Blackbox optimization for origami-inspired bistable structures

A mesh adaptive direct search algorithm for multiobjective optimization

Combined heat and power economic dispatch by mesh adaptive direct search algorithm

Inversion of surface wave phase velocities not only suffers from computational difficulties associated with being trapped by local minima for most local-search methods but also undergoes the high computational effort for most global optimization techniques due to its high nonlinearity and to its multimodality. In order to effectively overcome the above described difficulties, we proposed a new surface wave inversion scheme based on the Mesh Adaptive Direct Search (MADS) algorithm, a commonly used pattern recognition algorithm. The calculation efficiency and stability of the proposed procedure are tested on a four-layer synthetic model and a real-world example. Results from both synthetic and real field data demonstrate that the MADS algorithm applied to surface wave inversion should be considered good not only in terms of accuracy but also in terms of computation effort due to its global and fast convergence in the final stage of search.

The context of this research is multiobjective optimization where conflicting objectives are present. In this work, these objectives are only available as the outputs of a blackbox for which no derivative information is available. This work proposes a new extension of the mesh adaptive direct search (MADS) algorithm to multiobjective derivative-free optimization with bound constraints. This method does not aggregate objectives and keeps a list of non dominated points which converges to a (local) Pareto set as long as the algorithm unfolds. As in the single-objective optimization MADS algorithm, this method is built around a search step and a poll step. Under classical direct search assumptions, it is proved that the so-called DMulti-MADS algorithm generates multiple subsequences of iterates which converge to a set of local Pareto stationary points. Finally, computational experiments suggest that this approach is competitive compared to the state-of-the-art algorithms for multiobjective blackbox optimization.

In the design of optical metamaterials, some optimization problems require launching a numerical simulation. The Mesh Adaptive Direct Search algorithm is designed for such problems. The MADS algorithm does not require any derivative information about the problem being optimized, and no continuity or differentiability assumptions are made by MADS on the functions defining the simulation. A detailed discussion of the method is provided in the second section of the chapter, followed by a discussion of the NOMAD implementation of the method and its features. The final section of the chapter lists three instances of combining NOMAD with Finite-Difference Time-Domain electromagnetic simulations to tailor the broadband spectral response and near-field interactions of Split Ring Resonator metamaterials.

The calibration of hydrological models is formulated as a blackbox optimization problem where the only information available is the objective function value. Distributed hydrological models are generally computationally intensive, and their calibration may require several hours or days which can be an issue for many operational contexts. Different optimization algorithms have been developed over the years and exhibit different strengths when applied to the calibration of computationally intensive hydrological models. This paper shows how the dynamically dimensioned search (DDS) and the mesh adaptive direct search (MADS) algorithms can be combined to significantly reduce the computational time of calibrating distributed hydrological models while ensuring robustness and stability regarding the final objective function values. Five transitional features are described to adequately merge both algorithms. The hybrid approach is applied to the distributed and computationally intensive HYDROTEL model on three different river basins located in Québec (Canada).

Designing icephobic surfaces to delay ice formation is crucial for applications like aviation safety and cryopreservation. While classical nucleation theory (CNT) provides a thermodynamic foundation, real-world stochastic effects and complex wetting states make designing these surfaces difficult. The performance of icephobic surfaces is influenced by surface structure. However, finding the best designs for specific environmental conditions is still a challenge. In this work, we introduce a hybrid approach that combines experiments, CNT, and blackbox optimization to predict and optimize ice nucleation time on micropatterned surfaces. Cylindrical SU-8 micropillar arrays with different heights and spacings were created, and the apparent contact angles and freezing delay times were measured at -10 °C and -20 °C. An analytical model was developed to describe the wetting states between the Wenzel and Cassie-Baxter regimes, optimizing its parameters using the Mesh adaptive direct search (MADS) algorithm. This approach allows us to estimate contact angles and ice nucleation times for any surface geometry within the studied design space. The predicted contact angles matched experimental results with a mean absolute percentage error (MAPE) of 2.09% (R2 = 0.92) and the approximate nucleation times showed a MAPE of 27.3% (R2 = 0.75). Our method also identified the best micropillar geometries that maximize freezing delay and was validated with an independent data set, showing strong predictive ability. This work emphasizes the benefit of combining physics-based models with data-driven optimization for rapid design of icephobic surfaces.

Continuum and subcontinuum simulation of FDM process for 4D printed shape memory polymers

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.

It is proposed a first step to the model-based closed-loop control of a separated flow. In such situations, fluid mechanics phenomena are highly nonlinear and can be represented by means of the Navier-Stokes equations. However, such a model still rises difficult issues for control practice. This paper proposes an alternative, bilinear and delayed model, the accuracy of which is studied. The identification technique combines least-square technique with a Mesh Adaptive Direct Search (MADS) algorithm. The main feature of the model is state dependent structure of input delay.

Prediction of part distortion in Fused Deposition Modelling (FDM) of semi-crystalline polymers via COMSOL: Effect of printing conditions

Multistable structures have widespread applications in the design of deployable aerospace systems, mechanical metamaterials, flexible electronics, and multimodal soft robotics due to their capability of shape reconfiguration between multiple stable states. Recently, the snap-folding of rings, often in the form of circles or polygons, has shown the capability of inducing diverse stable configurations. The natural curvature of the rod segment (curvature in its stress-free state) plays an important role in the elastic stability of these rings, determining the number and form of their stable configurations during folding. Here, we develop a general theoretical framework for the elastic stability analysis of segmented rings (e.g., polygons) based on an energy variational approach. Combining this framework with finite element simulations, we map out all planar stable configurations of various segmented rings and determine the natural curvature ranges of their multistable states. The theoretical and numerical results are validated through experiments, which demonstrate that a segmented ring with a rectangular cross-section can show up to six distinct planar stable states. The results also reveal that, by rationally designing the segment number and natural curvature of the segmented ring, its one- or multiloop configuration can store more strain energy than a circular ring of the same total length. We envision that the proposed strategy for achieving multistability in the current work will aid in the design of multifunctional, reconfigurable, and deployable structures.

NDA Approval

Mechanical and piezoresistive performance of additively manufactured carbon fiber/PA12 hybrid honeycombs

We investigate surrogate-assisted strategies for global derivative-free optimization using the mesh adaptive direct search (MADS) blackbox optimization algorithm. In particular, we build an ensemble of surrogate models to be used within the search step of MADS to perform global exploration, and examine different methods for selecting the best model for a given problem at hand. To do so, we introduce an order-based error tailored to surrogate-based search. We report computational experiments for ten analytical benchmark problems and three engineering design applications. Results demonstrate that different metrics may result in different model choices and that the use of order-based metrics improves performance.