Compact representation of near-optimal integer programming solutions

It is often useful in practice to explore near-optimal solutions of an integer programming problem. We show how all solutions within a given tolerance of the optimal value can be efficiently and compactly represented in a weighted decision diagram. The structure of the diagram facilitates rapid proc...

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Vydáno v:Mathematical programming Ročník 182; číslo 1-2; s. 199 - 232
Hlavní autoři: Serra, Thiago, Hooker, J. N.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2020
Springer Nature B.V
Témata:
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Full Length Paper
Integer programming
Integers
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Solution space
Sound
Theoretical
Traveling salesman problem
Integer programming
90C31
90C10
Decision diagrams
Postoptimality
90C35
ISSN:0025-5610, 1436-4646
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Shrnutí:It is often useful in practice to explore near-optimal solutions of an integer programming problem. We show how all solutions within a given tolerance of the optimal value can be efficiently and compactly represented in a weighted decision diagram. The structure of the diagram facilitates rapid processing of a wide range of queries about the near-optimal solution space, as well as reoptimization after changes in the objective function. We also exploit the paradoxical fact that the diagram can be reduced in size if it is allowed to represent additional solutions. We show that a “sound reduction” operation, applied repeatedly, yields the smallest such diagram that is suitable for postoptimality analysis, and one that is typically far smaller than a tree that represents the same set of near-optimal solutions. We conclude that postoptimality analysis based on sound-reduced diagrams has the potential to extract significantly more useful information from an integer programming model than was previously feasible.
Bibliografie:ObjectType-Article-1
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-019-01390-3