5 research outputs found
A Dimension-Reduction Algorithm for Multi-Stage Decision Problems with Returns in a Partially Ordered Set
In this paper a two-stage algorithm for finding non-
dominated subsets of partially ordered sets
is established. A connection is then made with dimension reduction in time-dependent
dynamic programming via the notion of a bounding label, a function that bounds
the state-transition cost functions. In this context, the computational burden is partitioned
between a time-independent dynamic programming step carried out on the bounding label and
a direct evaluation carried out on a subset of “real" valued decisions. A computational
application to time-dependent fuzzy dynamic programming is presented
A Generalization of Dynamic Programming for Pareto Optimization in Dynamic Networks
The Algorithm in this paper is designed to find the
shortest path in a network given time-dependent cost functions. It has
the following features: it is recursive; it takes place bath in a
backward dynamic programming phase and in a forward evaluation phase; it
does not need a time-grid such as in Cook and Halsey and Kostreva and
Wiecek's "Algorithm One”; it requires only boundedness (above and
below) of the cost functions; it reduces to backward multi-objective
dynamic programming if there are constant costs. This algorithm has been
successfully applied to multi-stage decision problems where the costs
are a function of the time when the decision is made. There are examples
of further applications to tactical delay in production scheduling and
to production control