A BI-LEVEL LINEAR PROGRAMMING PROBLEM FOR COMPUTING THE NADIR POINT IN MOLP

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VAKILI J.; DEHGHANI H.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2016 | Volume:2 | Issue:7 Page(s): 31-42

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Title

A BI-LEVEL LINEAR PROGRAMMING PROBLEM FOR COMPUTING THE NADIR POINT IN MOLP

Author(s)

VAKILI J. | DEHGHANI H. | Issue Writer Certificate

Keywords

MULTI-OBJECTIVE LINEAR PROGRAMMING (MOLP)Q1

BI-LEVEL LINEAR PROGRAMMINGQ1

NADIR POINTQ1

Abstract

Computing the exact ideal and nadir criterion values is a very ‎ important subject in ‎ multi- ‎ objective linear programming (MOLP) ‎ problems ‎‎. In fact ‎, ‎ these values define the ideal and NADIR POINTs as lower and ‎ upper bounds on the nondominated points ‎. ‎ Whereas determining the ‎ ideal point is an easy work ‎, ‎ because it is equivalent to optimize a ‎ convex function (linear function) over a convex set which is a convex optimization problem ‎, ‎ but the problem of computing ‎ the NADIR POINT in MOLP is equivalent to solving a nonconvex optimization ‎ problem whose solving is very hard in the general case ‎. ‎‎ In this paper ‎, ‎ a BI-LEVEL LINEAR PROGRAMMING problem is presented for obtaining the nadirpoint in MOLP problems which can be used in general to optimize a ‎ linear function on the nondominated set ‎, ‎ as well ‎. Then ‎, ‎ as one of the solution methods of this problem ‎, ‎ a ‎ mixed-integer linear programming problem is presented which obtains ‎ the exact nadir values in one stage.

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APA: Copy

VAKILI, J., & DEHGHANI, H.. (2016). A BI-LEVEL LINEAR PROGRAMMING PROBLEM FOR COMPUTING THE NADIR POINT IN MOLP. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 2(7), 31-42. SID. https://sid.ir/paper/257296/en

Vancouver: Copy

VAKILI J., DEHGHANI H.. A BI-LEVEL LINEAR PROGRAMMING PROBLEM FOR COMPUTING THE NADIR POINT IN MOLP. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2016;2(7):31-42. Available from: https://sid.ir/paper/257296/en

IEEE: Copy

J. VAKILI, and H. DEHGHANI, “A BI-LEVEL LINEAR PROGRAMMING PROBLEM FOR COMPUTING THE NADIR POINT IN MOLP,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 2, no. 7, pp. 31–42, 2016, [Online]. Available: https://sid.ir/paper/257296/en

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