Efficient Heuristic Algorithms for Positive 0-1 Polynomial Programming Problems

We develop in this paper two types of heuristic methods for solving the positive 0-1 polynomial programming (PP) problem of finding a 0-1 vector x that maximizes cTx subject to f(x) ≤ b where c, b ≥ 0 and f is an m-vector of polynomials with non-negative coefficients. The various heuristics were fir...

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Veröffentlicht in:Management science Jg. 28; H. 7; S. 829 - 836
1. Verfasser: Granot, Frieda
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Hanover, MD., etc Institute of Management Sciences 01.07.1982
Institute for Operations Research and the Management Sciences
Schlagworte:
Algorithms
Computation
Computer programming
Constraints
Heuristic
Heuristic methods
Heuristics
Input output
Integers
Linear programming
Management science
Methodological problems
Objective functions
Optimal solutions
Polynomials
Variables
Zero
ISSN:0025-1909, 1526-5501
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Zusammenfassung:We develop in this paper two types of heuristic methods for solving the positive 0-1 polynomial programming (PP) problem of finding a 0-1 vector x that maximizes cTx subject to f(x) ≤ b where c, b ≥ 0 and f is an m-vector of polynomials with non-negative coefficients. The various heuristics were first tested on randomly generated sparse problems of up to 50 variables and 50 constraints, and their performance in terms of computational time and effectiveness was investigated. The results were very encouraging. Optimal solutions were consistently obtained by some of the heuristic methods in over 50% of the problems solved. The effectiveness was on the average better than 99% and no less than 96.5%. The computational time using these heuristics is on the average 5% of the time required to solve the PP problems to optimality. Some results for very sparse problems with up to 1000 variables and 200 constraints are also reported.
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ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.28.7.829