Modelling Dynamic Programming-Based Global Constraints in Constraint Programming

Abstract

Dynamic Programming (DP) can solve many complex problems in polynomial or pseudo-polynomial time, and it is widely used in Constraint Programming (CP) to implement powerful global constraints. Implementing such constraints is a nontrivial task beyond the capability of most CP users, who must rely on their CP solver to provide an appropriate global constraint library. This also limits the usefulness of generic CP languages, some or all of whose solvers might not provide the required constraints. A technique was recently introduced for directly modelling DP in CP, which provides a way around this problem. However, no comparison of the technique with other approaches was made, and it was missing a clear formalisation. In this paper we formalise the approach and compare it with existing techniques on MiniZinc benchmark problems, including the flow formulation of DP in Integer Programming. We further show how it can be improved by state reduction methods.

Methods Research and Software Development for Parameters Formalization of the Assignment Task Applicable to the Target Distribution

“…e task of target assignment in conditions of motion uncertainty, parameters and coordinates of targets and parameters of obstacles is relevant. If there is an absence of uncertainty, assignment tasks are successfully solved by the dynamic programming methods [3], then in conditions of uncertainty, these methods are difficult to apply. ere are works [4,5] in which assignment problems are solved by using expert knowledge, methods of the theory of fuzzy sets and fuzzy logic.…”