- Volume 20 Issue 1
In this paper a face optimization algorithm is developed for solving the problem (P) of optimizing a linear function over the set of efficient solution of a bicriterion linear program. We show that problem (P) can arise in a variety of practical situations. Since the efficient set is in general a nonoconvex set, problem (P) can be classified as a global optimization problem. The algorithm for solving problem (P) is guaranteed to find an exact optimal or almost exact optimal solution for the problem in a finite number of iterations. The algorithm can be easily implemented using only linear programming method.
- Ph. D. dissertation, University of Florida New Algorithmic Approaches for Interactive Multiple Objective Decision Making Aksoy,Y.
- Journal of Optimization Theory and Applications v.26 Existence of Efficient Solutions for Vector Maximization Problems Benson,H.P.
- Journal of Optimization Theory and Applications v.26 Vector Maximization with Two Objective Functions Benson,H.P.
- Journal of Mathematical Analysis and Applications v.98 Optimization over the Efficient Set Benson,H.P.
- European Journal of Operational Research v.25 An Algorithm for Optimizing over the Weakly-Efficient Set Benson,H.P.
- Journal of Global Optimization v.1 An All-Linear Programming Relaxation Algorithm for Optimization over the Efficient Set Benson,H.P.
- Working paper, Department of Decision and Information Sciences, University of Florida A Bisection-Extreme Poin Search Algorithm for Optimizing over the the Efficient Set in the Linear Dependence Case Benson,H.P.
- Discussion Paper, Department of Decision and Information Sciences, University of Florida A Face Search Heuristic Algorithm for Optimizing over the Efficient Set Benson,H.P.;Sayin,S.
- Engineering Costs and Production Economics v.10 Estimates of the Minimum Nondominated Criterion Values in Multiple-Criteria Decision-Making Dessouky,M.I.;Ghiassi,M.;Daves,W.J.
- European Journal of Operational Research v.33 Computational Experience Concerning Payoff Tables and Minimum Criterion Values over the Efficient Set Isermann,H.;Steuer,R.E.
- Linear Programming Murty,K.G.
- Mathematical Programming v.2 Algorithms for the Vector Maximization Problem Philips,J.
- Operations Research Letters v.4 Careful Usage of Pessimistic Values in Needed in Multiple Objective Optimization Weistroffer,H.R.