Multilevel Parallel Computations for Solving Multistage Multicriteria Optimization Problems

In the present paper, a novel approach for solving the computationally costly multicriteria optimization problems is considered. Within the framework of the developed approach, the obtaining of the efficient decisions is ensured by means of several different methods for the scalarization of the efficiency criteria. The proposed approach provides an opportunity to alter the scalarization methods and the parameters of these ones in the course of computations that results in the necessity of multiple solving the time-consuming global optimization problems. Overcoming the computational complexity is provided by reusing the computed search information and efficient parallel computing on high-performance computing systems. The performed numerical experiments confirmed the developed approach to allow reducing the amount and time of computations for solving the time-consuming multicriteria optimization problems.

[1]  A. Zhigljavsky.  Stochastic Global Optimization , 2008, International Encyclopedia of Statistical Science.

[2]  Victor P. Gergel,et al.  Multistage Global Search Using Various Scalarization Schemes in Multicriteria Optimization Problems , 2019, WCGO.

[3]  Patrick J. Driscoll,et al.  Decision Making in Systems Engineering and Management , 2007 .

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

[5]  E. Polak,et al.  On Multicriteria Optimization , 1976 .

[6]  Yaroslav D. Sergeyev,et al.  An Information Global Optimization Algorithm with Local Tuning , 1995, SIAM J. Optim..

[7]  R. Marler,et al.  Function-transformation methods for multi-objective optimization , 2005 .

[8]  Yaroslav D. Sergeyev,et al.  A deterministic global optimization using smooth diagonal auxiliary functions , 2015, Commun. Nonlinear Sci. Numer. Simul..

[9]  Panos M. Pardalos,et al.  Recent Advances in Global Optimization , 1991 .

[10]  Roman G. Strongin,et al.  Global optimization with non-convex constraints , 2000 .

[11]  D. Balandin,et al.  Multi-Objective Generalized H2 Control for Optimal Protection from Vibration , 2018, 2018 UKACC 12th International Conference on Control (CONTROL).

[12]  Remigijus Paulavičius,et al.  Simplicial Global Optimization , 2014 .

[13]  Ananthram Swami,et al.  A Survey on Modeling and Optimizing Multi-Objective Systems , 2017, IEEE Communications Surveys & Tutorials.

[14]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

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

[16]  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 .

[17]  Ilya Lebedev,et al.  Solving global optimization problems on GPU cluster , 2016 .

[18]  Roman G. Strongin,et al.  Global multidimensional optimization on parallel computer , 1992, Parallel Comput..

[19]  Roman G. Strongin,et al.  Parallel Computing for Globally Optimal Decision Making , 2003, PaCT.

[20]  Fabio Schoen,et al.  Global Optimization: Theory, Algorithms, and Applications , 2013 .

[21]  Y. Sergeyev,et al.  Parallel Asynchronous Global Search and the Nested Optimization Scheme , 2001 .

[22]  P. Siarry,et al.  Multiobjective Optimization: Principles and Case Studies , 2004 .

[23]  Ilya Lebedev,et al.  Globalizer - A Parallel Software System for Solving Global Optimization Problems , 2017, PaCT.

[24]  Yaroslav D. Sergeyev,et al.  Non-convex multi-objective optimization , 2017, Optim. Methods Softw..

[25]  Evgeny Kozinov,et al.  Accelerating multicriterial optimization by the intensive exploitation of accumulated search data , 2016 .

[26]  Roman G. Strongin,et al.  Parallel computing for globally optimal decision making on cluster systems , 2005, Future Gener. Comput. Syst..

[27]  Victor P. Gergel,et al.  Efficient multicriterial optimization based on intensive reuse of search information , 2018, Journal of Global Optimization.