Nonuniform covering method as applied to multicriteria optimization problems with guaranteed accuracy

V. V. Podinovskii and V. D. Nogin, Pareto Optimal Decisions in Multicriteria Optimization Problems (Fizmatlit, Moscow, 2007) [in Russian].

R. E. Steuer, Multiple Criteria Optimization: Theory, Computation and Application (Radio i Svyaz’, Moscow, 1992).

A. V. Lotov and I. I. Pospelova, Multiple Criteria Optimization: Theory, Computation and Application (MAKS, Moscow, 2008) [in Russian].

Multi-Objective Optimization-Interactive and Evolutionary Approaches Ed. by J. Branke, K. Deb, K. Miettinen, and R. Slowinski (Springer, Berlin, 2008).

S. Gass and T. Saaty, “Parametric Objective Function II,” Oper. Res. 3, 316–319 (1955).

P. S. Krasnoshchekov, V. V. Morozov, and V. V. Fedorov, “Decomposition in Design Problems,” Izv. Akad. Nauk, Ser. Tekh. Kibern., No. 2, 7–17 (1979).

A. V. Lotov, V. A. Bushenkov, G. K. Kamenev, and O. L. Chernykh, Computer and Search for Balanced Tradeoff: The Feasible Goals Method (Nauka, Moscow, 1997) [in Russian].

Yu. G. Evtushenko and M. A. Potapov, “Methods of Numerical Solutions of Multicriterion Problems,” Sov. Math. Dokl. 34, 420–423 (1987).

A. V. Lotov, V. A. Bushenkov, and G. K. Kamenev, Interactive Decision Maps: Approximation and Visualization of Pareto Frontier (Kluwer, Boston, 2004).

A. Lotov, V. Berezkin, G. Kamenev, and K. Miettinen, “Optimal Control of Cooling Process in Continuous Casting of Steel Using a Visualization-Based Multi-Criteria Approach,” Appl. Math. Model. 29, 653–672 (2005).

V. G. Zhadan, “A Method for the Parametric Representation of Objective Functions in Conditional Multicriterial Optimization,” USSR Comput. Math. Math. Phys. 26(1), 108–115 (1986).

V. G. Zhadan, “An Augmented Lagrange Function Method for Multicriterial Optimization Problems,” USSR Comput. Math. Math. Phys. 28(6), 1–11 (1988).

A. S. Antipin, A. I. Golikov, and E. V. Khoroshilova, “Sensitivity Function: Properties and Applications,” Comput. Math. Math. Phys. 51, 2000–2016 (2011).

A. P. Karpenko, D. A. Moor, and D. T. Mukhlisulina, “Multicriteria Optimization Based on Neural Network, Fuzzy and Neuro-Fuzzy Approximation of Decision Marker’s Utility Function,” Opt. Mem. Neural Networks (Inf. Opt.) 21(1), 1–10 (2012).

Yu. G. Evtushenko, “Numerical Methods for Finding Global Extrema (Case of a Nonuniform Mesh),” USSR Comput. Math. Math. Phys. 11(6), 38–54 (1971).

Yu. G. Evtushenko and V. A. Rat’kin, “Bisection Method for Global Optimization of Multivariable Functions,” Tekh. Kibern., No. 1, 119–127 (1987).

Yu. G. Evtushenko, V. U. Malkova, and A. A. Stanevichyus, “Parallelization of the Global Extremum Searching Process,” Autom. Remote Control 68, 787–798 (2007).

Y. Evtushenko, M. Posypkin, and I. Sigal, “A Framework for Parallel Large-Scale Global Optimization,” Comput. Sci. Res. Develop. 23(3), 211–215 (2009).

Yu. G. Evtushenko and M. A. Posypkin, “Versions of the Method of Nonuniform Coverings for Global Optimization of Mixed Integer Nonlinear Problems,” Dokl. Math. 83, 268–271 (2011).

Yu. G. Evtushenko and M. A. Posypkin, “An Application of the Nonuniform Covering Method to Global Optimization of Mixed Integer Nonlinear Problems,” Comput. Math. Math. Phys. 51, 1286–1298 (2011).

A. P. Karpenko, A. S. Seminikhin, and L. A. Chernaya, “Method for Approximately Constructing the Boundary of the Reachability Set for a Multisection Trunk Manipulator,” Nauka Obrazovanie, No. 1 (2011), http://tech-nogam.edu.ru/doc/165078/html .

A. V. Lotov, “Matching Economy Models with the Use of Reachability Sets,” Mathematical Methods for Analyzing the Interaction of Industrial and Regional Systems, Ed. by E. L. Berlyand and S. B. Barabash (Nauka, Novosibirsk, 1983) [in Russian].

L. V. Kantorovich and G. P. Akilov, Functional Analysis (Pergamon, Oxford, 1982; BKhV, St. Petersburg, 2004).

E. Zitzler, J. Knowles, and L. Thiele, “Quality Assessment of Pareto Set Approximations,” in Multiobjective Optimization: Interactive and Evolutionary Approaches, Lecture Notes Computer Science, Vol. 5252 (Springer, Berlin, 2008), pp. 373–404.

S. Bleuler, M. Laumanns, L. Thiele, and E. Zitzler, “PISA-A Platform and Programming Language Independent Interface for Search Algorithms,” Ed. by C. M. Fonseca, et al. in Conference on Evolutionary Multicriterion Optimization (EMO, 2003), Lecture Notes Computer Science, Vol. 2632 (Springer, Berlin, 2003), pp. 494–508.