Abstract
The problem (P) of optimizing a linear function over the efficient set of a multiple objective linear program has many important applications in multiple criteria decision making. Since the efficient set is in general a nonconvex set, problem (P) can be classified as a global optimization problem. Perhaps due to its inherent difficulty, it appears that no precisely-delineated implementable algorithm exists for solving problem (P) globally. In this paper a relaxation algorithm is presented for finding a globally optimal solution for problem (P). The algorithm finds an exact optimal solution to the problem after a finite number of iterations. A detailed discussion is included of how to implement the algorithm using only linear programming methods. Convergence of the algorithm is proven, and a sample problem is solved.
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Research supported by a grant from the College of Business Administration, University of Florida, Gainesville, Florida, U.S.A.
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Benson, H.P. An all-linear programming relaxation algorithm for optimizing over the efficient set. J Glob Optim 1, 83–104 (1991). https://doi.org/10.1007/BF00120667
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DOI: https://doi.org/10.1007/BF00120667