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Verified methods for computing Pareto sets: General algorithmic analysis

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In many engineering problems, we face multi-objective optimization, with several objective functions f₁,...,fₙ. We want to provide the user with the Pareto set-a set of all possible solutions x which cannot be improved in all categories (i.e., for which $f_j(x') ≥ f_j(x)$ for all j and $f_j(x ) > f_j(x)$ for some j is impossible). The user should be able to select an appropriate trade-off between, say, cost and durability. We extend the general results about (verified) algorithmic computability of maxima locations to show that Pareto sets can also be computed.
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  • Department of Differential Equations, Institute of Mathematics, Budapest University of Technology and Economics (BME), Egry József u. 1, 1111 Budapest, Hungary
  • Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, Texas 79968, USA
  • Aberth, O. (2007). Introduction to Precise Numerical Methods, Academic Press, San Diego, CA.
  • Beeson, M. (1978). Some relations between classical and constructive mathematics, Journal of Symbolic Logic 43(2): 228-246.
  • Beeson, M. (1985). Foundations of Constructive Mathematics: Metamathematical Studies, Springer, Berlin/Heidelberg/New York, NY.
  • Bishop, E. and Bridges, D.S. (1985). Constructive Analysis, Springer-Verlag, Berlin/Heidelberg/New York, NY.
  • Fernández, J. and Tóth, B. (2006). Obtaining the efficient set of biobjective competitive facility location and design problems, Proceedings of the 21th European Conference on Operations Research EURO XXI, Reykjavík, Iceland, pp. T-28.
  • Fernández, J. and Tóth, B. (2007). Obtaining an outer approximation of the efficient set of nonlinear biobjective problems, Journal of Global Optimization 38(2): 315-331.
  • Fernández, J. and Tóth, B. (2009). Obtaining the efficient set of nonlinear biobjective optimization problems via interval branch-and-bound methods, Computational Optimization and Applications 42(3):393-419.
  • Fernández, J., Tóth, B., Plastria, F. and Pelegrín, B. (2006). Reconciling franchisor and franchisee: A planar multiobjective competitive location and design model, in A. Seeger (Ed.) Recent Advances in Optimization, Lecture Notes in Economics and Mathematical Systems, Vol. 563, Berlin/Heidelberg/New York, NY, pp. 375-398.
  • Figueira, J., Greco, S. and Ehrgott, M. (Eds.) (2004). Multiple Criteria Decision Analysis: State of the Art Surveys, Kluwer, Dordrecht.
  • Kreinovich, V. (1975). Uniqueness implies algorithmic computability, Proceedings of the 4th Student Mathematical Conference, Leningrad, USSR, pp. 19-21, (in Russian).
  • Kreinovich, V. (1979). Categories of Space-Time Models, Ph.D. dissertation, Institute of Mathematics, Soviet Academy of Sciences, Siberian Branch, Novosibirsk, (in Russian).
  • Kreinovich, V., Lakeyev, A., Rohn, J. and Kahl, P. (1998). Computational Complexity and Feasibility of Data Processing and Interval Computations, Kluwer, Dordrecht.
  • Kushner, B.A. (1985). Lectures on Constructive Mathematical Analysis, American Mathematical Society, Providence, RI.
  • Nachbar, J.H. and Zame, W.R. (1996). Non-computable strategies and discounted repeated games, Economic Theory 8(1): 103-122.
  • Nickel, S. and Puerto, J. (2005). Location Theory: A Unified Approach, Springer-Verlag, Berlin.
  • Ruzika, S. and Wiecek, M.M. (2005). Approximation methods in multiopbjective programming. Journal of Optimization Theory and Applications 126(3): 473-501.
  • Tóth, B. and Fernández, J. (2006). Obtaining the efficient set of nonlinear biobjective optimization problems via interval branch-and-bound methods, Proceedings of the 12th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics SCAN'06, Duisburg, Germany.
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