Mesh Adaptive Direct Search Research Articles

Design and optimization of a modular Electro-Thermal Ice Protection System for a Horizontal Axis Wind Turbine

In this work, an Electro-Thermal Ice Protection System (IPS) design was refined and optimized on the NREL 5 MW reference wind turbine. These improvements involved optimization of the distribution of heat flux in both the stream-wise and span-wise directions to minimize power consumption and avoid run-back ice formation. The design conditions focus on a 3-hour rime ice accretion event. The chosen optimization algorithm is a derivative-free method called Mesh Adaptive Direct Search. his optimization effort results in a 55% reduction in power consumption necessary to maintain a completely clean blade surface. The power and energy losses associated with this new optimized design are compared with those from various ice shapes and with the clean blade conditions established in the initial design phase from previous work. The new optimized design allows to keep the blade clean from ice with much larger energy saving. Indeed, only initially, during the first two hours of ice accretion, the energy losses due to this IPS design are higher than without IPS. Beyond this short initial period, substantial energy savings are achieved, especially considering that after the accretion event, the blade remains ice-free, and there are no more power losses.

Near-Field Aeroacoustic Shape Optimization at Low Reynolds Numbers

We investigate the feasibility of gradient-free aeroacoustic shape optimization using the flux reconstruction (FR) approach to study two-dimensional flow at low Reynolds numbers. The overall sound pressure level (OASPL) is computed via the direct acoustic approach, and optimization is performed using the gradient-free mesh adaptive direct search (MADS) algorithm. The proposed framework is assessed across three problems. First, flow over an open cavity is investigated at a Reynolds number of Re=1500 and freestream Mach number of M∞=0.15, resulting in a 7.9 dB noise reduction. The second case considers tandem cylinders at Re=200 and M∞=0.2, achieving a 16.5 dB noise reduction by optimizing the distance between the cylinders and their diameter ratio. Finally, a NACA0012 airfoil is optimized at Re=10,000 and M∞=0.2 to reduce trailing edge noise. The airfoil’s shape is optimized to generate a new four-digit NACA airfoil at an appropriate angle of attack to reduce OASPL while maintaining the baseline time-averaged lift coefficient and preventing an increase in the baseline time-averaged drag coefficient. The optimized airfoil is silent at 0 dB and the drag coefficient is decreased by 24.95%. These results demonstrate the feasibility of shape optimization using MADS and FR for aeroacoustic design.

Robust Optimization of a Thermal Anti-Ice Protection System in Uncertain Cloud Conditions

This paper presents a framework for the robust optimization of the heat flux distribution for an anti-ice electrothermal ice protection system under uncertain conditions. The considered uncertainty regards a lack of knowledge concerning the characteristics of the cloud, i.e., the liquid water content and the median volume diameter of water droplets, and the accuracy of measuring devices, i.e., the static temperature probe. Uncertain parameters are modeled as random variables, and two sets of bounds are investigated. A forward uncertainty propagation analysis is carried out using a Monte Carlo approach exploiting a surrogate models. The optimization framework relies on a gradient-free algorithm (mesh adaptive direct search), and two different objective functions are considered, namely, the 95 quantile of the freezing mass rate and the statistical frequency of the fully evaporative operating regime. The framework is applied to a reference test case, revealing a potential to improve the heat flux distribution of the baseline design. A new heat flux distribution is proposed, and it presents a more efficient use of the thermal power, increasing flight safety even at nonnominal environmental conditions.

Joint user and throughput maximization in re‐configurable intelligent surface assisted beyond 5G/6G networks

AbstractCurrent fifth‐generation (5G) cellular networks must be upgraded to sixth‐generation (6G) networks as the data rate demands are increasing dramatically. In 6G, the re‐configurable intelligent surfaces (RISs) concept has recently received a lot of attention, it is a new technology that can be configured to optimize the wireless propagating environments and adjust wireless settings to improve the throughput of a network. RIS is emerging as a solution for Tera‐Hertz technologies. Therefore the joint user and the throughput maximization problem with RIS‐assisted B5G/6G wireless network is investigated in this paper subject to power transmission, quality of service (QoS), and phase shift constraints. The proposed research work focuses on RIS‐assisted wireless transmission, to collaboratively improve the admitted users and the throughput for all users in comparison to a traditional communications platform. The problem formulated is non‐convex resulting in the mixed integer non‐linear programming (MINLP) problem. MINLP problems are NP‐hard problems. A mesh adaptive direct search (MADS) algorithm is proposed to solve this problem efficiently. Extensive simulation work validates the proposed algorithm, in a RIS‐assisted network. Results achieved from the simulation show that by incorporating RIS in a network, efficient resource allocation increases throughput and maximizes the admitted users in a wireless network. The proposed MADS algorithm outperforms the existing advanced algorithms and its computational complexity is also low.

Computational Human Nasal Reconstruction Based on Facial Landmarks

This research presented a mathematical-based approach to the computational reconstruction of the human nose through images with anthropometric characteristics. The nasal baselines, which were generated from facial aesthetic subunits combined with the facial landmarks, were reconstructed using interpolation and Mesh adaptive direct search algorithms to generate points that would serve as the support for the layer-by-layer reconstruction. The approach is proposed as the basis for nasal reconstruction in aesthetics or forensics rather than focusing on the applications of image processing or deep learning. A mathematical model for the computational reconstruction was built, and then volunteers were the subjects of nasal reconstruction experiments. The validations based on the area errors—which are based on four samples and eight sub-regions with different values depending on the regions C1, C2, and C3 and nasal shapes of the volunteers—were measured to prove the results of the mathematical model. Evaluations have demonstrated that the computer-reconstructed noses fit the original ones in shape and with minimum area errors. This study describes a computational reconstruction based on a mathematical approach directly to facial anthropometric landmarks to reconstruct the nasal shape.

Design and optimization of the flexible poly-generation process for methanol and formic acid from CO2 hydrogenation under uncertain product prices

During the design of the carbon capture and hydrogen storage process, a static CO2 hydrogenation poly-generation process for methanol and formic acid synthesis was developed, thereby reducing recycling flow and feedstock losses in the single methanol synthesis process and increasing product diversity. Additionally, a novel flexible poly-generation process was proposed as the product prices fluctuated with the market environment throughout the plant's life cycle. For the static poly-generation process, a mixed integer nonlinear programming model was established, followed by the Mesh Adaptive Direct Search algorithm to determine the optimal parameter design. For flexible processes, with the unscented transform tool, a two-stage optimization strategy is proposed for obtaining optimal design and operating parameters that are computationally tractable. With an input CO2 flow rate of 200 kmol/h, the results show (1) the static process with an optimal Return On Investment of 13.05%, a fixed investment cost of $ 34.14 × 106, and an annual net profit of 4.46 × 106 $/year; and (2) the flexible process, in which the flexibility indices of the methanol and formic acid production units are 1.088 and 1.194, respectively, resulting the fixed investment cost increase to $ 39.19 × 106, an increase of 14.79%. Accordingly, the annual net profit increased by 8.97% to 4.86 × 106 $/year, while the Return On Investment decreased by 4.67%–12.44%. For investment decision-makers, the flexible poly-generation process can achieve higher profits and reduce potential market risks when they have adequate financing.

Optimization of multilayered electromagnetic shielding using mesh adaptive direct search

Optimization of multilayered electromagnetic shielding using mesh adaptive direct search

Radio resource management in energy harvesting cooperative cognitive UAV assisted IoT networks: A multi-objective approach

Cooperative communication through energy harvested relays in Cognitive Internet of Things (CIoT) has been envisioned as a promising solution to support massive connectivity of Cognitive Radio (CR) based IoT devices and to achieve maximal energy and spectral efficiency in upcoming wireless systems. In this work, a cooperative CIoT system is contemplated, in which a source acts as a satellite, communicating with multiple CIoT devices over numerous relays. Unmanned Aerial Vehicles (UAVs) are used as relays, which are equipped with onboard Energy Harvesting (EH) facility. We adopted a Power Splitting (PS) method for EH at relays, which are harvested from the Radio frequency (RF) signals. In conjunction with this, the Decode and Forward (DF) relaying strategy is used at UAV relays to transmit the messages from the satellite source to the CIoT devices. We developed a Multi-Objective Optimization (MOO) framework for joint optimization of source power allocation, CIoT device selection, UAV relay assignment, and PS ratio determination. We formulated three objectives: maximizing the sum rate and the number of admitted CIoT in the network and minimizing the carbon dioxide emission. The MOO formulation is a Mixed-Integer Non-Linear Programming (MINLP) problem, which is challenging to solve. To address the joint optimization problem for an epsilon optimal solution, an Outer Approximation Algorithm (OAA) is proposed with reduced complexity. The simulation results show that the proposed OAA is superior in terms of CIoT device selection and network utility maximization when compared to those obtained using the Nonlinear Optimization with Mesh Adaptive Direct-search (NOMAD) algorithm.

Rotorcraft low-noise trajectories design: black-box optimization using surrogates

This paper addresses the noise-minimal trajectory optimization problem for a specific type of aircraft: rotorcraft. It relies on a realistic noise footprint computation software provided by industry that is black-box. Locally optimal trajectories are computed through a tailored solution approach based on the Mesh-Adaptive Direct Search algorithm. We propose multiple surrogates defined according to our knowledge of the problem, including a surrogate relying on the physics of the problem (approximating the rotorcraft noise model), and another based on a machine learning (neural network) method. The proposed solution approach is further enhanced by the computation of an appropriate starting guess through a path planning algorithm tailored to the problem, and by the reduction of the variable space domain. The performance of the proposed methodology both in terms of quality of the solutions (trajectories exhibiting significant noise reduction compared to those currently flown in practice) and computing time is illustrated through numerical experiments on real-world case studies.

THD Minimization and Reliability Analysis of Cascaded Multilevel Inverter

Inverters are DC to AC power converters that are widely used in AC motor drives and distributed energy generation systems. Multi-Level Inverters (MLIs) have emerged as the preferred inverter technology because of their advantages of reduced switching losses and better harmonic profile. This paper deals with the Minimization of Total Harmonic Distortion (MTHD) of Symmetric Cascaded H-bridge Multi-Level Inverter (SCMLI) and Asymmetric Cascaded H-bridge Multi-Level Inverter (ACMLI). A hybrid memetic algorithm composed of heuristic PSO (Particle Swarm Optimization) algorithm and traditional MAS (Mesh Adaptive direct Search) is proposed to optimize the switching angles. In Photo Voltaic (PV) system, the input DC voltage generally varies from its nominal value due to the change in temperature and irradiance. Thus, the sensitivity analysis of THD and harmonics is also carried out considering the variations with non-integer magnitudes of input DC sources. The experimental prototype of SCMLI and ACMLI topology is developed and validated with simulation results. The reliability and Mean Time to Failure (MTTF) of SCMLI and ACMLI are investigated based on power losses of the MOSFET and thermal parameters.

Comparison of parallel optimization algorithms on computationally expensive groundwater remediation designs

Contaminated groundwater resources threaten human health and destroy ecosystems in many areas worldwide. Groundwater remediation is crucial for environmental recovery; however, it can be cost prohibitive. Planning a cost-effective remediation design can take a long time, as it may involve the evaluation of many management decisions, and the corresponding simulation models are computationally demanding. Parallel optimization can facilitate much faster management decisions for cost-effective groundwater remediation design using complex pollutant transport models. However, the efficiency of different parallel optimization algorithms varies depending on both the search strategy and parallelism. In this paper, we show the performance of a parallel surrogate-based optimization algorithm called parallel stochastic radial basis function (p-SRBF), which has not been previously used on contaminant remediation problems. The two case problems involve two superfund sites (i.e., the Umatilla Aquifer and Blaine Aquifer), and one objective evaluation takes 5 and 30 min for the two problems, respectively. Exceptional speedup (superlinear) is achieved with 4 to 16 cores, and excellent speedup is achieved using up to 64 cores, obtaining a good solution at 80 % efficiency. We compare our p-SRBF with three different parallel derivative-free optimization algorithms, including genetic algorithm, mesh adaptive direct search, and asynchronous parallel pattern search optimization, in terms of objective quality, computational reduction and robust behavior across multiple trials. p-SRBF outperforms the other algorithms, as it finds the best solution in both the Umatilla and Blaine cases and reduces the computational budget by at least 50 % in both problems. Additionally, statistical comparisons show that the p-SRBF results are better than those of the alternative algorithms at the 5 % significant level. This study enriches theoretical real-world groundwater remediation methods. The results demonstrate that p-SRBF is promising for environmental management problems that involve computationally expensive models.

High-fidelity gradient-free optimization of low-pressure turbine cascades

In this paper we demonstrate the ability to perform shape optimization of Low Pressure Turbine (LPT) cascades using a combination of Large Eddy Simulation (LES) and the Mesh Adaptive Direct Search (MADS) optimization algorithm. To our knowledge, this is the first instance of aerodynamic shape design of LPT cascade blades using LES. Current industry-standard optimization of LPT cascades is performed using the Reynolds Averaged Navier–Stokes (RANS) approach. However, this is limited by inherent inaccuracies of existing turbulence models, particularly in the presence of transitional and separated turbulent flows. To alleviate this, our approach utilizes LES in lieu of RANS, which has been shown to provide more accurate results in flow regimes where RANS often fails. We first validate our LES simulations for a baseline T106D LPT cascade against available experimental data, showing good agreement. We then perform shape optimization using two different objective functions. The first optimization cycle, specified to minimize total pressure loss coefficient while maintaining tangential force, shows an improvement of 16% relative to the baseline T106D. The second optimization cycle, specified to maximize tangential force while maintaining total pressure loss coefficient, shows an improvement of 29% relative to the baseline T106D. Based on these results we conclude that optimization of LPT cascades with LES is feasible, and can yield significant improvements in performance with reasonable computational cost. Hence, this work supports a transition to higher-fidelity LES simulations as the foundation for optimization of next-generation LPT cascades.

Escaping Unknown Discontinuous Regions in Blackbox Optimization

The design of key nonlinear systems often requires the use of expensive blackbox simulations presenting inherent discontinuities whose positions in the variable space cannot be analytically predicted. Without further precautions, the solution of related optimization problems leads to design configurations which may be close to discontinuities of the blackbox output functions. These discontinuities may betray unsafe regions of the design space, such as nonlinear resonance regions. To account for possible changes of operating conditions, an acceptable solution must be away from unsafe regions of the space of variables. The objective of this work is to solve a constrained blackbox optimization problem with the additional constraint that the solution should be outside unknown zones of discontinuities or strong variations of the objective function or the constraints. The proposed approach is an extension of the mesh adaptive direct search (\sf Mads) algorithm and aims at building a series of inner approximations of these zones. The algorithm, called \sf DiscoMADS, relies on two main mechanisms: revealing discontinuities and progressively escaping the surrounding zones. A convergence analysis supports the algorithm and preserves the optimality conditions of \sf Mads. Numerical tests are conducted on analytical problems and on three engineering problems illustrating the following possible applications of the algorithm: the design of a simplified truss, the synthesis of a chemical component, and the design of a turbomachine blade. The \sf DiscoMADS algorithm successfully solves these problems by providing a feasible solution away from discontinuous regions.

Quantifying uncertainty with ensembles of surrogates for blackbox optimization

Blackbox optimization tackles problems where the functions are expensive to evaluate and where no analytical information is available. In this context, a tried and tested technique is to build surrogates of the objective and the constraints in order to conduct the optimization at a cheaper computational cost. This work introduces an extension to a specific type of surrogates: ensembles of surrogates, enabling them to quantify the uncertainty on the predictions they produce. The resulting extended ensembles of surrogates behave as stochastic models and allow the use of efficient Bayesian optimization tools. The method is incorporated in the search step of the mesh adaptive direct search (MADS) algorithm to improve the exploration of the search space. Computational experiments are conducted on seven analytical problems, two multi-disciplinary optimization problems and two simulation problems. The results show that the proposed approach solves expensive simulation-based problems at a greater precision and with a lower computational effort than stochastic models.

Constrained stochastic blackbox optimization using a progressive barrier and probabilistic estimates

This work introduces the StoMADS-PB algorithm for constrained stochastic blackbox optimization, which is an extension of the mesh adaptive direct-search (MADS) method originally developed for deterministic blackbox optimization under general constraints. The values of the objective and constraint functions are provided by a noisy blackbox, i.e., they can only be computed with random noise whose distribution is unknown. As in MADS, constraint violations are aggregated into a single constraint violation function. Since all functions values are numerically unavailable, StoMADS-PB uses estimates and introduces so-called probabilistic bounds for the violation. Such estimates and bounds obtained from stochastic observations are required to be accurate and reliable with high but fixed probabilities. The proposed method, which allows intermediate infeasible iterates, accepts new points using sufficient decrease conditions and imposing a threshold on the probabilistic bounds. Using Clarke nonsmooth calculus and martingale theory, Clarke stationarity convergence results for the objective and the violation function are derived with probability one.

Insights on sustainable separation of ternary azeotropic mixture tetrahydrofuran/ethyl acetate/water using hybrid vapor recompression assisted side-stream extractive distillation

The energy-efficiency of the traditional distillation-based processes are low, which results in waste of resources and environmental pollution. Therefore, a sustainable extractive distillation (ED) process should be developed to reduce energy consumption and CO2 emissions while improve the energy efficiency. In this work, a systematic approach is developed for the first time, for the separation of ternary azeotropic mixture containing Tetrahydrofuran (THF)/Ethyl acetate (EtAC)/Water via the combination of side-stream distillation and vapor recompression heat pump techniques. Firstly, the conceptual design of the various intensified schemes such as single (or double) side-stream(s) ED configurations are developed. Subsequently, the developed configurations were optimized using mesh adaptive direct search algorithm to obtain the optimal operating conditions of the established processes. Vapor recompression heat pump technique is used to further reduce the energy consumption. The sustainability of the various established configurations is assessed via the comparison of total annual cost (TAC), CO2 emissions, energy consumption, and thermodynamic efficiency. Overall, it was revealed that the TAC, CO2 emissions, and energy-consumption for the integrated vapor recompression assisted side-stream ED process were reduced by 33%, 49%, and 38%, respectively, relative to the conventional triple column ED. Likewise, the thermodynamic efficiency was improved by 52%.

Multicriterion Resource Management in Energy-Harvested Cooperative UAV-Enabled IoT Networks

Cooperative communication by employing unmanned aerial vehicle (UAV)-based relays with radio-frequency (RF) energy harvesting (EH) has been emerged as a prominent solution to provide extended coverage, connectivity, capacity, energy efficiency, and reliability in the future Internet-of-Things (IoT) systems. For successful integration of UAV relays in IoT networks, efficient radio resource management (RRM) is critical. We developed a multicriterion framework for energy-efficient RRM in a cooperative IoT network. We considered UAVs as relays, onboard EH facilities and deployed to relay the messages from a satellite terminal to the network IoT devices. We adopted a power splitting (PS)-based EH scheme, i.e., PS relaying protocol, for RF-EH at UAV relays. We formulate a joint optimization problem for IoT device selection, UAV relay assignment, source power allocation, and PS ratio selection. In our multicriterion framework, we consider three conflicting objectives by applying a weighted-sum method: 1) maximizing the network sum rate; 2) maximizing the number of IoT devices to be served; and 3) minimizing the carbon dioxide emissions. We propose an outer approximation algorithm (OAA) to solve the formulated problem, which is a mixed-integer nonlinear programming (MINLP) problem. Simulation results of the proposed algorithm are compared with two existing solutions, namely, the nonlinear optimization by mesh adaptive direct search (NOMAD) algorithm and an evolutionary algorithm (EA). The performance of the NOMAD algorithm is better in terms of computational complexity. However, the simulation results reveal the supremacy of the proposed OAA in terms of network sum rate, the number of selected IoT devices, and network utility.

Exploring and exploiting ant colony optimization algorithm for vertical highway alignment development

AbstractThe vertical alignment optimization is about developing a minimum cost curvilinear vertical profile of constrained grade sections and appropriate non‐overlapping vertical curves passing through fixed control points with elevation constraints. Variations in ground profile and discreteness in unit cutting and filling costs make it a non‐convex, noisy, constrained optimization problem with many local minima. Further, the gradient related constraints and vertical curvature are non‐linear. This paper presents an innovative exploring and exploiting ant colony optimization (E&E‐ACO) algorithm with an appropriate point sampling, vertical curve fitting strategies, and an intuitive feasible region identification approach for solving the vertical alignment optimization problem. The E&E‐ACO algorithm extensively explores the feasible search space to generate a set of potential solutions and effectively exploit the space around the potential solutions for developing the optimized vertical alignment. The efficacy of the proposed method is demonstrated using two case studies. In one case study, the optimized solution by the proposed method had a marginally better objective function value and about three times lesser computational time than the solution by the mesh adaptive direct search method. The optimized alignment satisfied the elevation constraints of fixed control points and imitated the manually designed real‐world vertical alignment. The linearly varying exploration and exploitation parameters had better convergence rate than the other tested variations. Further, the proposed method at the end of 1000 iterations yielded about six times better result than the traditional ACO algorithm.

An Efficient Bi-Objective Optimization Workflow Using the Distributed Quasi-Newton Method and Its Application to Well-Location Optimization

SummaryAlthough it is possible to apply traditional optimization algorithms to determine the Pareto front of a multiobjective optimization problem, the computational cost is extremely high when the objective function evaluation requires solving a complex reservoir simulation problem and optimization cannot benefit from adjoint-based gradients. This paper proposes a novel workflow to solve bi-objective optimization problems using the distributed quasi-Newton (DQN) method, which is a well-parallelized and derivative-free optimization (DFO) method. Numerical tests confirm that the DQN method performs efficiently and robustly.The efficiency of the DQN optimizer stems from a distributed computing mechanism that effectively shares the available information discovered in prior iterations. Rather than performing multiple quasi-Newton optimization tasks in isolation, simulation results are shared among distinct DQN optimization tasks or threads. In this paper, the DQN method is applied to the optimization of a weighted average of two objectives, using different weighting factors for different optimization threads. In each iteration, the DQN optimizer generates an ensemble of search points (or simulation cases) in parallel, and a set of nondominated points is updated accordingly. Different DQN optimization threads, which use the same set of simulation results but different weighting factors in their objective functions, converge to different optima of the weighted average objective function. The nondominated points found in the last iteration form a set of Pareto-optimal solutions. Robustness as well as efficiency of the DQN optimizer originates from reliance on a large, shared set of intermediate search points. On the one hand, this set of searching points is (much) smaller than the combined sets needed if all optimizations with different weighting factors would be executed separately; on the other hand, the size of this set produces a high fault tolerance, which means even if some simulations fail at a given iteration, the DQN method’s distributed-parallel information-sharing protocol is designed and implemented such that the optimization process can still proceed to the next iteration.The proposed DQN optimization method is first validated on synthetic examples with analytical objective functions. Then, it is tested on well-location optimization (WLO) problems by maximizing the oil production and minimizing the water production. Furthermore, the proposed method is benchmarked against a bi-objective implementation of the mesh adaptive direct search (MADS) method, and the numerical results reinforce the auspicious computational attributes of DQN observed for the test problems.To the best of our knowledge, this is the first time that a well-parallelized and derivative-free DQN optimization method has been developed and tested on bi-objective optimization problems. The methodology proposed can help improve efficiency and robustness in solving complicated bi-objective optimization problems by taking advantage of model-based search algorithms with an effective information-sharing mechanism.NOTE: This paper is also published as part of the 2021 SPE Reservoir Simulation Conference Special Issue.

Gradient-free aerodynamic shape optimization using Large Eddy Simulation

In this paper we demonstrate the ability to perform gradient-free aerodynamic shape optimization using Large Eddy Simulation (LES) with the Mesh Adaptive Direct Search (MADS) optimization algorithm. We first outline the challenges associated with performing gradient-based optimization using LES, specifically chaotic divergence of the adjoint. We then introduce a Dynamic Polynomial Approximation (DPA) procedure, which allows the high-order solution polynomial representation used by the flow solver to be increased, or decreased, depending on the poll size being used by MADS. This allows rapid convergence towards the optimal design space using lower-fidelity simulations, followed by automatic transition to higher-fidelity simulations when close to the optimal design point. We demonstrate the utility of MADS for optimization of simple chaotic problems, specifically the Lorenz system. We then demonstrate the utility of DPA for aerodynamic optimization of a low Reynolds SD7003 airfoil, highlighting the benefits of the binary DPA approach. Finally, we perform aerodynamic optimization of a turbulent SD7003 airfoil with a final design that increases the mean lift to drag ratio by 32% relative to experimental data, demonstrating that shape optimization using LES and MADS is feasible for aerodynamic design.