Mixed Integer Optimization With NURBs HyPerModels

Global optimization problems widely exist in the fields of economic model, finance, engineering design and control. Since it is easy to fall into multiple local optimal solutions that are different from the global optimal solution, how to obtain the global optimal solution is a very important subject. Inspired by the recently proposed deterministic global optimization method – Granular Sieving (GrS) algorithm, this paper proposes a parallel method for global optimization – P-GrS. Supported by the mathematical theory of GrS, P-GrS can theoretically guarantee to find the global optimum and the complete set of global optimal solutions through the parallel design of GrS. The method has better performance than the traditional GrS in most bench mark functions, and the results show the feasibility and effectiveness of the algorithm.

Optimization of complex mechanics simulations with object-oriented software designs

A coevolutionary algorithm using Self-organizing map approach for multimodal multi-objective optimization

The utilization of the non-uniform rational B-spline (NURBS) toolpaths becomes more important than ever before. However, in traditional milling electrical discharge machining (EDM) of parametric curves, there commonly exist problems such as speed loss and an overincreased sampling period, which directly cause a decrease in machining efficiency. Moreover, traditional approaches normally suffer from a complex toolpath planning. In this paper, a real-time interpolator with a constant segment length is proposed to improve the milling EDM of NURBS curves. The proposed interpolator can directly process NURBS curves with their definition information. The toolpath planning can thus become simpler. A new two-stage interpolation method is adopted such that both a high speed accuracy and a relatively short sampling period can be achieved, and the magnitude of chord errors can also be reduced. While the first-stage interpolation samples a NURBS curve with a constant-length segment, the second-stage interpolation, or the re-interpolation, executes multiple interpolations in a sampling period to generate the required feed rate. A loop buffer is designed for the implementation of the real-time interpolator. Experimental results show that the proposed interpolator demonstrates a superior machining performance to that by traditional interpolators, especially in terms of chord errors and erosion rate.

Global optimization of mechanical design problems using heuristic methods such as Simulated annealing (SA) and genetic algorithms (GAs) have been able to find global or near-global minima where prior methods have failed. The use of these nongradient based methods allow the broad efficient exploration of multimodal design spaces that could be continuous, discrete or mixed. From a survey of articles in the ASME Journal of Mechanical Design over the last 10 years, we have observed that researchers will typically run these algorithms in continuous mode for problems that contain continuous design variables. What we suggest in this paper is that computational efficiencies can be significantly increased by discretizing all continuous variables, perform a global optimization on the discretized design space, and then conduct a local search in the continuous space from the global minimum discrete state. The level of discretization will depend on the complexity of the problem, and becomes an additional parameter that needs to be tuned. The rational behind this assertion is presented, along with results from four test problems.

Exploration of a design space is the first step in identifying sets of high-performing solutions to complex engineering problems. For this purpose, Bayesian network classifiers (BNCs) have been shown to be effective for mapping regions of interest in the design space, even when those regions of interest exhibit complex topologies. However, identifying sets of desirable solutions can be difficult with a BNC when attempting to map a space where high-performance designs are spread sparsely among a disproportionately large number of low-performance designs, resulting in an imbalanced classifier. In this paper, a method is presented that utilizes probabilities of class membership for known training points, combined with interpolation between those points, to generate synthetic high-performance points in a design space. By adding synthetic design points into the BNC training set, a designer can rebalance an imbalanced classifier and improve classification accuracy throughout the space. For demonstration, this approach is applied to an acoustics metamaterial design problem with a sparse design space characterized by a combination of discrete and continuous design variables.

A modification to the genetic algorithm (GA) based search procedure, based on the modeling of a biological immune system, is proposed as an approach to solving the multicriterion design problem. Such problems have received considerable attention, given that decisions in engineering design practice typically require allocation of resources to satisfy multiple, and frequently conflicting requirements. The approach is particularly amenable to problems with a mix of continuous, discrete, and integer design variables, where the GA has been shown to perform in an effective manner. The approach considered in the present work is based on the concept of converting the multicriterion problem into one with a scalar objective through the use of the utility function. The strength of the approach is in its ability to generate the Pareto-Edgeworth front of compromise solutions in a single execution of the GA. A characteristic feature of biological immune systems which allows for the generation of multiple specialist antibodies, is shown to be an effective approach to facilitate the generation of the Pareto-Edgeworth front. Solutions to problems in structural design are presented in support of the proposed approach.

본 연구에서는 최적화기법과 전산유체역학의 기술을 이용하여 저항의 관점에서 최적의 형상을 가지는 선형을 개발하는 알고리즘을 개발하였다. 최적화기법으로는 SQP(sequential quadratic programming)을 사용하였으며, 목적함수인 저항을 구하기 위하여 먼저 조파저항은 비선형 자유수면 경계조건을 고려한 선체주위 포텐셜유동을 계산할 수 있는 수치해석기법인 상 방향 패널이동법을 사용하였고, 선체에 미치는 전 저항을 구하기 위하여 ITTC 1957년 모형선-실선상관곡선을 이용하였다. 선형최적화 과정 중의 선체의 변경이나 계산 격자의 생성은 NURBS(Non-Uniform Rational B-Spline)기법을 사용하여 구현하였다. 이와 같은 방법을 사용하여 개발된 선형최적화 기법의 타당성을 검증하기 위하여 선형이 비교적 잘 알려진 건형인 Wigley선형과 Series 60(CB=0.6)선형에 대하여 설계속도 Fn=0.316에서 선형최적화를 위한 수치해석을 수행하고 그 결과를 초기선형과 서로 비교하였다. This paper presents the method for developing an optimum hull form with minimum wave resistance using SQP(sequential quadratic programming) as an optimization technique. The wave resistance is evaluated by a Rankine source panel method with non-linear free surface conditions and the ITTC 1957 friction line is used to predict the frictional resistance coefficient. The geometry of the hull surface is represented and modified using NURBS(Non-Uniform Rational B-Spline) surface patches. To verity the validity of the developed program the numerical calculations for Wigley hull and Series 60( <TEX>$C_B=0.6$</TEX>) hull have been performed and the results obtained by the numerical calculations have been compared with the original hulls.

Topology optimization (TO) aims at defining the ideal layout of structures in order to minimize the use of material within a given design space. Such goal is pursued by applying an optimization strategy, where the possible solutions are the feasible geometries, and the functional to minimize is the mass structure. Obtaining high performance in terms of mass reduction depends on many factors. The most well-known and widespread topological optimization approaches can be divided into two main categories: microscopic and macroscopic. In microscopic approaches, such as SIMP and BESO, the feasible domain available for the solid material is divided in a finite number of discrete elements (FEM). The density of the material of each element represents the design variables, which may vary with continuity in SIMP method (density approach) or being binary in BESO Method (evolutionary approach). In macroscopic approaches, such as Level Set, the parameters describing the evolution of the boundaries of the solid domain of the structure are the design variables. Again, a discretization of the design domain is required, even if the implementation of this strategy in the optimization algorithm doesn’t intrinsically need the decomposition in a finite number of elements.

Design space exploration can reveal the underlying structure of design problems of interest. In a set-based approach, for example, exploration can identify sets of designs or regions of the design space that meet specific performance requirements. For some problems, promising designs may cluster in multiple regions of the design space, and the boundaries of those clusters may be irregularly shaped and difficult to predict. Visualizing the promising regions can clarify the design space structure, but design spaces are typically high-dimensional, making it difficult to visualize the space in three dimensions. Techniques have been introduced to map high-dimensional design spaces to low-dimensional, visualizable spaces. Before the promising regions can be visualized, however, the first task is to identify how many clusters of promising designs exist in the high-dimensional design space. Unsupervised machine learning methods, such as spectral clustering, have been utilized for this task. Spectral clustering is generally accurate but becomes computationally intractable with large sets of candidate designs. Therefore, in this paper a technique for accurately identifying clusters of promising designs is introduced that remains viable with large sets of designs. The technique is based on spectral clustering but reduces its computational impact by leveraging the Nyström Method in the formulation of self-tuning spectral clustering. After validating the method on a simplified example, it is applied to identify clusters of high performance designs for a high-dimensional negative stiffness metamaterials design problem.

Rendezvous phasing special-point maneuvers mixed discrete-continuous optimization using simulated annealing

Real-time NURBS interpolation using FPGA for high speed motion control

This paper first reviews the application of design optimization techniques to axial compressor blade design, commenting on the feasibility of this approach for highly constrained, highly dimensional problems. It then analyzes an innovative method to characterize the design space, based on proper orthogonal decomposition (POD). The method was used to generate a reduced order model (ROM) from the true complex system, and revealed its potential to find optimum solutions in selected regions of the design space. Nomenclature A = matrix of expansion co efficients B = blockage C = blade tip clearance e = difference between predicted and true response f = blockage function k = number of retained principal components m = number of geometrical parameters n = number of blade configurations P, Q = generic poin ts in the design space p, q = loci of points in the transformed design space r = rank of X

During conceptual design, multidisciplinary optimization is often performed using computationally intensive direct methods. Prior work has shown that rapid design studies can be performed using fast indirect methods, but several optimization techniques including discrete dynamic programming, nonlinear inversion, and pseudospectral methods are required to construct a suitable initial guess within the design space. In this investigation, a simplied methodology is developed to eliminate these optimization techniques, enabling rapid design space exploration using continuation of indirect methods alone. This is made possible by initially converging to a simple solution that is outside of the design space of interest, and solutions within the design space of interest are quickly accessed through continuation from this initial solution. As an initial step to automate this continuation process, state transition tensors are used to predict optimal solutions throughout the design space. A methodology is developed to provide accurate predictions of trajectories with varying ight times, and the error of these predictions is controlled to regulate the continuation process. This approach provides exibility to adapt to future computational capabilities and serves as an initial step to bridge the gap between conceptual trajectory design and onboard trajectory planning.

Functional commonalities across product families have been considered by a large body of product family design community but this concept is not widely used in design. For a designer, a functional family refers to a set of designs evaluated based on the same set of qualities; the embodiments and the design spaces may differ, but the semantics of what is being measured (e.g., strength of a spring) remain the same. Based on this functional behaviour we introduce a product family hierarchy, where the designs can be classified into phenomenological design family, functional part family and embodiment part family. And then, we consider the set of possible performances of interest to the user at the embodiment level, and use multi-objective optimisation to identify the non-dominated solutions or the Pareto-front. The designs lying along this front are mapped to the design space, which is usually far higher in dimensionality, and then clustered in an unsupervised manner to obtain candidate product groupings which the designer may inspect to arrive at portfolio decisions. We highlight and discuss two recently suggested techniques for this purpose. First, with help of dimensionality reduction techniques, we show how these clusters in low-dimensional manifolds embedded in the high-dimensional design space. We demonstrate this process on three different designs (water faucets, compression springs and electric motors), involving both continuous and discrete design variables. Second, with the help of a data analysis of Pareto-optimal solutions, we decipher common design principles that constitute the product portfolio solutions. We demonstrate this so-called ‘innovization’ principles on a spring design problem. The use of multi-objective optimisation (evolutionary and otherwise) is the key feature of both approaches. The approaches are promising and further research should pave their ways to better design and manufacturing activities.