TY - JOUR
T1 - An interior multiple objective primal-dual linear programming algorithm using efficient anchoring points
AU - Arbel, Ami
PY - 1995/9
Y1 - 1995/9
N2 - We present an interior Multiple Objective Linear Programming (MOLP) algorithm based on the path-following primal-dual algorithm. In contrast to the simplex algorithm, which generates a solution path on the exterior of the constraints polytope by following its vertices, the path-following primal-dual algorithm moves through the interior of the polytope. Interior algorithms lend themselves to modifications capable of addressing MOLP problems in a way that is quite different from current solution approaches. In addition, moving through the interior of the polytope results in a solution approach that is less sensitive to problem size than simplex-based MOLP algorithms. The modification of the interior single-objective algorithm to MOLP problems, as presented here, is accomplished by combining the step direction vectors generated by applying the single-objective algorithm to each of the cost vectors into a combined direction vector along which we step from the current iterate to the next iterate.
AB - We present an interior Multiple Objective Linear Programming (MOLP) algorithm based on the path-following primal-dual algorithm. In contrast to the simplex algorithm, which generates a solution path on the exterior of the constraints polytope by following its vertices, the path-following primal-dual algorithm moves through the interior of the polytope. Interior algorithms lend themselves to modifications capable of addressing MOLP problems in a way that is quite different from current solution approaches. In addition, moving through the interior of the polytope results in a solution approach that is less sensitive to problem size than simplex-based MOLP algorithms. The modification of the interior single-objective algorithm to MOLP problems, as presented here, is accomplished by combining the step direction vectors generated by applying the single-objective algorithm to each of the cost vectors into a combined direction vector along which we step from the current iterate to the next iterate.
KW - Interior-point linear programming
KW - Karmarkar’s algorithm
KW - Multicriteria decision making
KW - Multiple objective linear programming
UR - http://www.scopus.com/inward/record.url?scp=84974856869&partnerID=8YFLogxK
U2 - 10.1057/jors.1995.156
DO - 10.1057/jors.1995.156
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AN - SCOPUS:84974856869
SN - 0160-5682
VL - 46
SP - 1121
EP - 1132
JO - Journal of the Operational Research Society
JF - Journal of the Operational Research Society
IS - 9
ER -