The concept of B-efficient solution in fair multiobjective optimization problems

Document Type : Research Article

Authors

• D. Foroutannia ¹
• A. Mahmodinejad ²

¹ Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

² Department of Mathematics, Sirjan University of Technology, Sirjan, Iran.

10.22067/ijnao.v7i1.43960

Abstract

A problem that sometimes occurs in multiobjective optimization is the existence of a large set of fairly effcient solutions. Hence, the decision making based on selecting a unique preferred solution is diffcult. Considering models with fair B-effciency relieves some of the burden from the decision maker by shrinking the solution set, since the set of fairly B-efficient solutions is contained within the set of fairly effcient solutions for the same problem. In this paper, first some theoretical and practical aspects of fairly B- effcient solutions are discussed. Then, some scalarization techniques are developed to generate fairly B-effcient solutions.

Keywords

• Fair optimization
• Nondominated
• Equitabilit y
• B-effciency
• Scalarization

20.1001.1.24236977.2017.7.1.4.3

---

References

1. Ehrgott, M. Multicriteria optimization, Springer Verlag, Berlin, 2005.

2. Geoffrion, A. M. Proper efficiency and the theory of vector maximization, Journal of Mathematical Analysis and Applications 22 (1968), 618-630.

3. Kostreva, M.M., and Ogryczak, W. Linear optimization with multiple equitable criteria, RAIRO Operations Research 33 (3) (1999), 275-297.

4. Kostreva, M.M., Ogryczak, W., and Wierzbicki, A. Equitable aggregations in multiple criteria analysis, European Journal of Operational Research 158 (2) (2004), 362-377.

5. Lorenz, M.O. Methods of measuring the concentration of wealth, American Statistical Association, New Series 70 (1905), 209-219.

6. Luc, D.T. Theory of Vector Optimization, Springer Verlag, Berlin, 1989.

7. Marshall, A.W., and Olkin, I. Inequalities: Theory of Majorization and Its Applications, Academic Press, New York, 1979.

8. Ogryczak, W. Multiple criteria linear programming model for portfolio selection, Annals of Operations Research 97 (2000), 143-162.

9. Ogryczak, W. Inequality measures and equitable approaches to location problems, European Journal of Operational Research 122 (2) (2000), 374-391.

10. Ogryczak, W., Luss, H., Pioro, M., Nace, D., and Tomaszewski, A. Fair optimization and networks: a survey, Journal of Applied Mathematics 2014 (2014), Article ID 612018, 25 pages.

11. Ogryczak, W., Wierzbicki, A., and Milewski, M. A multi-criteria approach to fair and efficient bandwidth allocation, Omega 36 (2008), 451-463.

12. Ogryczak, W., and Zawadzki, M. Conditional median: a parametric solution concept for location problems, Annals of Operations Research 110 (2002), 167-181.

13. Steuer, R.E. Multiple Criteria Optimization Theory, Computation and Applications, John Wiley and Sons, New York, 1986.

14. Viennet, R., Fonteix, C., and Marc, I. Multicriteria optimization using a genetic algorithm for determining a Pareto set, International Journal of Systems Science 27 (2) (1996), 255-260.