Discrete Design Parameters Research Articles

Exact electronic states with shallow quantum circuits from global optimisation

Quantum computers promise to revolutionise molecular electronic simulations by overcoming the exponential memory scaling. While electronic wave functions can be represented using a product of fermionic unitary operators, the best ansatz for strongly correlated electronic systems is far from clear. In this contribution, we construct universal wave functions from gate-efficient, spin symmetry-preserving fermionic operators by introducing an algorithm that globally optimises the wave function in the discrete ansatz design and continuous parameter spaces. Our approach maximises the accuracy that can be obtained with near-term quantum circuits and provides a practical route for designing ansätze in the future. Numerical simulations for strongly correlated molecules, including water and molecular nitrogen, and the condensed-matter Hubbard model, demonstrate the improved accuracy of gate-efficient quantum circuits for simulating strongly correlated chemistry.

Structural optimization of metamaterials based on periodic surface modeling

Metamaterials are engineered microstructures or composites which exhibit novel properties that are not found in nature. Structural optimization methods for shape and topology optimization have been developed in designing metamaterials. The computational cost of the traditional topology optimization methods is high due to the high-dimensional design space. Shape optimization and topology optimization are also performed separately. To improve the search efficiency, a new structural optimization method based on periodic surface modeling is proposed to simultaneously optimize the shape and topology of metamaterials. A wide variety of topology can be represented with a small number of parameters in the periodic surface models. Therefore, the search space is significantly reduced. A mixed-integer Bayesian optimization method is also developed with a new Gaussian process kernel, which incorporates both discrete and continuous design parameters in the periodic surface models. Both the mixed-integer Bayesian optimization method and conventional population-based genetic algorithms are used to solve the structural optimization problem. The design of mechanical metamaterials with high strength–weight ratio and negative Poisson’s ratio is demonstrated.

Efficient global optimization of constrained mixed variable problems

Due to the increasing demand for high performance and cost reduction within the framework of complex system design, numerical optimization of computationally costly problems is an increasingly popular topic in most engineering fields. In this paper, several variants of the Efficient Global Optimization algorithm for costly constrained problems depending simultaneously on continuous decision variables as well as on quantitative and/or qualitative discrete design parameters are proposed. The adaptation that is considered is based on a redefinition of the Gaussian Process kernel as a product between the standard continuous kernel and a second kernel representing the covariance between the discrete variable values. Several parameterizations of this discrete kernel, with their respective strengths and weaknesses, are discussed in this paper. The novel algorithms are tested on a number of analytical test-cases and an aerospace related design problem, and it is shown that they require fewer function evaluations in order to converge towards the neighborhoods of the problem optima when compared to more commonly used optimization algorithms.

A new hybrid method for size and topology optimization of truss structures using modified ALGA and QPGA

Modified Augmented Lagrangian Genetic Algorithm (ALGA) and Quadratic Penalty Function Genetic Algo­rithm (QPGA) optimization methods are proposed to obtain truss structures with minimum structural weight using both continuous and discrete design variables. To achieve robust solutions, Compressed Sparse Row (CSR) with reordering of Cholesky factorization and Moore Penrose Pseudoinverse are used in case of non-singular and singular stiffness matrix, respectively. The efficiency of the proposed nonlinear optimization methods is demonstrated on several practical exam­ples. The results obtained from the Pratt truss bridge show that the optimum design solution using discrete parameters is 21% lighter than the traditional design with uniform cross sections. Similarly, the results obtained from the 57-bar planar tower truss indicate that the proposed design method using continuous and discrete design parameters can be up to 29% and 9% lighter than traditional design solutions, respectively. Through sensitivity analysis, it is shown that the proposed methodology is robust and leads to significant improvements in convergence rates, which should prove useful in large-scale applications.

Electromagnetic Optimization Using Mixed-Parameter and Multiobjective Covariance Matrix Adaptation Evolution Strategy

Different variations of the covariance matrix adaptation evolution strategy (CMA-ES) are used in the design and optimization of electromagnetic (EM) problems. Two different schemes for the implementation of mixed-parameter CMA-ES and one scheme for the implementation of multiobjective CMA-ES are presented. Mixed-parameter CMA-ES is attractive in EM optimization when both continuous and discrete design parameters are involved. The first mixed-parameter scheme uses a Poisson mutation operator to update the discrete variables, and the second one forces an integer mutation on discrete variables with small variances. Multiobjective CMA-ES, developed in this paper, optimizes designs with respect to multiple objective functions simultaneously. It ranks the candidate solutions according to two levels: nondominated sorting and crowding distance. Several antenna and microwave design problems are presented to evaluate the performance of these schemes and compare them with other nature-based optimization algorithms.

Particle swarm-based structural optimization of laminated composite hydrokinetic turbine blades

Composite blade manufacturing for hydrokinetic turbine application is quite complex and requires extensive optimization studies in terms of material selection, number of layers, stacking sequence, ply thickness and orientation. To avoid a repetitive trial-and-error method process, hydrokinetic turbine blade structural optimization using particle swarm optimization was proposed to perform detailed composite lay-up optimization. Layer numbers, ply thickness and ply orientations were optimized using standard particle swarm optimization to minimize the weight of the composite blade while satisfying failure evaluation. To address the discrete combinatorial optimization problem of blade stacking sequence, a novel permutation discrete particle swarm optimization model was also developed to maximize the out-of-plane load-carrying capability of the composite blade. A composite blade design with significant material saving and satisfactory performance was presented. The proposed methodology offers an alternative and efficient design solution to composite structural optimization which involves complex loading and multiple discrete and combinatorial design parameters.

A Kind of New Design Optimization Strategyand its Application in Plate Finned-Tube Heat Exchanger

A whole new design optimization strategy for the plate finned-tube heat exchanger (PFTHX) was provided. According to the industrial application of the domestic heat exchanger manufacturers, the tube arrangement, fin number, etc. of a PFTHX with designated coil can be sifted stage by stage with: (1) the confine of size parameters of the coil, tube passes, the flow velocity of the fluids of both sides, (2) the confine of the pressure drop of the fluids of both sides, (3) the margin of heat transfer area, etc. The calculation amount can be reduced significantly and at the same time, all the solutions meeting the thermal indices and discrete design parameters can be obtained.

A hyperspherical particle swarm optimizer for robust engineering design

This paper presents a novel multi-objective particle swarm optimizer, called hyperspherical particle swarm optimization (HSPSO), which efficiently deals with robust engineering design problems. In contrast to traditional optimization methods which rely on single-point design configurations, the HSPSO method evolves multi-dimensional design surfaces while simultaneously optimizing several potentially conflicting objectives and minimizing product/process variations. The hyperspherical representation is accommodated by incorporating manufacturing tolerances for design variables, and sensitivity analysis is performed to maintain feasibility within the design region. Hyperspherical particles are automatically evaluated, and non-inferior solutions are identified by the Pareto-dominance strategy. To enhance the local search ability of the particle swarm optimization algorithm, a gradient descent algorithm is applied, and fitness evaluation is performed by using a crowding factor, which defines the density of the population along the Pareto front. The performance of the proposed HSPSO algorithm is highlighted by reporting on three robust engineering design problems, which involve a mixture of single objective and multiple conflicting objectives along with integer, discrete and continuous design parameters. Monte Carlo simulations are used to assess the reliability of the obtained results.

Integrated flight control system development using CEASIOM

Flight control system design typically involves hardware and software development, requiring the definition of both continuous and discrete design parameters. The control surface topology is an example of a discrete optimization problem, whereas the tuning of control system gains is an example of a continuous one. Contemporary design practice classically involves decoupling these two problems, however, they are intrinsically linked; for example, the maximum performance attainable by the control system software is determined by the control system topology employed. The cascaded effect is that no definitive sequential roadmap of development can be established, resulting in the requirement for an iterative framework using dynamic programming or optimization methods. This paper presents a framework for aircraft design together with the Flight Control System Designer Toolkit, and the Computerised Environment for Aircraft Synthesis and Integrated Optimisation Methods. The software platform was developed for the European Framework 6 Program Simulating Stability and Control and integrates both the reliability-driven hardware analysis and the performance-driven software design. A case study is presented, based on the NASA Boeing 747–100 model, in order to demonstrate the potential impact of introducing control design early into the design process and to show the intrinsic nature of the hardware–software FCS problem.

Reliability-based design optimization with cooperation between support vector machine and particle swarm optimization

Reliability-based design optimization (RBDO) is concerned with designing an engineering system to minimize a cost function subject to the reliability requirement that failure probability should not exceed a threshold. Conventional RBDO methods are less than satisfactory in dealing with discrete design parameters and complex limit state functions (nonlinear and non-differentiable). Methods that are flexible enough to address the concerns above, however, come at a high computational cost. To enhance computational efficiency without sacrificing model flexibility, we propose a new RBDO framework: PS2, which combines Particle Swarm Optimization (PSO), Support Vector Machine (SVM), and Subset Simulation (SS). SS can efficiently estimate small failure probabilities, based on which SVM is adopted to evaluate the reliability of candidate solutions using binary classification. PSO is employed to solve the discrete optimization problem. Primary emphasis is placed upon the cooperation between SVM and PSO. The cooperation is mutually beneficial since the SVM classifier helps PSO evaluate the feasibility of solutions with high efficiency while the optimal solutions obtained by PSO assist in retraining the SVM classifier to attain better accuracy. The PS2 framework is implemented to find the optimal design of a ten-bar truss, whose component sizes are selected from a commercial standard. The reliability constraints are non-differentiable with two failure modes: yield stress and buckling stress. The interactive process between PSO and SVM contributes greatly to the success of the PS2 framework. It is shown that in various trials the PS2 framework consistently outperforms both the double-loop and single-loop approaches in terms of computational efficiency, solution quality, and model flexibility.

Dimensional accuracy of ankle-foot orthoses constructed by rapid customization and manufacturing framework

Passive-dynamic ankle-foot orthoses (PD-AFOs) constitute a class of ankle braces that rely on material properties and physical features to establish functional characteristics such as bending or rotational stiffness. We have developed a novel framework that combines a fully parameterized PD-AFO computer-aided design (CAD) model and free-form fabrication to rapidly manufacture customized PD-AFOs. The three-dimensional locations of select anatomic landmarks serve to fit customize the PD-AFO CAD model. A virtual orthopedic alignment process and selection of discrete design parameter values further customize the orthosis, which is fabricated via selective laser sintering. CAD models were customized and full-scale orthoses were manufactured for two nondisabled subjects. The surface of one half-scale CAD model was marked with 3 mm hemispherical dimples, and four orthoses were manufactured in different build orientations and positions. Dimensional accuracy was determined by calculating discrepancies between corresponding CAD and fabricated orthoses interdimple distances. Subjective evaluations of the full-scale PD-AFOs following use in gait were positive. Dimension discrepancies were well under a 2 mm tolerance for the four half-scale orthoses. Mean foot plate, strut, and cuff component discrepancies were 0.31 +/- 0.28, 0.34 +/- 0.08, 0.52 +/- 0.39 mm, respectively, and 0.29 +/- 0.23 mm for the overall orthosis. Dimensional accuracy of the rapid customization and manufacturing framework was well within tolerances suggested in the literature.

Measurement and Optimization of Minimally Invasive Intervention Device Design Fitness Using a Multiobjective Weighted Isotropy Index

The recent transition from multiple-port to single-port systems in minimally invasive intervention (MII) procedures has created a need for more flexible, dexterous robotic manipulation devices capable of spanning an entire surgical workspace without the risk of collateral damage. The design of such devices requires a careful balance of the mechanical complexity needed to facilitate clinical functionality and the cost of manufacturing and operating the device. This paper presents a novel metric for measuring the design fitness of kinematically redundant robotic MII devices and for optimizing them to achieve that balance. The proposed fitness metric rewards designs that are conducive to collision avoidance and energy conservation while penalizing those with exorbitant design complexities that adversely affect the economic feasibility of an MII system. The authors’ metric is used here to design a kinematically redundant, single-port MII device capable of accessing the cardiothoracic cavity through a single subxiphoid port and reaching several regions of interest, consistent with procedures such as epicardial ablation and therapeutic substance injection, with minimal physiologic disturbance. The design of this device is determined by a morphological optimization process, which searches a discrete mechanical design parameter space, consisting of linkage parts, part dimensions, and actuator types, using genetic algorithms. The execution of specific surgical maneuvers is simulated for each candidate MII device design, and the design is improved until the fitness metric is maximized. The results of this optimization study demonstrate that redesigning a 20 degree-of-freedom (DOF) MII device using the proposed metric decreased the DOF in the design by 45% while ensuring near-optimal levels of kinematic flexibility. The results also demonstrate the ability of the fitness metric to elucidate the relationship between functionality and complexity and to produce suitable device designs over a broad range of performance and cost goals. The authors conclude that this new design fitness metric, while heuristic in nature, holds the potential to improve both the clinical value and the economy of a wide variety of single-port MII devices, including those used in cardiothoracic surgery.

Robust optimization of cardiovascular stents: a comparison of methods

Modern engineering design contains both creative and analytic components. This paper discusses the design process and illustrates links between design optimization and conceptual design through the re-design of a cardiovascular stent. A comparison is presented of two methods for design improvement: genetic algorithms (GA) and model-based robust engineering design (RED). Computational fluid dynamics (CFD) models are used to generate measurements of the quality of competing designs based on the concept of dissipated power. Alternative performance measures are also discussed. Environmental noise is introduced into the analysis and consideration is given to the treatment of discrete and continuous design parameters. Improved designs are identified using both methods and verified with further CFD analyses, and the benefits of each method are discussed.

Symbolic Stiffness Optimization of Planar Tensegrity Structures

During the design of mechanical systems one normally exploits numerical analysis and optimization tools. We make a plea for symbolic computation and give an example where structural displacements under load are computed symbolically. Geometrical design parameters enter in this computation. The set of equilibrium conditions, linear in the displacements, but nonlinear in the design parameters, is solved symbolically. The resulting expressions reveal the geometry which yield optimal properties for stiffness or stiffnessto-mass. This technique is applied to a class of repetitive mechanical systems, namely tensegrity structures. A large scale example with 1533 degrees-of-freedom is computed successfully. The results make it possible to optimize the structure with respect to stiffness properties, not only by appropriately selecting (continuous) design parameters, influencing geometry, but also by selecting the number of stages used to build up the structure (a discrete design parameter), influencing topology.

Multi-Objective Optimization of Communication Satellites with Two-Branch Tournament Genetic Algorithm

In spacecraft design, many specialized state-of-the-art design tools are employed to optimize the performance of various subsystems. However, there is no structured system-level concept-definition process. Consequently, designers usually compromise some mission goals to satisfy only one of the primary design objectives. The conceptual stage of the spacecraft design process is formulated into a multi-objective discrete optimization problem. The use of multi-objective design allows the designer to evaluate different design alternatives across the whole set of design objectives. This work addresses two key design objectives for the spacecraft design process: the minimization of total launch mass and the maximization of spacecraft overall reliability. To predict values for the objective and constraint functions, a satellite design tool, which includes a satellite sizing model and a deterministic reliability model, was built and integrated with a genetic algorithm that employs a two-branch tournament to address the dual objective problem. The multi-objective approach was successful in determining sets of discrete design parameters that would minimize the launch mass as well as maximize the reliability of a geostationary communication satellite, using specified payload requirements. The designs generated by this approach appear to fall into three regions of the tradeoff space between the satellite launch mass and the satellite reliability objectives.

On distributed signal detection with multiple local free parameters

In this work, we propose an efficient approach to the optimization of distributed multiradar systems with parallel topology, employing decision fusion from local detectors with discrete and continuous free design parameters. This approach, termed hierarchical optimization approach, can be applied to a variety of optimization criteria including the Neyman-Pearson (NP) and the locally optimum detection (LOD) criteria. It avoids the exhaustive search for the optimal discrete parameters and greatly reduces the computational load required for global system optimization. The effectiveness of the proposed approach is demonstrated by means of a numerical example, where ordered statistic (OS) constant false-alarm rate (CFAR) decentralized radar detection of Swerling I targets in Gaussian noise is considered.

MACHINE DESIGN OPTIMIZATION BY THE MONTE CARLO ANNEALING METHOD

The paper presents the application of the Monte Carlo annealing method for machine design optimization, The method generates the finite inhomogeneous Markov chain in the space of discrete design parameters with the transition probability dependent on the objective function and given by the Boltzmann-Gibbs distribution of equilibrium statistical mechanics. In this approach the search for the global minimum is simulated by a relaxation towards an equilibrium of the thermodynamic system with the energy proportional to an objective function. The method is applied for the cost optimization of a speed reductor. The performance and prospects of the method for machine design optimization are discussed.

Monte Carlo structural optimization in discrete variables with annealing algorithm

AbstractThe paper describes the basic ideas of Monte Carlo annealing algorithms for structural optimization with discrete design parameters. The algorithm generates randomly a set of design parameters, with probability depending on the objective function and given by the Boltzmann–Gibbs distribution. In this model the search for the global minimum is simulated by a relaxation process of the statistical mechanical system with the Hamiltonian proportional to the objective function. The rate of the convergence of the method and its dependence upon the annealing probability are discussed. Numerical implementation of the method for the weight optimization of the ten‐bar planar cantilever truss is presented. The results of numerical simulation are compared with those obtained by the dual methods. The principal conjecture is that the method is fairly efficient and has great potential for applicaton in engineering design.