Size Of Design Space Research Articles

A Speculative Divide-and-Conquer Optimization Method for Large Analog/Mixed-Signal Circuits: A High-Speed FFE SST Transmitter Example

We propose a speculative divide-and-conquer (SDnC) method that enables optimization of a large analog/mixed-signal (AMS) circuit. Because modules of AMS circuits strongly interact with neighbor modules, they cannot be optimized individually. Therefore, design parameters of all modules must be co-optimized for the global optimization, and thus, the design space exponentially grows with the circuit size. Although metaheuristic algorithms can enhance optimization efficiency, they cannot handle very large circuits due to the exponentially increased size of design space to explore. The proposed method utilized the divide-and-conquer (DnC) strategy in the circuit optimization while taking into account modules’ interactions, allowing modules to be individually evaluated and optimized. Therefore, this DnC-based optimization method hierarchically and systematically reduces both the optimization complexity and the evaluation complexity, and thus, this method is very scalable with the circuit size. The proposed method can also be combined with other metaheuristic algorithms such as particle swarm optimization (PSO) or artificial intelligence for faster optimization. In experiment, the proposed method enabled optimization of a high-speed link transmitter that has 2400–15 000 transistors and 45–47 independent design parameters for the first time. The optimization time was improved by 43 and three orders of magnitudes compared to parameter sweep and PSO, respectively. The penalties of speed-up by DnC were only 3.4% and 9.3% estimation errors in power consumption and eye height, respectively. Because of the greatly improved speed, the proposed method also enables quantitative analysis on performance-power tradeoff of a large AMS circuit.

Machine Learning in Advanced IC Design: A Methodological Survey

The increasing complexity and size of design space poses significant challenges for integrated circuit (IC) design. This article discusses the potential of machine learning (ML) methods to address these challenges and provides a comprehensive survey of the current state of knowledge along both IC design problems and ML-based solutions. The article also summarizes the open problems at the intersection of advanced IC design and ML.

Machine learning-based inverse design methods considering data characteristics and design space size in materials design and manufacturing: a review.

In the last few decades, the influence of machine learning has permeated many areas of science and technology, including the field of materials science. This toolkit of data driven methods accelerated the discovery and production of new materials by accurately predicting the complicated physical processes and mechanisms that are not fully described by existing materials theories. However, the availability of a growing number of increasingly complex machine learning models confronts us with the question of "which machine learning algorithm to employ". In this review, we provide a comprehensive review of common machine learning algorithms used for materials design, as well as a guideline for selecting the most appropriate model considering the nature of the design problem. To this end, we classify the material design problems into four categories of: (i) the training data set being sufficiently large to capture the trend of design space (interpolation problem), (ii) a vast design space that cannot be explored thoroughly with the initial training data set alone (extrapolation problem), (iii) multi-fidelity datasets (small accurate dataset and large approximate dataset), and (iv) only a small dataset available. The most successful machine learning-based surrogate models and design approaches will be discussed for each case along with pertinent literature. This review focuses mostly on the use of ML algorithms for the inverse design of complicated composite structures, a topic that has received a lot of attention recently with the rise of additive manufacturing.

Innovation level in set-based design: an integrated approach with chosen-to-fit and custom-to-fit solutions

Set-Based Design (SBD) is superior in risk reduction, knowledge creation, and innovation. However, its implementation demands more resources than traditional strategies. Thus, it is crucial to balance design space size and available resources to disseminate SBD. This paper proposes a method to define the level of innovation of subsystems enabling a hybrid development strategy, integrating the SBD and the Point-Based Design (PBD). We undertook a research action in a technological innovation design subject to significant knowledge and human/financial resource restrictions. The team allocated most resources in the SBD and focused efforts on critical subsystems. The exploratory and scientific nature of SBD enabled learning about the product without prior knowledge for supporting decision-making. By presenting the state-of-the-art regarding innovation level in SBD and proposing a method to define the level of innovation and a hybrid development strategy, this research paves the way for SBD in projects with significant resource restrictions.

Multi-Fidelity Gradient-Based Optimization for High-Dimensional Aeroelastic Configurations

The simultaneous optimization of aircraft shape and internal structural size for transonic flight is excessively costly. The analysis of the governing physics is expensive, in particular for highly flexible aircraft, and the search for optima using analysis samples can scale poorly with design space size. This paper has a two-fold purpose targeting the scalable reduction of analysis sampling. First, a new algorithm is explored for computing design derivatives by analytically linking objective definition, geometry differentiation, mesh construction, and analysis. The analytic computation of design derivatives enables the accurate use of more efficient gradient-based optimization methods. Second, the scalability of a multi-fidelity algorithm is assessed for optimization in high dimensions. This method leverages a multi-fidelity model during the optimization line search for further reduction of sampling costs. The multi-fidelity optimization is demonstrated for cases of aerodynamic and aeroelastic design considering both shape and structural sizing separately and in combination with design spaces ranging from 17 to 321 variables, which would be infeasible using typical, surrogate-based methods. The multi-fidelity optimization consistently led to a reduction in high-fidelity evaluations compared to single-fidelity optimization for the aerodynamic shape problems, but frequently resulted in a cost penalty for cases involving structural sizing. While the multi-fidelity optimizer was successfully applied to problems with hundreds of variables, the results underscore the importance of accurately computing gradients and motivate the extension of the approach to constrained optimization methods.

LIMITATIONS OF DESIGN SPACE-BASED INDICATORS FOR EARLY ROBUSTNESS ASSESSMENT

AbstractThis paper seeks to address the gap between qualitative Robust Design principles and parameter optimization. The former often fails to consider the challenging amount of details in embodiment and configuration design, while the latter is the widely accepted main thrust in traditional Robust Design. The gap is addressed by exploring the value of five quantitative robustness indicators for Design Space Exploration based on variables, objectives and constraints: The set level indicators, Design Space Size and Pareto Set Dispersion, and the point level indicators, Neighbourhood Performance, Failure Rate and Distance to Failure. As a background for the discussion of the limitations of these indicators an industrial case is presented. The case is an incremental encoder and includes two configurations for comparison, five objectives, eight variables, and a range of constraints. The design spaces are sampled and they show conflicting objectives, dispersed spaces and variables dependencies. Based on this it is suggested that set level indicators are more suitable than point level indicators of early robustness evaluation, but the available indicators are limited in their considerations of design space discontinuity and conflicts.

QUANTUM COMBINATORIAL DESIGN

AbstractCombinatorial Design such as configuration design, design optioneering, component selection, and generative design, is common across engineering. Generating solutions for a combinatorial design task often involves the application of classical computing solvers that can either map or navigate design spaces. However, it has been observed that classical computing resource power-law scales with many design space models. This observation suggests classical computing may not be capable of modelling our future design space needs.To meet future design space modelling needs, this paper examines quantum computing and the characteristics that enables its resources to scale polynomially with design space size. The paper then continues to present a combinatorial design problem that is subsequently represented, constrained and solved by quantum computing. The results of which are the derivation of an initial set of circuits that represent design space constraints. The study shows the game-changing possibilities of quantum computing as an engineering design tool and is the start of an exciting new journey for design research.

Evolutionary design of optimal surface topographies for biomaterials

Natural evolution tackles optimization by producing many genetic variants and exposing these variants to selective pressure, resulting in the survival of the fittest. We use high throughput screening of large libraries of materials with differing surface topographies to probe the interactions of implantable device coatings with cells and tissues. However, the vast size of possible parameter design space precludes a brute force approach to screening all topographical possibilities. Here, we took inspiration from Nature to optimize materials surface topographies using evolutionary algorithms. We show that successive cycles of material design, production, fitness assessment, selection, and mutation results in optimization of biomaterials designs. Starting from a small selection of topographically designed surfaces that upregulate expression of an osteogenic marker, we used genetic crossover and random mutagenesis to generate new generations of topographies.

Optimization of the manufacturing process of a complex amphotericin B liposomal formulation using quality by design approach.

In this work, the manufacturing process of a complex liposomal amphotericin B (AmB) product was optimized using quality by design (QbD) approach. A comprehensive QbD-based process understanding and design space (DS) to the critical process parameters (CPPs) is essential to the drug development and consistent quality control. The process was based on the acid-aided formation of drug-lipid complexes in a methanol-chloroform mixture (step I) followed by spray drying (step II), hydration and liposome formation by microfluidization (step III), and lyophilization (step IV). Firstly, the risk assessment was conducted to identify the critical process parameters among the four key steps. Nine CPPs and five CQAs (API Monomer identity (absorbance main peak at 321nm), API Aggregation identity (absorbance peak ratio, OD 415nm/321nm), particle size, in-vitro toxicity, and the cake quality) were determined based on their severity and occurrences with their contribution to the quality target product profile (QTPP). Based on the risk assessment results, the final screening design of experiments (DoE) was developed using fractional factorial design. Secondly, the empirical equation was developed for each CQA based on experimental data. The impact of CPPs on the CQAs was analyzed using the coefficient plot and contour plot. In addition to the effect of individual formulation parameters and process parameters, the effects of the four key separate steps were also evaluated and compared. In general, the curing temperature during microfluidization has been identified as the most significant CPP. Finally, design space exploration was carried out to demonstrate how the critical process parameters can be varied to consistently produce a drug product with desired characteristics. The design space size increased at the higher value of the curing temperature, the API to phospholipid ratio (API:PL), and the lower value of the DSPG to phospholipid ratio (PG:PL) and aspirator rate.

A Metamodel Based on Non-Uniform Rational Basis Spline Hyper-Surfaces for Optimisation of Composite Structures

This study presents a new strategy to generate a surrogate model used for design purposes. The metamodel is based on Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces and is able to fit non-convex sets of target points (TPs). The proposed method aims at determining all the parameters involved in the definition of the NURBS hyper-surface, i.e. control points (CPs) coordinates, weights, degrees, CPs number and knot-vector components. To this purpose, the problem of finding a suitable metamodel is formulated as a constrained non-linear programming problem (CNLPP) wherein the above variables are optimised in order to fit a set of TPs. Nevertheless, when the number of CPs and the degrees of the basis functions are included among the design variables, the resulting problem is defined over a space having a variable dimension. This problem is solved by means of a special genetic algorithm able to determine simultaneously the optimum value of both the design space size (related to the integer variables of the NURBS hyper-surface) and the NURBS hyper-surface continuous parameters. The NURBS-based metamodel is then used to emulate the first buckling load of a composite stiffened panel and it is used in the framework of a meaningful design problem.

Non-Uniform Rational Basis Spline hyper-surfaces for metamodelling

This study presents an original metamodelling technique based on Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces. The proposed approach is able to fit general non-convex sets of target points (TPs) by extending the NURBS formalism to the N-dimensional (N-D) case. The shape of such a hyper-surface is tuned by several parameters: the number of control points (CPs), their coordinates and the related weights, the degrees of the blending functions and the knot-vector components defined along each direction. The goal of the proposed strategy is to automatically determine (i.e. without the user’s intervention) the full set of parameters defining the NURBS hyper-surface approximating a given set of TPs, without considering simplifying hypotheses. To this purpose, the problem is formulated as a constrained nonlinear programming problem (CNLPP) wherein the optimization variables are all the parameters tuning the shape of the NURBS hyper-surface. Nevertheless, when the number of CPs and the degrees of the basis functions are included among the design variables, the resulting problem is defined over a space having a changing dimension. This problem is solved by means of an original genetic algorithm able to determine, simultaneously, the optimum value of both the design space size (related to the integer variables of the NURBS hyper-surface) and the NURBS hyper-surface continuous parameters. The effectiveness of the proposed approach is shown by means of two meaningful test cases. In addition, the proposed method has been applied to a benchmark taken from the literature and the results have been compared to those provided by the Proper Generalized Decomposition method.

A surrogate model based on Non-Uniform Rational B-Splines hypersurfaces

This study aims at providing an original metamodeling technique based on the Non-Uniform Rational B-Splines (NURBS) formalism. The proposed approach is able to fit general non-convex sets of target points (TPs) by extending the NURBS formalism to the N-dimensional (N-D) case, getting in this way a general NURBS hypersurface. The shape of such a hypersurface is tuned by several parameters: the number of control points (CPs), their coordinates and related weights, the degrees of the blending functions and the knot-vector components defined along each direction. The goal of the proposed strategy is to find the best NURBS hypersurface approximating a given set of TPs. To this purpose the problem is formulated as an unconstrained least-square distance problem wherein the optimisation variables are all the parameters tuning the shape of the NURBS hypersurface. Nevertheless, when the number of CPs and the degrees of the basis functions are included among the design variables the resulting problem is defined over a space having a variable dimension. To deal with this aspect, a special genetic algorithm, able to solve problems characterised by a variable number of design variables, is considered to determine automatically (i.e. without the user’s intervention) the optimum value of both the design space size (related to the integer variables of the NURBS hypersurface) and the NURBS hypersurface continuous parameters. The effectiveness of the proposed approach is proven by means of a meaningful benchmark.

Inverse design of an ultra-compact broadband optical diode based on asymmetric spatial mode conversion.

The objective-first inverse-design algorithm is used to design an ultra-compact optical diode. Based on silicon and air only, this optical diode relies on asymmetric spatial mode conversion between the left and right ports. The first even mode incident from the left port is transmitted to the right port after being converted into an odd mode. On the other hand, same mode incident from the right port is reflected back by the optical diode dielectric structure. The convergence and performance of the algorithm are studied, along with a transform method that converts continuous permittivity medium into a binary material design. The optimal device is studied with full-wave electromagnetic simulations to compare its behavior under right and left incidences, in 2D and 3D settings as well. A parametric study is designed to understand the impact of the design space size and initial conditions on the optimized devices performance. A broadband optical diode behavior is observed after optimization, with a large rejection ratio between the two transmission directions. This illustrates the potential of the objective-first inverse-design method to design ultra-compact broadband photonic devices.

An Integrated Exploration and Virtual Platform Framework for Many-Accelerator Heterogeneous Systems

The recent advent of many-accelerator systems-on-chip (SoC), driven by the need for maximizing throughput and power efficiency, has led to an exponential increase in the hardware/software co-design complexity. The reason of this increase is that the designer has to explore a vast number of architectural parameter combinations for each single accelerator, as well as inter-accelerator configuration combinations under specific area, throughput, and power constraints, given that each accelerator has different computational requirements. In such a case, the design space size explodes. Thus, existing design space exploration (DSE) techniques give poor-quality solutions, as the design space cannot be adequately covered in a fair time. This problem is aggravated by the very long simulation time of the many-accelerator virtual platforms (VPs). This article addresses these design issues by (a) presenting a virtual prototyping solution that decreases the exploration time by enabling the evaluation of multiple configurations per VP simulation and (b) proposing a DSE methodology that efficiently explores the design space of many-accelerator systems. With the use of two fully developed use cases, namely an H.264 decoding server for multiple video streams and a parallelized denoising system for MRI scans, we show that the proposed DSE methodology either leads to Pareto points that dominate over those of a typical DSE scenario or finds new solutions that might not be found by the typical DSE. In addition, the proposed virtual prototyping solution leads to DSE runtime reduction reaching 10 × for H.264 and 5 × for Rician denoise.

Using Rigid-Body Mechanism Topologies to Design Path Generating Compliant Mechanisms

For a path generation problem, this paper uses the base topology of a single degree-of-freedom (DOF) rigid-body mechanism solution to synthesize fully distributed compliant mechanisms that can trace the same path. Two different strategies are proposed to employ the base topology in the structural optimization so that its design space size can be intelligently reduced from an arbitrary complexity. In the first strategy, dimensional synthesis directly determines the optimal size and shape of the compliant mechanism solution while maintaining the exact base topology. In the second, the base topology establishes an initial mesh network to determine the optimal topology and dimensions simultaneously. To increase the possibility of converging to an optimal design, the objective metrics to evaluate the path generation ability are computed in a novel manner. A section-by-section analysis with a rigid-body transformation is implemented to examine the full path of each candidate mechanism. A two-objective genetic algorithm (GA) is employed to find a group of viable designs that tradeoff minimizing the average Euclidean distance between the desired and actual paths with minimizing the peak distance between corresponding points on those paths. Two synthesis examples generating straight-line and curved paths are presented to demonstrate the procedure's utility.

A comparative evaluation of multi-objective exploration algorithms for high-level design

This article presents a detailed overview and the experimental comparison of 15 multi-objective design-space exploration (DSE) algorithms for high-level design. These algorithms are collected from recent literature and include heuristic, evolutionary, and statistical methods. To provide a fair comparison, the algorithms are classified according to the approach used and examined against a large set of metrics. In particular, the effectiveness of each algorithm was evaluated for the optimization of a multiprocessor platform, considering initial setup effort, rate of convergence, scalability, and quality of the resulting optimization. Our experiments are performed with statistical rigor, using a set of very diverse benchmark applications (a video converter, a parallel compression algorithm, and a fast Fourier transformation algorithm) to take a large spectrum of realistic workloads into account. Our results provide insights on the effort required to apply each algorithm to a target design space, the number of simulations it requires, its accuracy, and its precision. These insights are used to draw guidelines for the choice of DSE algorithms according to the type and size of design space to be optimized.

Response improvement in complex experiments by co-information composite likelihood optimization

We propose an adaptive procedure for improving the response outcomes of complex combinatorial experiments. New experiment batches are chosen by minimizing the co-information composite likelihood (COIL) objective function, which is derived by coupling importance sampling and composite likelihood principles. We show convergence of the best experiment within each batch to the globally optimal experiment in finite time, and carry out simulations to assess the convergence behavior as the design space size increases. The procedure is tested as a new enzyme engineering protocol in an experiment with a design space size of order 107.

Dynamic-Size Multiple Populations Genetic Algorithm for Multigravity-Assist Trajectory Optimization

The problem of the optimal design of a multigravity-assist space trajectory, with a free number of deep space maneuvers, in its general form poses a multimodal objective function in which design space size is variable. This paperpresents a genetic-basedmethoddeveloped to handle global, variable-size, design space optimization problems where the number of design variables varies from one solution to another. Subpopulations of fixed-size design spaces are randomly initialized. Standard genetic operations are carried out for a stage of generations. A new population is then created by reproduction from all members in all subpopulations based on their relative fitnesses. The resulting subpopulations have different sizes from their initial sizes in general. The process repeats, leading to an increase in the size of subpopulations of more fit solutions and a decrease in the size of subpopulations of less fit solutions. This method has the capability to determine the number of swing-bys, the planets to swing by, launch and arrival dates, and the number of deep space maneuvers as well as their locations, magnitudes, and directions in an optimal sense. This newmethod is applied to several interplanetary trajectory design problems. The results presented in this paper show that solutions obtained using this tool match known solutions for complex case studies.

An Integrated System for the Aerodynamic Design of Compression Systems—Part I: Development

The design of gas turbine engines is a complex problem. This complexity has led to the adoption of a modular design approach, in which a conceptual design phase fixes the values for some global parameters and dimensions in order to facilitate the subdivision of the overall task into a number of simpler subproblems. This approach, while making a complex problem more tractable, necessarily has to rely on designer experience and simple evaluations to specify these process-intrinsic constraints at a point in the design process where very little knowledge about the final design exists. Later phases of the design process, using higher-fidelity tools but acting on a limited region of the design space, can only refine an already established design. While substantial improvements in performance have been possible with the current approach, further gains are becoming increasingly hard to achieve. A gas turbine is a complex multidisciplinary system: a more integrated design approach can facilitate a better exploitation of the trade-offs between different modules and disciplines, postponing the setting of these critical interface parameters (such as flow areas, radii, etc.) to a point where more information exists, reducing their impact on the final design. In the resulting large, possibly multimodal, highly constrained design space, and with a large number of objectives to be considered simultaneously, finding an optimal solution by simple trial-and-error can prove extremely difficult. A more intelligent search approach, in which a numerical optimizer takes the place of the human designer in seeking optimal designs, can enable the design space to be explored significantly more effectively, while also yielding a substantial reduction in development times thanks to the automation of the design process. This paper describes the development of a system for the integrated design and optimization of gas turbine engines, linking a metaheuristic optimizer to a geometry modeler and to evaluation tools with different levels of fidelity. In recognition of the substantial increase in design space size required by the integrated approach, an improved parameterization based on the concept of principal components’ analysis was implemented, allowing a rotation of the design space along its most significant directions and a reduction in its dimensionality, proving essential for a faster and more effective exploration of the design space.

Strategies for global optimization in photonics design

This paper reports on two important issues that arise in the context of the global optimization of photonic components where large problem spaces must be investigated. The first is the implementation of a fast simulation method and associated matrix solver for assessing particular designs and the second, the strategies that a designer can adopt to control the size of the problem design space to reduce runtimes without compromising the convergence of the global optimization tool. For this study an analytical simulation method based on Mie scattering and a fast matrix solver exploiting the fast multipole method are combined with genetic algorithms (GAs). The impact of the approximations of the simulation method on the accuracy and runtime of individual design assessments and the consequent effects on the GA are also examined. An investigation of optimization strategies for controlling the design space size is conducted on two illustrative examples, namely, 60° and 90° waveguide bends based on photonic microstructures, and their effectiveness is analyzed in terms of a GA's ability to converge to the best solution within an acceptable timeframe. Finally, the paper describes some particular optimized solutions found in the course of this work.