Abstract
This paper presents a reference point-based interactive algorithm, which has been specifically designed to deal with stochastic multiobjective programming problems. This algorithm combines the classical information used in this kind of methods, i.e. values that the decision maker regards as desirable for each objective, with information about the probabilities the decision maker wishes to accept. This novel aspect allows the method to fully take into account the randomness of the final outcome throughout the whole solution process. These two pieces of information have been introduced in an adapted achievement-scalarizing function, which assures each solution obtained to be probability efficient.
Similar content being viewed by others
References
Ballestero E (2001) Stochastic goal programming: a mean–variance approach. Eur J Oper Res 131: 476–481
Ballestero E (2005) Using stochastic goal programming: some applications to management and a case of industrial production. Inf Syst Oper Res J 43: 63–77
Belton V, Greco S, Eskelinen P, Molina J, Ruiz F, Slowinski R (2008) Interactive Multiobjective Optimization from a Learning Perspective. In: Branke J, Deb K, Miettinen K, Slowinski R (eds) Multiobjective optimization: interactive and evolutionary approaches. Springer, Heidelberg, pp 405–434
Ben Abdelaziz F, Mejri S (2001) Application of goal programming in a multi-objective reservoir operation model in tunisia. Eur J Oper Res 133: 352–361
Benayoun R, Montgolfier J, Tergny J, Laritchev O (1971) Linear programming with multiple objective functions: step method (STEM). Math Program 1: 366–375
Caballero C, Cerda E, Muñoz MM, Rey L (2000) Relations among several efficiency concepts in stochastic multiple objective programming. In: Haimes YY, Steuer R (eds) Research and practice in multiple criteria decision making. Lectures notes in economics and mathematical systems. Springer, Berlin, pp 57–68
Caballero R, Cerda E, Muñoz MM, Rey L, Stancu Minasian IM (2001) Efficient solution concepts and their relations in stochastic multiobjective programming. J Optim Theory Appl 110: 53–74
Goicoechea A, Hansen DR, Duckstein L (1982) Multi-objective decision analysis with engineering and business applications. Wiley, New York
Kataoka S (1963) A stochastic programming model. Econometrica 31: 181–196
Larsen N, Mausser H, Uryasev S (2002) Algorithms for optimization of value-at-risk. In: Pardalos P, Tsitsiringos VK (eds) Financial engineering, e-Commerce and supply chain. Kluwer Academic Publishers, Boston, pp 129–157
Luque M, Caballero R, Molina J, Ruiz F (2007) Equivalent information for multiobjective interactive procedures. Manage Sci 53: 125–134
Luque M, Miettinen K, Eskelinen P, Ruiz F (2009) Incorporating preference information in interactive reference point methods for multiobjective optimization. Omega 37(2): 450–462
Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer Academic Publishers, Massachusetts
Miettinen K, Mäkelä MM (2002) On scalarizing functions in multiobjective optimization. OR Spectrum 24: 193–213
Prékopa A (1995) Stochastic programming. Kluwer Academic Publishers, Dordrecht
Ruiz F, Luque M, Cabello JM (2008) A classification of the weighting schemes in reference point procedures for multiobjective programming. J Oper Res Soc (to appear)
Ruszczyński A, Shapiro A (2003) Stochastic programming. Handbooks in operations research and management science vol 10. Elsevier, Amsterdam
(1990)Slowinski R, Teghem J (eds) Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty. Kluwer Academic Publishers, Dordrecht
Stancu-Minasian IM (1984) Stochastic programming with multiple objective functions. D. Reidel Publishing Company, Dordrecht
Teghem J, Dufrane D, Thauvoye M, Kunsch P (1986) STRANGE: an interactive method for multi-objective linear programming under uncertainty. Eur J Oper Res 26: 65–82
Teghem J, Kunsch P (eds) (1985) Application of multiobjective stochastic linear programming to power systems planning. Eng Costs Prod Econ 9:83–89
Urli B, Nadeau R (1990) Stochastic MOLP with incomplete information: an interactive approach with recourse. J Oper Res Soc 41: 1143–1152
Urli B, Nadeau R (2004) PROMISE/scenarios: an interactive method for multiobjective stochastic linear programming under partial uncertainty. Eur J Oper Res 155: 361–372
Wierzbicki AP (1977) Basic properties of scalarizing functionals for multiobjective optimization. Mathematische Operationsforschung Statistik Optimization 8: 55–60
Wierzbicki AP (1980) The use of reference objectives in multiobjective optimization. In: Fandel G, Gal T (eds) Multiple criteria decision making theory and application. Lecture notes in economics and mathematical systems, vol 177. Springer, Heidelberg, pp 468–486
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Muñoz, M.M., Luque, M. & Ruiz, F. INTEREST: a reference-point-based interactive procedure for stochastic multiobjective programming problems. OR Spectrum 32, 195–210 (2010). https://doi.org/10.1007/s00291-008-0153-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00291-008-0153-4