Journal Article10.1287/OPRE.17.4.600
Efficient Heuristic Procedures for Integer Linear Programming with an Interior
TL;DR: In this article, the authors present and evaluate some new heuristic procedures for seeking an approximate solution of pure integer linear programming problems having only inequality constraints, and present an optimal "bound-and-scan" algorithm that may be used in conjunction with these approximate procedures.
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Abstract: This paper presents and evaluates some new heuristic procedures for seeking an approximate solution of pure integer linear programming problems having only inequality constraints. The computation time required by these methods after obtaining the optimal noninteger solution by the simplex method has generally been only a small fraction of that used by the simplex method for the problems tested which have 15 to 300 original variables. Furthermore, the solution obtained by the better procedures consistently has been close to optimal and frequently has actually been optimal. Plans for generalizing these methods also are outlined. A companion paper presents an optimal "bound-and-scan" algorithm that may be used in conjunction with these approximate procedures.
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Citations
Heuristics for integer programming using surrogate constraints
TL;DR: In this paper, a class of surrogate constraint heuristics are proposed for integer programming problems. But they are based on a simple framework that illuminates the character of several earlier heuristic proposals and provides a variety of new alternatives.
A Genetic Algorithm for the Multidimensional Knapsack Problem
P. C. Chu,John E. Beasley +1 more
TL;DR: A heuristic operator which utilises problem-specific knowledge is incorporated into the standard genetic algorithm approach and is capable of obtaining high-quality solutions for problems of various characteristics.
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Exploring relaxation induced neighborhoods to improve MIP solutions
TL;DR: Two new approaches to exploring interesting, domain-independent neighborhoods in MIP are considered, the more effective of the two, which is called Relaxation Induced Neighborhood Search (RINS), constructs a promising neighborhood using information contained in the continuous relaxation of the MIP model.
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The multidimensional 0–1 knapsack problem: An overview
TL;DR: This paper surveys the main results of the multidimensional 0–1 knapsack problem and focuses on the theoretical properties as well as approximate or exact solutions of this special 0-1 program.
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The feasibility pump
TL;DR: The outcome is that FP, in spite of its simple foundation, proves competitive with ILOG-Cplex both in terms of speed and quality of the first solution delivered.
References
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Frederick S. Hillier,Gerald J. Lieberman +1 more
- 01 Jan 1967
TL;DR: The Simplex Method duality theory and sensitivity analysis for linear programming has been studied extensively in the field of operations research as mentioned in this paper, including the application of queueing theory inventory theory forecasting Markovian decision processes and applications decision analysis simulation.
3.8K
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.
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An Algorithm for the Traveling Salesman Problem
John D. C. Little,Katta G. Murty,Dura W. Sweeney,Caroline Karel +3 more
- 03 Feb 2019
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.
1K
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.
633
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