Which efficient solution in multi objective programming problem should be taken?

In practical problems, which can be stated in the form of multi objective programming problem, we have usually a large set of efficient solutions. So, which solution from this set should be taken, appears as a natural question here. In the paper we propose some sustainable principles and simple numerical method for such choice. The method respects aspirations and priorities of decision makers and enables iterations for possible improvement of the solution. In this way decision makers can clearly understand why a particular solution is obtained and when and how it can be improved. The features of the method are explained by a practical example. An applications to bilevel programming problems are also presented, where the both side mapping, between the set of efficient solutions and the set of all possible priorities, is shown. It is illustrated in detail through several linear and nonlinear examples.

[1]  Ralph E. Steuer Multiple criteria optimization , 1986 .

[2]  Young-Jou Lai,et al.  Fuzzy Multiple Objective Decision Making , 2016 .

[3]  R. Benayoun,et al.  Linear programming with multiple objective functions: Step method (stem) , 1971, Math. Program..

[4]  Josip Matejas,et al.  Comparative analysis of application efficiency of two iterative multi objective linear programming methods (MP method and STEM method) , 2018, Central Eur. J. Oper. Res..

[5]  Josip Matejas,et al.  A new iterative method for solving multiobjective linear programming problem , 2014, Appl. Math. Comput..

[6]  C. Hwang,et al.  Fuzzy Multiple Objective Decision Making: Methods And Applications , 1996 .

[7]  Kalyanmoy Deb,et al.  Solving Bilevel Multicriterion Optimization Problems With Lower Level Decision Uncertainty , 2016, IEEE Transactions on Evolutionary Computation.

[8]  Xiaotie Deng,et al.  Complexity Issues in Bilevel Linear Programming , 1998 .

[9]  Sang M. Lee,et al.  Goal programming for decision analysis , 1972 .

[10]  Surabhi Sinha Fuzzy mathematical programming applied to multi-level programming problems , 2003, Comput. Oper. Res..

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

[12]  Surabhi Sinha,et al.  Fuzzy programming approach to multi-level programming problems , 2003, Fuzzy Sets Syst..

[13]  Ibrahim A. Baky Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems , 2009, Fuzzy Sets Syst..

[14]  D. E. Bell,et al.  Conflicting Objectives in Decisions , 1978 .

[15]  Tunjo Perić,et al.  A Fuzzy Linear Programming Approach To Solve Bi- Level Multi-Objective Linear Programming Problems , 2020 .

[16]  Julius Zilinskas,et al.  A preference-based multi-objective evolutionary algorithm R-NSGA-II with stochastic local search , 2016, Central European Journal of Operations Research.

[17]  Bernard Roy,et al.  Problems and methods with multiple objective functions , 1971, Math. Program..

[18]  Abraham Charnes,et al.  Management Models and Industrial Applications of Linear Programming , 1961 .

[19]  Stanley Zionts,et al.  Methods for Solving Management Problems Involving Multiple Objectives , 1980 .

[20]  D. H. Marks,et al.  A review and evaluation of multiobjective programing techniques , 1975 .

[21]  Pierre Hansen,et al.  New Branch-and-Bound Rules for Linear Bilevel Programming , 1989, SIAM J. Sci. Comput..

[22]  Kailash Lachhwani,et al.  On solving multi-level multi objective linear programming problems through fuzzy goal programming approach , 2014 .

[23]  Peter C. Fishburn,et al.  LEXICOGRAPHIC ORDERS, UTILITIES AND DECISION RULES: A SURVEY , 1974 .

[24]  Ibrahim A. Baky Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach , 2010 .

[25]  Kalyanmoy Deb,et al.  A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications , 2017, IEEE Transactions on Evolutionary Computation.

[26]  Jaap Spronk,et al.  Multiple Criteria Decision Methods and Applications , 1985 .

[27]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[28]  Tapan Kumar Roy,et al.  Fuzzy goal programming approach to multilevel programming problems , 2007, Eur. J. Oper. Res..

[29]  Roger M. Y. Ho,et al.  Goal programming and extensions , 1976 .

[30]  Savita Mishra,et al.  Weighting method for bi-level linear fractional programming problems , 2007, Eur. J. Oper. Res..

[31]  Ue-Pyng Wen,et al.  Efficient solutions for the linear bilevel programming problem , 1992 .

[32]  P. Yu Multiple-Criteria Decision Making: "Concepts, Techniques, And Extensions" , 2012 .