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October  2009, 5(4): 791-824. doi: 10.3934/jimo.2009.5.791

Robust multiobjective dynamic programming: Minimax envelopes for efficient decisionmaking under scenario uncertainty

Matthew H. Henry 1, and  Yacov Y. Haimes 2,

1. 

Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Road, MS 17-N406, Laurel, MD 20723-6099, United States
2. 

University of Virginia, 112 Olsson Hall, P.O. Box 400736, Charlottesville, VA 22904-4736, United States

Received  February 2007 Revised  June 2009 Published  August 2009

Many sequential decision problems are characterized by multiple objectives and can be formulated as multiobjective dynamic programs. A subset of these problems concerns systems that are only partially observable such that the system response to implemented policies is known to belong to a set of possible system responses but is not uniquely known prior to policy selection. A new methodology is developed to identify optimal strategies in finite-horizon multiobjective decision problems for systems of this type. These strategies will either be minimax efficient with respect to a partial ordering in the multiobjective space or, where minimax efficient strategies do not exist, minimax optimal with respect to a total ordering in a scalar space induced by decisionmaker preferences over the set of objectives. In formulating the dynamic program, system uncertainty is described by a finite set of scenario-specified system models, and the likelihood of any particular scenario is assumed to be unknown. By accounting for different scenarios, the multiobjective dynamic program and the resulting strategies are robust with respect to uncertainty in the underlying policy-response relationships. The solution concept is developed with assurances that the principle of optimality holds. An illustrative example demonstrates the methodology.
Keywords: Multi-objective and goal programming, Dynamic programming, Minimax problems, Necessary conditions and sufficient conditions for optimality..
Mathematics Subject Classification: Primary: 90C29, 90C47, 90C39; Secondary: 49K3.
Citation: Matthew H. Henry, Yacov Y. Haimes. Robust multiobjective dynamic programming: Minimax envelopes for efficient decisionmaking under scenario uncertainty. Journal of Industrial and Management Optimization, 2009, 5 (4) : 791-824. doi: 10.3934/jimo.2009.5.791
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