A bi-level linear programming problem for computing the nadir point in MOLP
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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 optimizationproblem 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, amixed-integer linear programming problem is presented which obtains the exact nadir values in one stage.
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Journal title
volume 2 issue 7
pages 31- 42
publication date 2016-12-10
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