Nonsmooth optimization through Mesh Adaptive Direct Search and Variable Neighborhood Search

Audet, Charles; Béchard, Vincent; Digabel, Sébastien Le

doi:10.1007/s10898-007-9234-1

Cited by 156 publications

(108 citation statements)

References 32 publications

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“…Figure 3 is developed as a general representation of both direct-search and trust-region search which will be described next. The disadvantages of local direct-search CDFO are the high dependence on the initial point, entrapment within closest local optimum, and large number of function calls to guarantee convergence (Audet et al, 2008b;Conn et al, 2009b). In order to increase the probability for convergence to the global optimum, multi-start approaches are proposed, which are not efficient in cases where the model of interest is computationally expensive.…”

Section: Global Optimization Advances In Cdfomentioning

confidence: 99%

“…Allowing pattern-search methods to handle a dense set of polling directions instead of a finite set of polling directions was a significant development for studying the convergence of generally constrained derivative-free problems which are Lipschitz even near a limit point (Audet and Dennis, 2006;Audet et al, 2008b). A recent methodology proposed in (Vicente and Custódio, 2012) studies convergence of local-search adaptive search in the case of discontinuous objective functions and general constraints, which is useful for many real applications.…”

Section: Global Optimization Advances In Cdfomentioning

confidence: 99%

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Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Boukouvala

Misener

Floudas

2016

European Journal of Operational Research

199

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This manuscript reviews recent advances in deterministic global optimization for Mixed-Integer Nonlinear Programming (MINLP), as well as Constrained DerivativeFree Optimization (CDFO). This work provides a comprehensive and detailed literature review in terms of significant theoretical contributions, algorithmic developments, software implementations and applications for both MINLP and CDFO. Both research areas have experienced rapid growth, with a common aim to solve a wide range of real-world problems. We show their individual prerequisites, formulations and applicability, but also point out possible points of interaction in problems which contain hybrid characteristics. Finally, an inclusive and complete test suite is provided for both MINLP and CDFO algorithms, which is useful for future benchmarking.

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Section: Global Optimization Advances In Cdfomentioning

confidence: 99%

Section: Global Optimization Advances In Cdfomentioning

confidence: 99%

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Boukouvala

Misener

Floudas

2016

European Journal of Operational Research

199

View full text Add to dashboard Cite

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“…Search step evaluate the functions on a finite number of points of M (k, ∆ k ) Poll step compute p MADS directions D k ∈ R n×p construct the frame P k ⊆ M (k, ∆ k ) with x k , D k , and ∆ k evaluate the functions on the p points of P k [2] Updates determine the type of success of iteration k solution update (x k+1 ) mesh update (∆ k+1 ) k ← k + 1 check the stopping conditions, goto [1] (see [18]). A corollary of this result is that without constraints and if f is strictly differentiable, then ∇ f (x) = 0.…”

Section: Variable Neighborhood Search (Vns) Strategymentioning

confidence: 99%

Parameter Analysis of the VPIN (Volume‐Synchronized Probability of Informed Trading) Metric

Song

Simon

2015

Quantitative Financial Risk Management

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“…Although the MADS algorithm is quite powerful in local search, it needs some special considerations to be successful in global search too. Variable Neighborhood Search (VNS) is an algorithm integrated into NOMAD to improve global search of the design space [25]. While the default value of VNS budget is equal to 75% of overall budget, two more global search budgets have been also investigated using VNS equal to 85% and 95% of the overall budget.…”

Section: Nomadmentioning

confidence: 99%

Physics-based Surrogate Optimization of Francis Turbine Runner Blades, Using Mesh Adaptive Direct Search and Evolutionary Algorithms

Bahrami

Tribes

Fellenberg

et al. 2015

International Journal of Fluid Machinery and Systems

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A robust multi-fidelity optimization methodology has been developed, focusing on efficiently handling industrial runner design of hydraulic Francis turbines. The computational task is split between low-and high-fidelity phases in order to properly balance the CFD cost and required accuracy in different design stages. In the low-fidelity phase, a physics-based surrogate optimization loop manages a large number of iterative optimization evaluations. Two derivative-free optimization methods use an inviscid flow solver as a physics-based surrogate to obtain the main characteristics of a good design in a relatively fast iterative process. The case study of a runner design for a low-head Francis turbine indicates advantages of integrating two derivative-free optimization algorithms with different local-and global search capabilities. Keywords:Physics-based surrogate optimization, Francis turbine runner blade, multi-fidelity algorithm Hydraulic Turbine Design Optimization ProcessBig changes in global energy demand, increasing environmental concerns, and growth potential of cost-efficient hydroelectric energy, have recently resulted in more demand to design hydraulic turbines which are more efficient and durable. As design challenges are getting more complex, runner designers rely more than ever on engineering and simulation tools, especially computational fluid dynamics (CFD), to obtain reliable designs with a competitive time and cost. Although runner designers already employ CFD tools to evaluate their designs, there is a strong need to integrate CFD analyses more tightly in the design chain using efficient optimization methods to obtain more efficient design processes.The full range of CFD methods have been utilized in the optimization of hydraulic turbine runner blades. Low-fidelity inviscid models (e.g. potential flow) have been employed by some researches such as Holmes and McNabb [1]. However, they are not accurate enough in their prediction of flow behavior, mainly due to lack of physics. High-fidelity viscous models have been used alone to optimize the runner as well (e.g. using turbulent RANS solvers, by Franco-Nava et al. [2] and Pilev et al. [3]); but they are too expensive and slow for iterative industrial runner design processes. To reduce high-fidelity analyses in the optimization loop, surrogatebased optimization approaches have been increasingly employed by researchers, using either mathematical surrogates or physic-based surrogates. Mathematical surrogates are computationally inexpensive approximation models constructed from a given number of highfidelity evaluations. For instance, artificial neural network was applied by Derakhshan et al. [4] to reduce Navier-Stokes solver calls during the optimization of a low-head axial hydro turbine by an evolutionary algorithm. Another popular mathematical surrogate, radial basis functions, was employed by Georgopoulou et al. [5].Although those mathematical surrogates have been used for blade shape optimizations, they still require a large number of high-

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Nonsmooth optimization through Mesh Adaptive Direct Search and Variable Neighborhood Search

Cited by 156 publications

References 32 publications

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Parameter Analysis of the VPIN (Volume‐Synchronized Probability of Informed Trading) Metric

Physics-based Surrogate Optimization of Francis Turbine Runner Blades, Using Mesh Adaptive Direct Search and Evolutionary Algorithms

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