MULTICRITERIA FINITE DYNAMIC PROGRAMMING
Abstract
Dynamic programming has long been recognized as a valuable tool in solving certain sequential decision processes not amenable to more elegant forms of analysis. In this thesis, the fundamental concepts of dynamic programming are extended to a class of finite, deterministic dynamic programs involving multiple objectives. This class includes multicriteria extensions of the well-known traveling salesman, short-test path, and knapsack problems, among others, and thus is of considerable interest. A comprehensive framework within which the problem of interest can be studied with respect to a general preference relation (rho) over the set of feasible solutions is presented. The relation (rho) can be used to represent a wide variety of preference structures, including ones incorporating efficiency, a full or partially specified value function, or merely a set of paired comparisons, the latter of particular interest from the standpoint of an interactive implementation of the methodology. Several interpretations of the Principle of Optimality are considered. Monotonicity is extended to the general case, and the underlying properties of (rho) which accord it its power, properties obscured in the traditional, single criterion case by the structure of the real numbers, are examined. It is seen that, in practice, conditions sufficient to ensure monotonicity (and hence the ability of dynamic programming to produce the optimal solution(s)) are fairly restrictive. For problems for which monotonicity cannot be verified, an alternative approach, called generalized dynamic programming, is suggested. It is shown that conventional dynamic programming, in which the overall preference relation (rho) is used in determining the functional equations at each state, is but a special case of this new, more general approach. Generalized dynamic programming, allowing for the existence of separate, state-specific relations used in determining the functional equations, is illustrated on a stochastic traveling salesman problem.
Degree
Ph.D.
Subject Area
Management
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