-objective global optimization problems, the algorithms based on the statistical models of objective functions and the concept of rational decision theory are well suitable. In the present paper that approach to constructing of single-objective algorithms is generalized and extended to multi-objective optimization. An algorithm, based on the proposed approach, is implemented. Several numerical examples are presented to illustrate the performance of the implemented algorithm.

[1]  Yaroslav D. Sergeyev,et al.  Numerical computations and mathematical modelling with infinite and infinitesimal numbers , 2012, ArXiv.

[2]  Antanas Zilinskas,et al.  Axiomatic approach to statistical models and their use in multimodal optimization theory , 1982, Math. Program..

[3]  Panos M. Pardalos,et al.  A survey of recent developments in multiobjective optimization , 2007, Ann. Oper. Res..

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

[5]  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.

[6]  S. M. Elsakov,et al.  Homogeneous algorithms for multiextremal optimization , 2010 .

[7]  Aimo A. Törn,et al.  Global Optimization , 1999, Science.

[8]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[9]  Randy L. Haupt,et al.  Practical Genetic Algorithms , 1998 .

[10]  Joshua D. Knowles,et al.  Multiobjective Optimization on a Budget of 250 Evaluations , 2005, EMO.

[11]  A. Keane,et al.  Design search and optimization in aerospace engineering , 2007, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[12]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

[13]  Panos M. Pardalos,et al.  Introduction to Global Optimization , 2000, Introduction to Global Optimization.

[14]  Hirotaka Nakayama,et al.  Sequential Approximate Multiobjective Optimization Using Computational Intelligence , 2009, Vector Optimization.

[15]  Serpil Sayin,et al.  Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming , 2000, Math. Program..

[16]  Michael T. M. Emmerich,et al.  Single- and multiobjective evolutionary optimization assisted by Gaussian random field metamodels , 2006, IEEE Transactions on Evolutionary Computation.

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

[18]  A. ilinskas.  Axiomatic characterization of a global optimization algorithm and investigation of its search strategy , 1985 .

[19]  A. A. Zhigli︠a︡vskiĭ,et al.  Stochastic Global Optimization , 2007 .

[20]  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 .

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

[22]  Jonas Mockus,et al.  Bayesian Approach to Global Optimization , 1989 .

[23]  Kalyanmoy Deb,et al.  Multiobjective optimization , 1997 .

[24]  Antanas Zilinskas,et al.  On strong homogeneity of two global optimization algorithms based on statistical models of multimodal objective functions , 2011, Appl. Math. Comput..

[25]  Panos M. Pardalos,et al.  Handbook of Multicriteria Analysis , 2010 .

[26]  Peter C. Fishburn,et al.  Utility theory for decision making , 1970 .

[27]  Wolfgang Ponweiser,et al.  On Expected-Improvement Criteria for Model-based Multi-objective Optimization , 2010, PPSN.

[28]  H. Kushner.  A versatile stochastic model of a function of unknown and time varying form , 1962 .

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