Journal ArticleDOI
Generalized dynamic programming methods in integer programming
TLDR
In this article, a general integer programming algorithm consisting of problem relaxation, solution of the relaxed problem parametrically by dynamic programming, and generation of kth best solutions until a feasible solution is found is presented.Abstract:
When regarded as a shortest route problem, an integer program can be seen to have a particularly simple structure. This allows the development of an algorithm for finding thekth best solution to an integer programming problem with max{O(kmn), O(k logk)} operations. Apart from its value in the parametric study of an optimal solution, the approach leads to a general integer programming algorithm consisting of (1) problem relaxation, (2) solution of the relaxed problem parametrically by dynamic programming, and (3) generation ofkth best solutions until a feasible solution is found. Elementary methods based on duality for reducingk for a given problem relaxation are then outlined, and some examples and computational aspects are discussed.read more
Citations
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Journal ArticleDOI
Shortest-path algorithms: Taxonomy and annotation
Narsingh Deo,Chi-Yin Pang +1 more
TL;DR: A classification scheme to characterize algorithms for solving shortestpath problems is evolved and a more complete listing of 222 references carefully culled out of a larger body of literature on shortest-path algorithms through the year 1979 is provided.
Journal ArticleDOI
Non-standard approaches to integer programming
TL;DR: The group approach of Gomory is surveyed, showing the importance of subadditivity in integer programming and the generation of valid inequalities, as well the relation to the parametric problem cited above of solving for all right-hand sides.
Journal ArticleDOI
Data Structures and Computer Science Techniques in Operations Research
TL;DR: Some important data structures and computer science techniques, and their applications to operations research problems are discussed, and some of which are novel are novel.
Book ChapterDOI
The Group-Theoretic Approach in Mixed Integer Programming
TL;DR: An overview of the mathematical foundations and recent theoretical and computational advances in the study of the grouptheoretic approach in mixed integer programming and fundamental results about the structure of group relaxations are discussed.
Development and testing of dynamic traffic assignment and simulation procedures for atis/atms applications
TL;DR: A simulation-assignment methodology has been developed to describe user's path choices in the network in response to real-time information, and the resulting flow patterns that propagate through the network, yielding information about overall quality of service and effectiveness, as well as localized information pointing to problem spots and opportunities for improvement.
References
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Book
Dynamic Programming
TL;DR: The more the authors study the information processing aspects of the mind, the more perplexed and impressed they become, and it will be a very long time before they understand these processes sufficiently to reproduce them.
Journal ArticleDOI
An Additive Algorithm for Solving Linear Programs with Zero-One Variables
TL;DR: In this paper, an algorithm for solving linear programs with variables constrained to take only one of the values 0 or 1 is proposed, where the only operations required under the algorithm are additions and subtractions.
Journal ArticleDOI
A procedure for computing the k best solutions to discrete optimization problems and its application to the shortest path problem
TL;DR: It is shown how the K shortest (loopless) paths in an n-node network with positive and negative arcs can be computed with an amount of computation which is O(Kn 3 ).
Journal ArticleDOI
A Method for the Solution of the Nth Best Path Problem
Walter Hoffman,Richard Pavley +1 more