Journal ArticleDOI
Improved Combinatorial Programming Algorithms for a Class of All-Zero-One Integer Programming Problems
John F. Pierce,Jeffrey S. Lasky +1 more
TLDR
Pierce and Pierce as mentioned in this paper used combinatorial programming to solve a class of integer programming problems in which all elements are zero or one, by representing the problem elements in a binary computer as bits in a word and employing logical "and" and "or" operations in the problem-solving process.Abstract:
In an earlier paper [Pierce, J. F. 1968. Application of combinatorial programming to a class of all-zero-one integer programming problems. Management Sci.15 3, November 191--209.] combinatorial programming procedures were presented for solving a class of integer programming problems in which all elements are zero or one. By representing the problem elements in a binary computer as bits in a word and employing logical “and” and “or” operations in the problem-solving process, a number of problems involving several hundred integer variables were solved in a matter of seconds.
In the present paper a number of improvements in these earlier algorithms are presented, including a new search strategy, methods for reducing the original problem, and mechanisms for feasibility filtering in multi-word problems. With these improvements problem-solving efficiency has been increased in many instances by an order of magnitude. In addition, the present paper contains computational experience obtained in solving problems for the k-best solutions.read more
Citations
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Journal ArticleDOI
Set Partitioning: A survey
Egon Balas,Manfred Padberg +1 more
TL;DR: A survey of theoretical results and solution methods for the set partitioning problem can be found in this article, and while we have tried not to omit anything important, we have no claim to completeness. Critical comments pointing out possible omissions or misstatements are welcome.
Journal ArticleDOI
Application of 0-1 integer programming to multitarget tracking problems
TL;DR: This paper presents a new approach to the solution of multi-target tracking problems that is approached as an unsupervised pattern recognition problem and has the computational structure of the set packing and set partitioning problems of 0-1 integer programming.
Journal ArticleDOI
A new relaxation algorithm and passive sensor data association
TL;DR: In this paper, the measurement-target association problem is formulated as one of maximizing the joint likelihood function of the measurement partition, which leads to a generalization of the 3D assignment (matching) problem, which is known to be NP hard.
Journal ArticleDOI
Optimal solution of set covering/partitioning problems using dual heuristics
M. L. Fisher,P. Kedia +1 more
TL;DR: An algorithm for a mixed set covering/partitioning model that includes as special cases the well-known set covering problem and set partitioning problem is presented.
Journal ArticleDOI
Exact solution of crew scheduling problems using the set partitioning model: Recent successful applications
Roy E. Marsten,Fred Shepardson +1 more
TL;DR: This paper focuses on recent developments that have made this model more attractive and have resulted in several successful implementations, as well as new solution techniques employing Lagrangian relaxation and subgradient optimization.
References
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Journal ArticleDOI
The Truck Dispatching Problem
George B. Dantzig,J. H. Ramser +1 more
TL;DR: A procedure based on a linear programming formulation is given for obtaining a near optimal solution to the optimum routing of a fleet of gasoline delivery trucks between a bulk terminal and a large number of service stations supplied by the terminal.
Book ChapterDOI
An Automatic Method for Solving Discrete Programming Problems
Ailsa H. Land,Alison G. Doig +1 more
TL;DR: In the late 1950s there was a group of teachers and research assistants at the London School of Economics interested in linear programming and its extensions, in particular Helen Makower, George Morton, Ailsa Land and Alison Doig.
Book
An Algorithm for the Traveling Salesman Problem
TL;DR: A “branch and bound” algorithm is presented for solving the traveling salesman problem, where the set of all tours feasible solutions is broken up into increasingly small subsets by a procedure called branching.
Journal ArticleDOI
Integer Programming: Methods, Uses, Computations
TL;DR: This paper attempts to present the major methods, successful or interesting uses, and computational experience relating to integer or discrete programming problems, as well as some special purpose algorithms for use on highly structured problems.
Journal ArticleDOI
On an Integer Program for a Delivery Problem
TL;DR: In this paper, an actual truck delivery problem of general applicability is stated as an integer program and the successful computational performance of Gomory's "cutting plane" algorithm for a set of nine particular problems is discussed.