Complicated Design Problems Research Articles

A Double Exponential Particle Swarm Optimization with non-uniform variates as stochastic tuning and guaranteed convergence to a global optimum with sample applications to finding optimal exact designs in biostatistics

Nature-inspired metaheuristic algorithms, like Particle Swarm Optimization (PSO), are powerful general-purpose optimization tools but they invariably do not come with rigorous theoretical justifications and can fail to find a global optimum. By treating PSO as a random search optimization process and repairing the famous Global Search Convergence Theorem by imposing an additional condition in the proof, we create a novel theory-based algorithm called the Double Exponential Particle Swarm optimization algorithm (DExPSO) that converges to a global optimum. In particular, we show the common practice of using uniform variates as stochastic components in PSO and related algorithms does not satisfy the sufficient conditions in DExPSO and hence may provide a reason why PSO and other nature-inspired algorithms, like QPSO, LcRiPSO, and CSO can fail to converge. Additionally, in more complicated design problems, we show that DExpSO tends to converge to the support points of the optimal design more frequently and faster than PSO and its variants do. Moreover, there is a possibility to modify other PSO variants to DExPSO variants, and such hybridization offers promising improvement in the quality of the global search. Our applications include finding designs that minimize the integrated mean squared prediction error and locally D-optimal exact designs for a 68-compartmental model to assess radioactive particles retained in the human lung after exposure. Because PSO, and more generally, metaheuristics are used across disciplines, including ecology, pharmacokinetics and pharmacodynamics studies, agriculture, engineering, and computer science, there are potentially broad and deep implications of our results.

Finite Element In-Depth Verification: Base Displacements of a Spherical Dome Loaded by Edge Forces and Moments

Nowadays, engineers possess a wealth of numerical packages in order to design civil engineering structures. The finite element method offers a variety of sophisticated element types, nonlinear materials, and solution algorithms, which enable engineers to confront complicated design problems. However, one of the difficult tasks is the verification of the produced numerical results. The present paper deals with the in-depth verification of a basic problem, referring to the axisymmetric loading by edge forces/moments of a spherical dome, truncated at various roll-down angles, φo. Two formulations of analytical solutions are derived by the bibliography; their results are compared with those produced by the implementation of the finite element method. Modelling details, such as the finite element type, orientation of joints, application of loading, boundary conditions, and results’ interpretation, are presented thoroughly. Four different ratios of the radius of curvature, r and shell’s thickness, and t are examined in order to investigate the compatibility between the implementation of the finite element method to the “first-order” shell theory. The discussion refers to the differences not only between the numerical and analytical results, but also between the two analytical approaches. Furthermore, it emphasizes the necessity of contacting even linear elastic preliminary verification numerical tests as a basis for the construction of more elaborated and sophisticated models.

Design of graphene-based terahertz absorber and machine learning prediction model

In today's revolution of artificial intelligence, machine learning (ML) has come up with providing most rapid, accurate solution towards many complicated design problems. In this paper, a regression-based machine learning model has been developed, trained, and tested to forecast the performance of the Terahertz absorber. Different parameter variations of the dual circular ring Graphene FSS absorber viz., periodicity, thicknesses and radius of circular rings have been performed to attain maximum absorption of 99.9 % at center frequency 10.5 THz and bandwidth 1 THz (10.0 THz – 11.0 THz). The efficiency of nine different regression models (Keras regressor, Histogram gradient regressor, adaboost regressor, gradient boosting regressor, random forest regressor, decision tree regressor, k neighbours regressor, ridge regression, and linear regression) were tested against accurately predicting the absorption values and their performances were compared using R2 score and RSME. The study yielded very good R2 scores (near to 1.0) in case of random forest regression, thereby, demonstrating its effectiveness for future absorptivity prediction. The developed model considerably reduces time and effort in accurate prediction of the design parameters for THz absorber for any given absorptivity.

Neural Networks Applicability for Design of Reinforced Concrete Sections for Bending

Solving engineering design tasks requires the use of analytical formulas and dependencies. The direct inclusion of mathematical expressions in the artificial neural network (ANN) is not possible. This research studies the possibility of applying the neural networks method for designing of single or double-side reinforced concrete sections. A Visual Basic for Applications (VBA) macro was developed in the MS Excel environment to solve the task of determining the required area of the reinforcement by given geometric dimensions and bending moment and applying classical analytical formulas for reinforced concrete sections design. The training of the pre-configured neural network is performed by approximately 34000 sets of matching input parameters. The presented results from the trained ANN are compared and analysed against the exact analytical solutions. The study presents an approach to the application of structural design calculations. The results suggest that the approach is applicable to more complicated structural design problems.

Kriging-Based Space Exploration Global Optimization Method in Aerodynamic Design

For complicated aerodynamic design problems, the efficient global optimization method suffered from the defect of the incorrect portrayal of the design space, resulting in bad global convergence and efficiency performance. To this end, a Kriging-based global optimization method, named the Kriging-based space exploration method (KSE), was proposed in this paper. It selected multiple promising local minima and classified them into partially and fully explored minima in terms of the fitting quality of the surrogate model. Then, the partially explored minima would be furtherly exploited. During the local search, an enhanced trust-region method was adopted to make deep exploitation. By combining local and global searches, the proposed method could improve the fitting quality of the surrogate model and the optimization efficiency. The KSE was compared to other global surrogate-based optimization methods on 12 bound-constrained testing functions with 2 to 16 design variables and 2 aerodynamic optimization problems with 24 to 77 design variables. The results indicated that the KSE generally took fewer function evaluations to find the global optima or reach the target value in most test problems, holding better efficiency and robustness.

Optimum sizing of members of truss structures using direct design and a self-adaptive mutationdifferential evolution

Direct design using nonlinear inelastic analysis has been recently enabled for structural design as this approach can directly predict the behaviour of a structure as a whole, which eliminates capacity checks for individual structural members. However, the use of direct design is often accompanied by excessive computational efforts, especially for complicated structural design problems such as optimization or reliability analysis. In this study, we introduce an efficient method for the sizing optimization of truss structures employing nonlinear inelastic analysis for the direct design of structures. The objective function is the total weight of the structure while the strength and serviceability constraints are evaluated with nonlinear inelastic analysis. To save computational cost, an improved differential evolution (DE) algorithm is employed. Compared to the conventional DE algorithm, the proposed method has two major improvements: (1) a self-adaptive mutation strategy based on the p-best method to enhance the balance between global and local searches and (2) use of the multi-comparison technique (MCT) to reduce redundant structural analyses. The numerical results of a 72-bar truss case study demonstrate that the performance of the proposed method has significant advantages over the traditional DE method.

A Unique Transdisciplinary Engineering-Based Integrated Approach for the Design of Temporary Refugee Housing Using Kano, HOQ/QFD, TRIZ, AD, ISM and DSM Tools

The continued displacement of refugees from their homes and homelands (now greater than 50 million people worldwide) places increased focus and attention on evolving the designs of temporary housing that is available to be provided to the refugee population, especially in rural areas where housing does not already exist and must be constructed in very little time. Complex engineering problems involving social issues, such as this case study, benefit from the use of Integrated Transdisciplinary (TD) Tools (ITDT) to effectively and efficiently address the design questions related to them. The integrated use of TD Tools such as Kano Analysis, KJ Diagrams, Critical to Quality (CTQ), House of Quality (HOQ)/Quality Function Design (QFD), Theory of Inventive Problem Solving (TRIZ), Axiomatic Design (AD), Interpretive Structural Modeling (ISM), and Design Structure Matrix (DSM) through an end-to-end unique design process leads to innovation and elimination of design conflicts for especially complicated design problems. The objective of this study is to examine the design of temporary refugee housing using integrated TD tools mentioned above. This research concludes that the use of the ITDT approach provides an innovative, decoupled design.

Numerical and experimental study on comprehensive optimization for the KPIs of ship propulsion shafting design based on MDO

Ship propulsion shafting as an important part of the main power plant, its design quality affects the safety, stability and sustainability of ship operation directly, and it includes many components, which subjects to complex external loads during operation. Its design process is a complicated system design problem, which involves structure science, statics, rotor dynamics and other disciplines. To improve the quality and efficiency of shafting design, the Multi-disciplinary Design Optimization (MDO) strategy was adopted to achieve the optimal design in this paper. Further, the multi-objective optimization framework was established by analyzing the characteristics of the shafting design. The optimization strategy was employed to write the optimization algorithm and multidisciplinary design optimization scheme was obtained. In order to demonstrate the feasibility of this proposed method, a shafting testing platform (STP) was taken as an example, the vertical displacements of its two bearings were determined as design variables, and its key preference indexes (KPIs) comprehensive optimization objective function was acquired due to its practice states. Then, the MDO framework of the STP was constructed. The design variables were optimized by application of multi-objective Genetic Algorithm (MOGA), and the feasibility of this design idea was verified by several designed experiments.

A Review on Strut and Tie Methods

Strut and tie method (STM) provides simplified solutions to complicated design problems. It was an evolutionary discovery which lead to an improved understanding of shear and flexural deformations of the structures. STM is applicable to the regions of the structure where beam theory is not valid. Numerous studies were conducted in this field, and various modifications are being attached to the conventional STM. Indeterminate models replaced determinate models, and nonlinear analysis replaced linear elastic analysis. New ideas like automatic generation of models based on optimisation techniques, simplified inelastic analysis using secant stiffness method and 3-dimensional analysis were also introduced. This paper summarises some of these studies and discusses their merits and limitations. Some suggestions to simplify these complicated methods are also included.

Physics-Based Approach for a Neural Networks Enabled Design of All-Dielectric Metasurfaces

Machine learning methods have found novel application areas in various disciplines as they offer low-computational cost solutions to complex problems. Recently, metasurface design has joined among these applications, and neural networks enabled significant improvements within a short period of time. However, there are still outstanding challenges that needs to be overcome. Here, we propose a data pre-processing approach based on the governing laws of the physical problem to eliminate dimensional mismatch between high dimensional optical response and low dimensional feature space of metasurfaces. We train forward and inverse models to predict optical responses of cylindrical meta-atoms and to retrieve their geometric parameters for a desired optical response, respectively. Our approach provides accurate prediction capability even outside the training spectral range. Finally, using our inverse model, we design and demonstrate a focusing metalens as a proof-of-concept application, thus validating the capability of our proposed approach. We believe our method will pave the way towards practical learning-based models to solve more complicated photonic design problems.

Transceiver Design for AF MIMO Relay Systems With a Power Splitting Based Energy Harvesting Relay Node

In this article, a dual-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay communication system is studied. With a splitting (PS) protocol, the relay node harvests the radio frequency (RF) energy in the signals sent by the source node and utilizes the harvested energy to forward signals from the source node to the destination node. We aim at maximizing the source-destination mutual information (MI) through a joint design of the source matrix, the relay matrix, and the PS ratios under the source node power constraint and the relay node harvested energy constraint. We consider a general sum energy constraint at the relay node with different PS ratios across relay antennas, which includes existing works based on uniform PS or per data stream energy constraint as special cases. Moreover, a practical nonlinear energy harvesting (EH) model is adopted, where the harvested energy is bounded as the incident RF signal power increases. We establish the structure of the source matrix and the relay matrix, which simplifies the complicated transceiver design problem with matrix variables to a power distribution problem with scalar variables. Three approaches are proposed to efficiently solve the optimal power distribution problem. In particular, the first proposed algorithm solves the original nonconvex power allocation problem using the sequential quadratic programming, while the other two algorithms convert the original problem to convex problems by exploiting a tight upper bound and a tight lower bound of the objective function, respectively. Numerical simulations demonstrate that when the EH circuit works in the linear region, the proposed algorithms have a larger system MI than existing PS and TS based MIMO AF relay systems. The peak harvest power constraint plays an important role in choosing the location of the relay node.

P-lsGOF: A parallel learning-selection-based global optimization framework

When optimizing complicated engineering design problems, the search spaces are usually extremely nonlinear, leading to the great difficulty of finding optima. To deal with this challenge, this paper introduces a parallel learning-selection-based global optimization framework (P-lsGOF), which can divide the global search space to numbers of sub-spaces along the variables learned from the principal component analysis. The core search algorithm, named memory-based adaptive differential evolution algorithm (MADE), is parallel implemented in all sub-spaces. MADE is an adaptive differential evolution algorithm with the selective memory supplement and shielding of successful control parameters. The efficiency of MADE on CEC2017 unconstrained problems and CEC2011 real-world problems is illustrated by comparing with recently published state-of-the-art variants of success-history based adaptative differential evolution algorithm with linear population size reduction (L-SHADE) The performance of P-lsGOF on CEC2011 problems shows that the optimized results by individually conducting MADE can be further improved.

Transferring freeform lens design into phase retrieval through intermediate irradiance transport.

Freeform lens design for the prescribed irradiance without thin element and paraxial approximations is very complicated. We propose to transport a point source irradiance before the required freeform lens into an intermediate irradiance estimate next to the lens. In this way, the complicated freeform lens design problem could be transferred into a simpler problem of retrieving the phase from the intermediate and target irradiances. The phase retrieval solution can help construct an approximate lens, which is subsequently used to update the intermediate irradiance. Several iterations could bring a good performance, as demonstrated by two challenging designs.

Homogenization of plasmonic crystals: seeking the epsilon-near-zero effect.

By using an asymptotic analysis and numerical simulations, we derive and investigate a system of homogenized Maxwell's equations for conducting material sheets that are periodically arranged and embedded in a heterogeneous and anisotropic dielectric host. This structure is motivated by the need to design plasmonic crystals that enable the propagation of electromagnetic waves with no phase delay (epsilon-near-zero effect). Our microscopic model incorporates the surface conductivity of the two-dimensional (2D) material of each sheet and a corresponding line charge density through a line conductivity along possible edges of the sheets. Our analysis generalizes averaging principles inherent in previous Bloch-wave approaches. We investigate physical implications of our findings. In particular, we emphasize the role of the vector-valued corrector field, which expresses microscopic modes of surface waves on the 2D material. We demonstrate how our homogenization procedure may set the foundation for computational investigations of: effective optical responses of reasonably general geometries, and complicated design problems in the plasmonics of 2D materials.

Dynamic Voltage and Frequency Scaling in NoCs With Supervised and Reinforcement Learning Techniques

Computer architects often face the challenging task of balancing various design considerations, such as performance, power, cost, and reliability. With its unprecedented success in numerous domains and disciplines, machine learning could be a promising approach to solving complicated architecture design and optimization problems. IEEE Transactions on Computers continues to lead research in this area, recently publishing more than 10 papers that propose innovative, viable, and promising ways to take the advantage of machine learning in computer architecture. Discusses how the IEEE Transactions on Computers will closely follow these exciting developments in applying machine learning to computer architectures and provide the latest academic and industry research.

Robust Beamforming Design for MISO Bursty Interference Channels Under Traffic Uncertainties

In this paper, we consider a coordinated beamforming design for a multiple-input single-output bursty interference channel. In practical scenarios, the distributed medium access control mechanisms or the decentralized networking protocols across different users contribute to the bursty nature of network traffic. The potential gains provided by such burstiness can be exploited by feeding back the interference state information to the transmitters. Errors may occur during such feedback, thus causing uncertainties in the user traffic and resulting in complicated beamforming design problems. In this paper, we model such traffic uncertainties by using a hidden Markov model (HMM). Assuming that perfect channel state information (CSI) is available at the transmitters, our goal is to maximize the average system utility subjected to average power constraints under traffic uncertainties. We also extend the optimization problem to the imperfect CSI case. However, the resulting problem is highly nonconvex. Hence, we apply a series of convex approximation techniques. We further improve the approximation accuracy by using our proposed successive convex approximation (SCA) algorithms (HMM-SCA). In our simulation results, we observe that our proposed HMM-SCA provides a $46.3\%$ improvement in weighted sum rate over the SCA algorithm, in which the interference is assumed to be always present (NB-SCA). For the average weighted geometric mean rate, we observe that our proposed HMM-SCA also provides a $41.3\%$ improvement over the NB-SCA when user fairness is considered. Therefore, it is crucial to exploit bursty traffic for a practical wireless communication system when channel estimation errors are considered.

A decision-making methodology for material selection using genetic algorithm

Material selection is a challenging task for designers due to the immense number of different materials available today. Choosing the right materials plays an important role in numerous engineering applications because an inappropriate selection of materials can significantly affect the performance of the final product. As a result, a number of techniques have been proposed to select materials in the engineering design process. However, most of the proposed systems are knowledge intensive and cannot deal with the situation where the information of weight criteria is incomplete or unknown. So, in this paper a logical approach is presented for choosing an optimal material by employing the genetic algorithm. The proposed material selection procedure reduces the personal bias for assigning the weight of different attributes. Seven examples are included to demonstrate the applicability of the suggested approach. The findings of this work provide the insights for further researches on more complicated design problems such as simultaneous material selection and geometry optimisation.

An introduction to partial differential equations constrained optimization

Partial differential equation (PDE) constrained optimization is designed to solve control, design, and inverse problems with underlying physics. A distinguishing challenge of this technique is the handling of large numbers of optimization variables in combination with the complexities of discretized PDEs. Over the last several decades, advances in algorithms, numerical simulation, software design, and computer architectures have allowed for the maturation of PDE constrained optimization (PDECO) technologies with subsequent solutions to complicated control, design, and inverse problems. This special journal edition, entitled “PDE-Constrained Optimization”, features eight papers that demonstrate new formulations, solution strategies, and innovative algorithms for a range of applications. In particular, these contributions demonstrate the impactfulness on our engineering and science communities. This paper offers brief remarks to provide some perspective and background for PDECO, in addition to summaries of the eight papers.

Integrated selection of gearbox, gear ratio, and motor through scaling rules

ABSTRACTThe optimal selection of gearbox, gear ratio, and motor is a complicated design problem. To solve this issue, this article proposes a novel model-based, integrated methodology that improves the concept of optimal gear ratio. The method accounts for the chief relations between the characteristics of motor, gearbox, and gear ratio through scaling rules. The main nonideal behaviors and limitations of off-the-shelf components are included. The gear ratio minimizing the motor size is finally obtained. The result reduces the need of iterations in the design and aids in finding the optimal combination of motor and gearbox.

A new sequential sampling method for constructing the high-order polynomial surrogate models

PurposeThis paper aims to study the sampling methods (or design of experiments) which have a large influence on the performance of the surrogate model. To improve the adaptability of modelling, a new sequential sampling method termed as sequential Chebyshev sampling method (SCSM) is proposed in this study.Design/methodology/approachThe high-order polynomials are used to construct the global surrogated model, which retains the advantages of the traditional low-order polynomial models while overcoming their disadvantage in accuracy. First, the zeros of Chebyshev polynomials with the highest allowable order will be used as sampling candidates to improve the stability and accuracy of the high-order polynomial model. In the second step, some initial sampling points will be selected from the candidates by using a coordinate alternation algorithm, which keeps the initial sampling set uniformly distributed. Third, a fast sequential sampling scheme based on the space-filling principle is developed to collect more samples from the candidates, and the order of polynomial model is also updated in this procedure. The final surrogate model will be determined as the polynomial that has the largest adjusted R-square after the sequential sampling is terminated.FindingsThe SCSM has better performance in efficiency, accuracy and stability compared with several popular sequential sampling methods, e.g. LOLA-Voronoi algorithm and global Monte Carlo method from the SED toolbox, and the Halton sequence.Originality/valueThe SCSM has good performance in building the high-order surrogate model, including the high stability and accuracy, which may save a large amount of cost in solving complicated engineering design or optimisation problems.