Benchmarking Global Optimization and Constraint Satisfaction Codes

Shcherbina, Oleg; Neumaier, Arnold; Sam-Haroud, Djamila; Vu, Xuan-Ha; Nguyen, Tuan-Viet

doi:10.1007/978-3-540-39901-8_16

Cited by 57 publications

(46 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In a third set of experiments we selected three problems (prodpl0, prodpl1 and optmass) from the Coconut Benchmark [46] with m + n ≥ 100. For these medium-size problems we use Minos [35], that uses sparse linear algebra, for solving the linear programming as well as the linearly constrained nonlinear programming subproblems.…”

Section: Influence Of Linear Relaxations Of the Penalized Constraintsmentioning

confidence: 99%

“…In Table 3, n is the number of variables and m is the number of constraints (recall that the number within parentheses is the number of linear constraints), "It" is the number of iterations of Algorithm 2.1 (outer iterations), "#Nodes" is the total number of iterations of Algorithm 4.1 (inner iterations), and f (x * ) is the global minimum. Both versions found the global minimum reported in the literature [46]. The feature being evaluated is related to the performance of the αBB method for solving the Augmented Lagrangian subproblems.…”

Section: Influence Of Linear Relaxations Of the Penalized Constraintsmentioning

confidence: 99%

See 1 more Smart Citation

Global minimization using an Augmented Lagrangian method with variable lower-level constraints

2009

View full text Add to dashboard Cite

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the ε k -global minimization of the Augmented Lagrangian with simple constraints, where ε k → ε. Global convergence to an ε-global minimizer of the original problem is proved. The subproblems are solved using the αBB method. Numerical experiments are presented.

show abstract

Section: Influence Of Linear Relaxations Of the Penalized Constraintsmentioning

confidence: 99%

Section: Influence Of Linear Relaxations Of the Penalized Constraintsmentioning

confidence: 99%

Global minimization using an Augmented Lagrangian method with variable lower-level constraints

2009

View full text Add to dashboard Cite

show abstract

“…A very recent web site, the GAMS Global Library [12] started collecting real life global optimization problems with industrial relevance, but currently most problems on this site are without computational results. Our benchmark (described in more detail in [32]) includes most of the problems from these collections.…”

Section: Testingmentioning

confidence: 99%

“…We present test results for the global optimization systems BARON, GlobSol, ICOS, LGO/GAMS, LINGO, OQNLP Premium Solver, for comparison the local solver MINOS, and (in the next section) a basic combination strategy COCOS implemented in the COCONUT environment. All tests were made on the COCONUT benchmarking suite described in Shcherbina et al [32]. For generalities on benchmarking and the associated difficulties, in particular for global optimization, see Deliverable D10.…”

Section: Testingmentioning

confidence: 99%

“…Size k denotes models whose number of variables (after creating the corresponding DAG and simplifying it) has k decimal digits. Library 1 (from Global Library [12]) and Library 2 (from CUTE [5], in the version of Vanderbei [33]) consist of global (and some local) optimization problems with nonempty feasible domain, while Library 3 (from EPFL [32]) consists of pure constraint satisfaction problems (constant objective function), almost all being feasible. The resulting 12 model classes are labeled as lib2s1 (= size 1 models from Library 2), etc.. We restricted testing to models with less than 1000 variables since the models of size 3 already pose so many difficulties that working on the (much more CPU time consuming) larger models is likely to give no additional insight for the current generation of solvers.…”

Section: Testingmentioning

confidence: 99%

See 1 more Smart Citation

A comparison of complete global optimization solvers

et al. 2005

Self Cite

View full text Add to dashboard Cite

Abstract. Results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables. OverviewAs the recent survey Neumaier [24] of complete solution techniques in global optimization documents, there are now about a dozen solvers for constrained global optimization that claim to solve global optimization and/or constraint satisfaction problems to global optimality by performing a complete search.Within the COCONUT project [30,31], we evaluated many of the existing software packages for global optimization and constraint satisfaction problems. This is the first time that different constrained global optimization and constraint satisfaction algorithms are compared on a systematic basis and with a test set that allows to derive statistically significant conclusions. We tested the global solvers BARON, GlobSol, ICOS, LGO, LINGO, OQNLP, Premium Solver, the local solver MINOS, and a basic combination strategy COCOS implemented in the COCONUT platform. 1The testing process turned out to be extremely time-consuming, due to various reasons not initially anticipated. A lot of effort went into creating appropriate interfaces, making the comparison fair and reliable, and making it possible to process a large number of test examples in a semiautomatic fashion.In a recent paper about testing local optimization software, Dolan & Moré [6,7] write: We realize that testing optimization software is a notoriously difficult problem and that there may be objections to the testing presented in this report. For example, performance of a particular solver may improve significantly if non-default options are given. Another objection is that we only use one starting point per problem and that the performance of a solver may be sensitive to the choice of starting point. We also have used the default stopping criteria of the solvers. This choice may bias results but should not affect comparisons that rely on large time differences. In spite of these objections, we feel that it is essential that we provide some indication of the performance of optimization solvers on interesting problems.These difficulties are also present with our benchmarking studies. Section 2 describes our testing methodology. We use a large test set of over 1000 problems from various collections. Our main performance criterium is currently how often the attainment of the global optimum, or the infeasibility of a problem, is correctly or incorrectly claimed (within some time limit). All solvers are tested with the default options suggested by the providers of the codes, with the request to stop at a time limit or after the solver believed that first global solution was obtained.These are very high standards, much more demanding than what had been done by anyone before. Thorough comparisons are indeed very rare, due to the difficulty of performing extensive and meaningful testing. Indeed, we know of only two comparative studies [17,22] in global ...

show abstract

Interval Differential Evolution Using Structural Information of Global Optimization Problems

Cassenote

Derenievicz

Silva

2019

Progress in Artificial Intelligence

View full text Add to dashboard Cite

Benchmarking Global Optimization and Constraint Satisfaction Codes

Abstract: Abstract. A benchmarking suite describing over 1000 optimization problems and constraint satisfaction problems covering problems from different traditions is described, annotated with best known solutions, and accompanied by recommended benchmarking protocols for comparing test results.

Cited by 57 publications

References 9 publications

Global minimization using an Augmented Lagrangian method with variable lower-level constraints

Global minimization using an Augmented Lagrangian method with variable lower-level constraints

A comparison of complete global optimization solvers

Interval Differential Evolution Using Structural Information of Global Optimization Problems

Contact Info

Product

Resources

About