Advantages of simplicial partitioning for Lipschitz optimization problems with linear constraints

Paulavičius, Remigijus; Žilinskas, Julius

doi:10.1007/s11590-014-0772-4

Cited by 35 publications

(20 citation statements)

References 39 publications

(46 reference statements)

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“…However, simplex partitions were applied in a similar algorithm called DISIMPL [32][33][34]42]. Experiments showed, that the proposed simplicial DISIMPL algorithm gives very competitive results to the DIRECT algorithm using standard test problems and performs particularly well when the search space and the numbers of local and global minimizers may be reduced by taking into account symmetries of the objective function.…”

Section: Modifications and Applications Of The Direct Algorithmmentioning

confidence: 99%

Application of Reduced-set Pareto-Lipschitzian Optimization to truss optimization

et al. 2015

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In this paper, a recently proposed global Lipschitz optimization algorithm PLOR (Pareto-Lipschitzian Optimization with Reduced-set) is further developed, investigated and applied to truss optimization problems. Partition patterns of the PLOR algorithm are similar to those of DIRECT (DIviding RECTangles), which was widely applied to different real-life problems. However here a set of all Lipschitz constants is reduced to just two: the maximal and the minimal ones. In such a way the PLOR approach is independent of any user-defined parameters and balances equally local and global search during the optimization process. An expanded list of other well-known DIRECT-type algorithms is used in investigation and experimental comparison using the standard test problems and truss optimization problems. The experimental investigation shows that the PLOR algorithm gives very competitive results to other DIRECT-type algorithms using standard test problems and performs pretty well on real truss optimization problems.

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Section: Modifications and Applications Of The Direct Algorithmmentioning

confidence: 99%

Application of Reduced-set Pareto-Lipschitzian Optimization to truss optimization

et al. 2015

Self Cite

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“…Although BO has been used to solve global optimization problems in bounded-box search spaces [1-3, 7, 8, 18], more interesting and realistic cases are related to constrained global optimization (CGO) [19][20][21], where constraints are not defined as simple limits on the values of the variables spanning the search space. The traditional way of solving the constrained problems consists in solving an unconstrained problem where the original objective function is penalized depending on the violation of feasibility.…”

Section: Introductionmentioning

confidence: 99%

Sequential model based optimization of partially defined functions under unknown constraints

Candelieri

2019

J Glob Optim

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This paper presents a sequential model based optimization framework for optimizing a black-box, multi-extremal and expensive objective function, which is also partially defined, that is it is undefined outside the feasible region. Furthermore, the constraints defining the feasible region within the search space are unknown. The approach proposed in this paper, namely SVM-CBO, is organized in two consecutive phases, the first uses a Support Vector Machine classifier to approximate the boundary of the unknown feasible region, the second uses Bayesian Optimization to find a globally optimal solution within the feasible region. In the first phase the next point to evaluate is chosen by dealing with the trade-off between improving the current estimate of the feasible region and discovering possible disconnected feasible sub-regions. In the second phase, the next point to evaluate is selected as the minimizer of the Lower Confidence Bound acquisition function but constrained to the current estimate of the feasible region. The main of the paper is a comparison with a Bayesian Optimization process which uses a fixed penalty value for infeasible function evaluations, under a limited budget (i.e., maximum number of function evaluations). Results are related to five 2D test functions from literature and 80 test functions, with increasing dimensionality and complexity, generated through the Emmental-type GKLS software. SVM-CBO proved to be significantly more effective as well as computationally efficient.

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“…However, to the best of our knowledge, there is little work of the DIRECT-type algorithm for constrained problems (Jones 2001;Finkel 2005;Paulavičius and Žilinskas 2016). Finkel (2005) compared three constrainthandling techniques and revealed that the penalty method is better for DIRECT.…”

Section: Introductionmentioning

confidence: 99%

“…Finkel (2005) compared three constrainthandling techniques and revealed that the penalty method is better for DIRECT. Paulavičius and Žilinskas (2016) presented a simplicial partitioning-based DIRECT algorithm to handle linear constraints.…”

Section: Introductionmentioning

confidence: 99%

Constrained global optimization via a DIRECT-type constraint-handling technique and an adaptive metamodeling strategy

Liu

Chen

et al. 2016

Struct Multidisc Optim

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Recent metamodel-based global optimization algorithms are very promising for box-constrained expensive optimization problems. However, few of them can tackle constrained optimization problems. This article presents an improved constrained optimization algorithm, called eDIRECT-C, for expensive constrained optimization problems. In the eDIRECT-C algorithm, we present a novel DIRECT-type constraint-handling technique that separately handles feasible and infeasible cells. This technique has no user-defined parameter and is beneficial for exploring the undetected feasible regions and boundary of feasible regions. We also employ an adaptive metamodeling strategy to build appropriate metamodel types for objective and constraints respectively. This strategy yields more accurate predictions and therefore significantly speeds up the convergence. To assess the performance of eDIRECT-C, we compare it with some state-of-the-art metamodel-based constrained optimization algorithms and the original DIRECT algorithm on 13 benchmark problems and 4 engineering examples. The comparative results imply that the proposed algorithm is very promising for constrained problems in terms of the convergence speed, quality of final solutions and success rate.

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Advantages of simplicial partitioning for Lipschitz optimization problems with linear constraints

Cited by 35 publications

References 39 publications

Application of Reduced-set Pareto-Lipschitzian Optimization to truss optimization

Application of Reduced-set Pareto-Lipschitzian Optimization to truss optimization

Sequential model based optimization of partially defined functions under unknown constraints

Constrained global optimization via a DIRECT-type constraint-handling technique and an adaptive metamodeling strategy

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