Using efficient anchoring points for generating search directions in interior multiobjective linear programming

Using efficient anchoring points for generating search directions in interior multiobjective linear programming

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Article ID: iaor1995338
Country: United Kingdom
Volume: 45
Issue: 3
Start Page Number: 330
End Page Number: 344
Publication Date: Mar 1994
Journal: Journal of the Operational Research Society
Authors:
Abstract:

This paper modifies the affine-scaling primal algorithm to multiobjective linear programming (MOLP) problems. The modification is based on generating search directions in the form of projected gradients augmented by search directions pointing toward what are referred to as anchoring points. These anchoring points are located on the boundary of the feasible region and, together with the current, interior, iterate, define a cone which makes the next step towards a solution of the MOLP problem. These anchoring points can be generated in more than one way. This paper presents an approach that generates efficient anchoring points where the choice of termination solution available to the decision maker at each iteration consists of a set of efficient solutions. This set of efficient solutions is being updated during the iterative process so that only the most preferred solutions are retained for future considerations. Current MOLP algorithms are simplex-based and make their progress toward the optimal solution by following an exterior trajectory along the vertices of the constraints polytope. Since the proposed algorithm makes its progress through the interior of the constraints polytope, there is no need for vertex information and, therefore, the search for an acceptable solution may prove less sensitive to problem size. Reference is made to the resulting class of MOLP algorithms that are based on the affine-scaling primal algorithm as affine-scaling interior multiobjective linear programming algorithms.

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