A Survey on Direct Search Methods for Blackbox Optimization and Their Applications

Audet, Charles

doi:10.1007/978-1-4939-1124-0_2

Cited by 62 publications

(51 citation statements)

References 109 publications

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“…The NOMAD implementation [15] of the MADS algorithm [16] for nonsmooth constrained optimization was used to search for the optimal study design. MADS is designed for blackbox optimization problems [17] in which the cost function and constraints are evaluated by a time-consuming simulation code. The optimization problem had four bound-constrained variables, three of them being continuous, and the fourth one (n 1 / being discrete.…”

Section: Optimal Design Search Algorithmmentioning

confidence: 99%

Optimal adaptive sequential designs for crossover bioequivalence studies

Audet

DiLiberti

et al. 2015

Pharmaceutical Statistics

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In prior works, this group demonstrated the feasibility of valid adaptive sequential designs for crossover bioequivalence studies. In this paper, we extend the prior work to optimize adaptive sequential designs over a range of geometric mean test/reference ratios (GMRs) of 70-143% within each of two ranges of intra-subject coefficient of variation (10-30% and 30-55%). These designs also introduce a futility decision for stopping the study after the first stage if there is sufficiently low likelihood of meeting bioequivalence criteria if the second stage were completed, as well as an upper limit on total study size. The optimized designs exhibited substantially improved performance characteristics over our previous adaptive sequential designs. Even though the optimized designs avoided undue inflation of type I error and maintained power at ≥ 80%, their average sample sizes were similar to or less than those of conventional single stage designs.

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Section: Optimal Design Search Algorithmmentioning

confidence: 99%

Optimal adaptive sequential designs for crossover bioequivalence studies

Audet

DiLiberti

et al. 2015

Pharmaceutical Statistics

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“…The observables may appear in the cost function or in some of the constraints. Unlike in derivative-free optimization (see [1,12]), in EML the H function is not treated as a black-box. On the contrary, there is an emphasis on exploiting the structure of the Machine Learning model to boost the search process.…”

Section: Introductionmentioning

confidence: 99%

“…The new propagator can be instantiated multiple times to model networks with more than two layers, or it can be combined with Neuron Constraints to encode almost any type of ANN, including recurrent networks. 1 The bounds for the new propagator are based on a non-linear Lagrangian relaxation, with the multipliers being optimized via a subgradient method. Lagrangian relaxation has proved to be a powerful technique for performing reduced-cost filtering in CP, mainly in the context of linear relaxations of integer programs (e.g., [32][33][34]).…”

Section: Introductionmentioning

confidence: 99%

A lagrangian propagator for artificial neural networks in constraint programming

Lombardi

Gualandi²

2015

Constraints

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This paper discusses a new method to perform propagation over a (two-layer, feed-forward) Neural Network embedded in a Constraint Programming model. The method is meant to be employed in Empirical Model Learning, a technique designed to enable optimal decision making over systems that cannot be modeled via conventional declarative means. The key step in Empirical Model Learning is to embed a Machine Learning model into a combinatorial model. It has been showed that Neural Networks can be embedded in a Constraint Programming model by simply encoding each neuron as a global constraint, which is then propagated individually. Unfortunately, this decomposition approach may lead to weak bounds. To overcome such limitation, we propose a new network-level propagator based on a non-linear Lagrangian relaxation that is solved with a subgradient algorithm. The method proved capable of dramatically reducing the search tree size on a thermal-aware dispatching problem on multicore CPUs. The overhead for optimizing the Lagrangian multipliers is kept within a reasonable level via a few simple techniques. This paper is an extended version of [27], featuring an improved structure, a new filtering technique for the network inputs, a set of overhead reduction techniques, and a thorough experimentation.

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“…Blackbox optimization is used when the objective functions or the constraints of a problem can only be calculated through a computer code, as it is the case in this problem. Blackbox optimization methods have been applied successfully to many engineering problems (Audet, 2014). In the field of hydrology, blackbox optimization has been used to find the optimal locations for GMONs (Alarie et al, 2013), which are devices used to measure snow water equivalent in remote areas of watersheds.…”

Section: Introductionmentioning

confidence: 99%

Scenario-Tree Modeling for Stochastic Short-Term Hydropower Operations Planning

Séguin

Audet

Côté

2017

J. Water Resour. Plann. Manage.

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The authors investigate the complexity needed in the structure of the scenario trees to maximize energy production in a rolling-horizon framework. Three comparisons, applied to the stochastic short-term unit commitment and loading problem are conducted. The first one involves generating a set of scenario trees built from inflow forecast data over a rolling-horizon. The second replaces the entire set of scenario trees by the median scenario. The third replaces the set of trees by scenario fans. The method used to build scenario trees, based on minimization of the nested distance, requires three parameters: number of stages, number of child nodes at each stage, and aggregation of the period covered by each stage. The authors formulate the question of finding the best values of these parameters as a blackbox optimization problem that maximizes the energy production over the rolling-horizon. Numerical experiments on three hydropower plants in series suggest that using a set of scenario trees is preferable to using the median scenario, but using a fan of scenarios yields a comparable solution with less computational effort.

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A Survey on Direct Search Methods for Blackbox Optimization and Their Applications

Cited by 62 publications

References 109 publications

Optimal adaptive sequential designs for crossover bioequivalence studies

Optimal adaptive sequential designs for crossover bioequivalence studies

A lagrangian propagator for artificial neural networks in constraint programming

Scenario-Tree Modeling for Stochastic Short-Term Hydropower Operations Planning

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