An all-linear programming relaxation algorithm for optimizing over the efficient set. (English) Zbl 0739.90056

Summary: 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. 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.


90C29 Multi-objective and goal programming
90-08 Computational methods for problems pertaining to operations research and mathematical programming
90B50 Management decision making, including multiple objectives
Full Text: DOI


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