Mesh Adaptive Direct Search Algorithm Research Articles

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.

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.

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.

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.

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.

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.

Improved design of heat-pump extractive distillation based on the process optimization and multi-criteria sustainability analysis

In order to achieve the sustainable separation design of azeotropic mixtures, this study proposed a systematic framework for distillation process optimization and intensification based on a composite sustainability index. Binary minimum azeotropic mixture ethanol-ethyl propionate was studied as an illustrative example. Specifically, three extractive distillation configurations were firstly applied on the separation and the sustainability of distillation processes were evaluated comprehensively. The composite sustainability index was constructed with the indicators of the economic, environmental, technical and social dimensions, and fuzzy weighting method was used to determine the weight of each indicator. Then, the process can be optimized with the objective of the composite sustainability index by the mesh adaptive direct search algorithm. After that, the heat-pump is further implemented to make full use of the latent heat of vapor stream in the distillation system . The T-H diagram of two upgraded processes clearly demonstrates the heat recovery while considering the specified minimum heat-transfer temperature difference.

Energy efficient resource allocation in cache‐enabled fog networks

AbstractTo gain high energy efficiency and low latency, fog computing can be considered as a promising enabling technology for supporting future IoT networks. Exponentially increasing data rate demand of smart IoT devices in the fifth‐Generation (5G) networks require new resource management and power allocation schemes. Fog computing involves the deployment of data storage devices (fog nodes) near the proximity of IoT nodes. The fog nodes collaborate to process requests generated from users. These nodes can store data in their storage capacity and supports in achieving quality‐of‐service (QoS) requirements. A joint node association and energy efficiency maximization problem is formulated in this article. The proposed problem is a non‐linear concave programming problem under cache size, association, and optimal power allocation constraints. A mesh adaptive direct search algorithm (MADS) is used to solve the formulated problem to find the sub‐optimal results. The efficient performance of the algorithm can be seen in comparison with more complex algorithms namely, outer approximation algorithm and exhaustive search algorithm. Extensive simulations are done to observe the detailed performance analysis of the IoT‐Fog network. As a result, energy‐efficient resource allocation is done under cache and QoS constraints with very little complexity and low computational power and delays.

Simulation and optimization of continuous catalytic reforming: Reducing energy cost and coke formation

Continuous catalytic naphtha reformers are one of the main refinery units producing hydrogen. Reliable and comprehensive modeling of such a complex and integrated refinery unit plays a pivotal role in optimization to increase the efficiency of the process. A reaction network with 26 pseudo components and 58 reactions, considering coke formation and catalyst activity, was proposed to predict the outlet compositions of reactors in more detail. The whole unit, including reaction and purification sections, was simulated to cover all products. NOMAD optimizer, with the mesh adaptive direct search algorithm, is used to minimize energy costs. Non-linear constraints were defined to guarantee the quality of the final products. The optimized decision variables reduced the energy cost by 13.5%, mainly caused by a significant decline in natural gas consumption. The simulation also indicated an increase of 4800 ton/y in reformate production, which the product is rich in aromatics. By contrast, LPG, hydrogen-rich gas, and coke production dropped by nearly 4355, 321, and 127 ton/y, respectively. The coke production decline can significantly increase the catalyst lifetime and decrease the operating cost of the catalyst regeneration unit.

Biobjective Optimization of Well Placement: Algorithm, Validation, and Field Testing

Summary We describe the development and validation of a novel algorithm for field-development optimization problems and document field-testing results. Our algorithm is founded on recent developments in bound-constrained multiobjective optimization of nonsmooth functions for problems in which the structure of the objective functions either cannot be exploited or are nonexistent. Such situations typically arise when the functions are computed as the result of numerical modeling, such as reservoir-flow simulation within the context of field-development planning and reservoir management. We propose an efficient implementation of a novel parallel algorithm, namely BiMADS++, for the biobjective optimization problem. Biobjective optimization is a special case of multiobjective optimization with the property that Pareto points may be ordered, which is extensively exploited by the BiMADS++ algorithm. The optimization algorithm generates an approximation of the Pareto front by solving a series of single-objective formulations of the biobjective optimization problem. These single-objective problems are solved using a new and more efficient implementation of the mesh adaptive direct search (MADS) algorithm, developed for nonsmooth optimization problems that arise within reservoir-simulation-based optimization workflows. The MADS algorithm is extensively benchmarked against alternative single-objective optimization techniques before the BiMADS++ implementation. Both the MADS optimization engine and the master BiMADS++ algorithm are implemented from the ground up by resorting to a distributed parallel computing paradigm using message passing interface (MPI) for efficiency in industrial-scale problems. BiMADS++ is validated and field tested on well-location optimization (WLO) problems. We first validate and benchmark the accuracy and computational performance of the MADS implementation against a number of alternative parallel optimizers [e.g., particle-swarm optimization (PSO), genetic algorithm (GA), and simultaneous perturbation and multivariate interpolation (SPMI)] within the context of single-objective optimization. We also validate the BiMADS++ implementation using a challenging analytical problem that gives rise to a discontinuous Pareto front. We then present BiMADS++ WLO applications on two simple, intuitive, and yet realistic problems, and a model for a real problem with known Pareto front. Finally, we discuss the results of the field-testing work on three real-field deepwater models. The BiMADS++ implementation enables the user to identify various compromise solutions of the WLO problem with a single optimization run without resorting to ad hoc adjustments of penalty weights in the objective function. Elimination of this “trial-and-error” procedure and distributed parallel implementation renders BiMADS++ easy to use and significantly more efficient in terms of computational speed needed to determine alternative compromise solutions of a given WLO problem at hand. In a field-testing example, BiMADS++ delivered a workflow speedup of greater than fourfold with a single biobjective optimization run over the weighted-sums objective-function approach, which requires multiple single-objective-function optimization runs. NOTE: This paper is also published as part of the 2021 SPE Reservoir Simulation Conference Special Issue.

Combining Cross-Entropy and MADS Methods for Inequality Constrained Global Optimization

This paper proposes a way to combine the Mesh Adaptive Direct Search (MADS) algorithm with the Cross-Entropy (CE) method for nonsmooth constrained optimization. The CE method is used as an exploration step by the MADS algorithm. The result of this combination retains the convergence properties of MADS and allows an efficient exploration in order to move away from local minima. The CE method samples trial points according to a multivariate normal distribution whose mean and standard deviation are calculated from the best points found so far. Numerical experiments show the efficiency of this method compared to other global optimization heuristics. Moreover, applied on complex engineering test problems, this method allows an important improvement to reach the feasible region and to escape local minima.

SWIPT-Assisted Energy Efficiency Optimization in 5G/B5G Cooperative IoT Network

Resource use in point-to-point and point-to-multipoint communication emerges with the tremendous growth in wireless communication technologies. One of the technologies is wireless power transfer which may be used to provide sufficient resources for energy-constrained networks. With the implication of cooperative communication in 5G/B5G and the Internet of Things (IoT), simultaneous wireless information and power transfer (SWIPT)-assisted energy efficiency and appropriate resource use become challenging tasks. In this paper, multiple IoT-enabled devices are deployed to cooperate with the source node through intermediate/relay nodes powered by radio-frequency (RF) energy. The relay forwards the desired information generated by the source node to the IoT devices with the fusion of decode/amplify processes and charges itself at the same time through energy harvesting technology. In this regard, a problem with throughput, energy efficiency, and joint throughput with user admission maximization is formulated while assuring the useful, practical network constraints, which contemplate the upper/lower bounds of power transmitted by the source node, channel condition, and energy harvesting. The formulated problem is a mixed-integer non-linear problem (MINLP). To solve the formulated problem, the rate of individual IoT-enabled devices (b/s), number of selected IoT devices, and the sum-rate maximization are prosecuted for no-cooperation, cooperation with diversity, and cooperation without diversity. Moreover, a comparison of the outer approximation algorithm (OAA) and mesh adaptive direct search algorithm (MADS) for non-linear optimization with the exhaustive search algorithm is provided. The results with reference to the complexity of the algorithms have also been evaluated which show that 4.68×10−10 OAA and 7.81×10−11 MADS as a percent of ESA, respectively. Numerous simulations are carried out to exhibit the usefulness of the analysis to achieve the convergence to ε-optimal solution.

DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization

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.

Stochastic mesh adaptive direct search for blackbox optimization using probabilistic estimates

We present a stochastic extension of the mesh adaptive direct search (MADS) algorithm originally developed for deterministic blackbox optimization. The algorithm, called StoMADS, considers the unconstrained optimization of an objective function f whose values can be computed only through a blackbox corrupted by some random noise following an unknown distribution. The proposed method is based on an algorithmic framework similar to that of MADS and uses random estimates of function values obtained from stochastic observations since the exact deterministic computable version of f is not available. Such estimates are required to be accurate with a sufficiently large but fixed probability and to satisfy a variance condition. The ability of the proposed algorithm to generate an asymptotically dense set of search directions is then exploited using martingale theory to prove convergence to a Clarke stationary point of f with probability one.

Towards a Framework for Nonlinear Predictive Control using Derivative-Free Optimization

The use of derivative-based solvers to compute solutions to optimal control problems with non-differentiable cost or dynamics often requires reformulations or relaxations that complicate the implementation or increase computational complexity. We present an initial framework for using the derivative-free Mesh Adaptive Direct Search (MADS) algorithm to solve Nonlinear Model Predictive Control problems with non-differentiable features without the need for reformulation. The MADS algorithm performs a structured search of the input space by simulating selected system trajectories and computing the subsequent cost value. We propose handling the path constraints and the Lagrange cost term by augmenting the system dynamics with additional states to compute the violation and cost value alongside the state trajectories, eliminating the need for reconstructing the state trajectories in a separate phase. We demonstrate the practicality of this framework by solving a robust rocket control problem, where the objective is to reach a target altitude as close as possible, given a system with uncertain parameters. This example uses a non-differentiable cost function and simulates two different system trajectories simultaneously, with each system having its own free final time.

Data-driven storage location method for put system in Chinese flower auction centres

ABSTRACT The rapid increase in daily transactions poses severe challenges for Chinese flower auction centres, including more frequent travels for distribution workers and longer waiting times for buyers. Two distinctive features of Chinese flower auctions further complicate the studied process: buyer identities and purchased volumes of present buyers are not known in advance. Buyer identities become known only after their first bid and purchased volumes by present buyers remain uncertain until the end of the auction. To address these problems, we propose a data-driven storage location method for put systems in Chinese flower auction centres which reserves predetermined locations near the distribution I/O point to large potential buyers before their actual arrival and the remaining locations to other arriving buyers according to the closest open location policy. We use the mesh adaptive direct search algorithm to determine the size of the reserved area and release time of any unoccupied locations to later arriving buyers. The proposed method is verified via a case study, and results show that it outperforms the existing method by a fairly large margin.