Abstract
This paper presents a new surrogate constraint analysis that gives rise to a family of strong valid inequalities called surrogate-knapsack (S-K) cuts. The analytical procedure presented provides a strong S-K cut subject to constraining the values of selected cut coefficients, including the right-hand side. Our approach is applicable to both zero-one integer problems and problems having multiple choice (generalized upper bound) constraints. We also develop a strengthening process that further tightens the S-K cut obtained via the surrogate analysis. Building on this, we develop a polynomial-time separation procedure that successfully generates an S-K cut that renders a given non-integer extreme point infeasible. We show how sequential lifting processes can be viewed in our framework, and demonstrate that our approach can obtain facets that are not available to standard lifting methods. We also provide a related analysis for generating "fast cuts". Finally, we present computational results of the new S-K cuts for solving 0-1 integer programming problems. Our outcomes disclose that the new cuts are capable of reducing the duality gap between optimal continuous and integer feasible solutions more effectively than standard lifted cover inequalities, as used in modern codes such as the CPLEX mixed 0-1 integer programming solver.
| Original language | English |
|---|---|
| Pages (from-to) | 151-172 |
| Number of pages | 22 |
| Journal | Computational Optimization and Applications |
| Volume | 8 |
| Issue number | 2 |
| Publication status | Published - 1997 Dec 1 |
| Externally published | Yes |
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Keywords
- Chvátal Gomory cuts
- Fractional surrogate constraint cuts
- Knapsack polytope
- Liftings
- Separation procedure
- Surrogate-knapsack cuts
ASJC Scopus subject areas
- Management Science and Operations Research
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
Cite this
Generating Cuts from Surrogate Constraint Analysis for Zero-One and Multiple Choice Programming. / Glover, Fred; Sherali, Hanif D.; Lee, Youngho.
In: Computational Optimization and Applications, Vol. 8, No. 2, 01.12.1997, p. 151-172.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Generating Cuts from Surrogate Constraint Analysis for Zero-One and Multiple Choice Programming
AU - Glover, Fred
AU - Sherali, Hanif D.
AU - Lee, Youngho
PY - 1997/12/1
Y1 - 1997/12/1
N2 - This paper presents a new surrogate constraint analysis that gives rise to a family of strong valid inequalities called surrogate-knapsack (S-K) cuts. The analytical procedure presented provides a strong S-K cut subject to constraining the values of selected cut coefficients, including the right-hand side. Our approach is applicable to both zero-one integer problems and problems having multiple choice (generalized upper bound) constraints. We also develop a strengthening process that further tightens the S-K cut obtained via the surrogate analysis. Building on this, we develop a polynomial-time separation procedure that successfully generates an S-K cut that renders a given non-integer extreme point infeasible. We show how sequential lifting processes can be viewed in our framework, and demonstrate that our approach can obtain facets that are not available to standard lifting methods. We also provide a related analysis for generating "fast cuts". Finally, we present computational results of the new S-K cuts for solving 0-1 integer programming problems. Our outcomes disclose that the new cuts are capable of reducing the duality gap between optimal continuous and integer feasible solutions more effectively than standard lifted cover inequalities, as used in modern codes such as the CPLEX mixed 0-1 integer programming solver.
AB - This paper presents a new surrogate constraint analysis that gives rise to a family of strong valid inequalities called surrogate-knapsack (S-K) cuts. The analytical procedure presented provides a strong S-K cut subject to constraining the values of selected cut coefficients, including the right-hand side. Our approach is applicable to both zero-one integer problems and problems having multiple choice (generalized upper bound) constraints. We also develop a strengthening process that further tightens the S-K cut obtained via the surrogate analysis. Building on this, we develop a polynomial-time separation procedure that successfully generates an S-K cut that renders a given non-integer extreme point infeasible. We show how sequential lifting processes can be viewed in our framework, and demonstrate that our approach can obtain facets that are not available to standard lifting methods. We also provide a related analysis for generating "fast cuts". Finally, we present computational results of the new S-K cuts for solving 0-1 integer programming problems. Our outcomes disclose that the new cuts are capable of reducing the duality gap between optimal continuous and integer feasible solutions more effectively than standard lifted cover inequalities, as used in modern codes such as the CPLEX mixed 0-1 integer programming solver.
KW - Chvátal Gomory cuts
KW - Fractional surrogate constraint cuts
KW - Knapsack polytope
KW - Liftings
KW - Separation procedure
KW - Surrogate-knapsack cuts
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UR - http://www.scopus.com/inward/citedby.url?scp=0031219862&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0031219862
VL - 8
SP - 151
EP - 172
JO - Computational Optimization and Applications
JF - Computational Optimization and Applications
SN - 0926-6003
IS - 2
ER -