2011
DOI: 10.1007/978-1-4614-1927-3_9
|View full text |Cite
|
Sign up to set email alerts
|

Symmetry in Mathematical Programming

Abstract: Abstract. Symmetry is mainly exploited in mathematical programming in order to reduce the computation times of enumerative algorithms. The most widespread approach rests on: (a) finding symmetries in the problem instance; (b) reformulating the problem so that it does not allow some of the symmetric optima; (c) solving the modified problem. Sometimes (b) and (c) are performed concurrently: the solution algorithm generates a sequence of subproblems, some of which are recognized to be symmetrically equivalent and… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
38
0

Year Published

2011
2011
2019
2019

Publication Types

Select...
5

Relationship

2
3

Authors

Journals

citations
Cited by 26 publications
(38 citation statements)
references
References 53 publications
(73 reference statements)
0
38
0
Order By: Relevance
“…The upper bounding solution x ′ is found by solving (1) locally with MINLP heuristics [1,2], whilst the lower bound is computed by automatically constructing and solving a convex relaxation of (1). If x ′ n −x n ≤ ε then x ′ is feasible and at most ε-suboptimal; if x ′ is the best optimum so far, it is stored as the incumbent.…”
Section: Introductionmentioning
confidence: 99%
“…The upper bounding solution x ′ is found by solving (1) locally with MINLP heuristics [1,2], whilst the lower bound is computed by automatically constructing and solving a convex relaxation of (1). If x ′ n −x n ≤ ε then x ′ is feasible and at most ε-suboptimal; if x ′ is the best optimum so far, it is stored as the incumbent.…”
Section: Introductionmentioning
confidence: 99%
“…Because of the large number of symmetric optima, however, sBB solvers are still far from finding any nontrivial solution. A study of the formulation group of (4) suggests adjoining the symmetry breaking constraints ∀i ≤ N {1} x i−1,1 ≤ x i1 to (4), yielding a reformulation for which sBB makes considerably more progress [15]. Identifying this reformulation chain, which leads to a more easily solvable MP, required considerable effort and resources.…”
Section: Motivating Examplesmentioning
confidence: 99%
“…ROSE can also obtain a convex relaxation of (4) based on the ideas given in [20,3,4]. Computational results for sBB on (4) are reported in [15]. It may be noted that the above examples were chosen arbitrarily by a large set of ROSE applications (see Sect.…”
Section: Expression Tree Librarymentioning
confidence: 99%
See 2 more Smart Citations