Optimus is a Process Integration and Design Optimization (

PIDO PIDO stands for Process Integration and Design Optimization. Process Integration is needed as many software tools are used in a multi-domain system design. Control software is developed in a different toolchain than the mechanical properties of a sy ...

) platform developed by Noesis Solutions. Noesis Solutions takes part in key research projects, such as PHAROS and MATRIX. Optimus allows the integration of multiple engineering software tools (

CAD Computer-aided design (CAD) is the use of computers (or ) to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve co ...

Multibody dynamics Multibody system is the study of the dynamic behavior of interconnected rigid or flexible bodies, each of which may undergo large translational and rotational displacements. Introduction The systematic treatment of the dynamic behavior of inte ...

finite elements The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...

computational fluid dynamics Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate th ...

, ...) into a single and automated workflow. Once a simulation process is captured in a workflow, Optimus will direct the simulations to explore the design space and to optimize product designs for improved functional performance and lower cost, while also minimizing the time required for the overall design process.

Process integration

The Optimus GUI enables the creation of a graphical simulation workflow. A set of functions supports the integration of both commercial and in-house software. A simple workflow can cover a single simulation program, whereas more advanced workflows can include multiple simulation programs. These workflows may contain multiple branches, each with one or more simulation programs, and may include special statements that define looping and conditional branching. Optimus’ workflow execution mechanism can range from a step-by-step review of the simulation process up to deployment on a large (and non-heterogeneous) computation cluster. Optimus is integrated with several resource management systems to support parallel execution on a computational cluster.

Design optimization

Optimus includes a wide range of methods and models to help solve design optimization problems: *

Design of Experiments The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...

( DOE) * Response Surface Modeling ( RSM) *

Numerical optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

, based on local or global algorithms, both for single or multiple objectives with continuous and/or discrete design variables

Design of Experiments (DOE)

: Design of Experiments (DOE) defines an optimal set of experiments in the design space in order to obtain the most relevant and accurate design information at minimal cost. Optimus supports the following DOE methods: : * Adaptive DOE (new) : * Full Factorial (2-level & 3-level) : * Adjustable Full Factorial : * Fractional Factorial : * Plackett-Burman : * Space Filling : * Central composite : * Random : * Latin-Hypercube : * Starpoints : * Diagonal : *

Optimal design In the design of experiments, optimal designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statist ...

(I-, D- & A-optimal) : * User-defined

Response Surface Modeling (RSM)

Response Surface Modeling ( RSM) is a collection of mathematical and statistical techniques that are useful to model and analyze problems in which a design response of interest is influenced by several design parameters. DOE methods in combination with RSM can predict design response values for combinations of input design parameters that were not previously calculated, with very little simulation effort. RSM thus allows further post-processing of DOE results. Optimus’ Response Surface Modeling range from classical

Least Squares The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...

methods to advanced Stochastic Interpolation methods, including

Kriging In statistics, originally in geostatistics, kriging or Kriging, also known as Gaussian process regression, is a method of interpolation based on Gaussian process governed by prior covariances. Under suitable assumptions of the prior, kriging giv ...

Neural Network A neural network is a network or circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up of biological ...

Radial Basis Functions A radial basis function (RBF) is a real-valued function \varphi whose value depends only on the distance between the input and some fixed point, either the origin, so that \varphi(\mathbf) = \hat\varphi(\left\, \mathbf\right\, ), or some other fixed ...

and

Gaussian Process In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. e ...

models. To maximize RSM accuracy, Optimus can also generate the best RSM automatically – drawing from a large set of RSM algorithms and optimizing the RSM using a cross-validation approach.

Numerical Optimization

Optimus supports a wide range of single-objective and multi-objective methods. Multi-objective optimization methods usually generate a so-called „Pareto front“ or use a weighting function to generate a single Pareto point. Based on the search methods, Optimus optimization methods (both single and multi-objective) can be categorized into: * local optimization methods - searching for an optimum based on local information of the optimization problem (such as gradient information). Methods include : * SQP (

Sequential Quadratic Programming Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization. SQP methods are used on mathematical problems for which the objective function and the constraints are twice continuously differentiable. SQP me ...

) : * NLPQL : * Generalized Reduced Gradient : * NBI, weighted methods (multi-objective) *

global optimization Global optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the max ...

methods - searching for the optimum based on global information of the optimization problem. These are usually probability-based searching methods. Methods include : *

Genetic algorithm In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to gene ...

s (

Differential Evolution In evolutionary computation, differential evolution (DE) is a method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. Such methods are commonly known as metaheuristics as ...

, Self-adaptive Evolution, ...) : *

Simulated Annealing Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. It ...

: * CMA-ES : * NSEA+, mPSO (multi-objective) * hybrid optimization methods, e.g. Efficient Global Optimization, combining the local and the global approach into one approach which usually relies on response surface modeling to find a global optimum. * an Automatic optimisation method is also available. That would automatically selects the best strategy for the user. * Partner (eArtius) & open library (Dakota) are integrated into Optimus via this functionality User can also integrate their own optimization strategy in the Optimus environment.

Robust design optimization & Taguchi method

In order to assess the influence of real-world uncertainties and tolerances on a given design, Optimus contains

Monte Carlo Simulation Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be determini ...

as well as a First-Order Second Moment method to estimate and improve the robustness of a design. Optimus calculates and optimizes the probability of failure using advanced reliability methods, including First-Order and Second-Order Reliability Methods. Optimus also includes a dedicated set of functionalities to set up a

Taguchi Taguchi (written: lit. "rice field mouth") is a Japanese surname. Notable people with the surname include: *, Japanese speed skater *, Japanese engineer and statistician *, Japanese writer *, Japanese voice actress *, Japanese singer-songwriter, a ...

study through the definition of control factors, noise factors and signal factors in case of a dynamic study.

Genichi Taguchi was an engineer and statistician. From the 1950s onwards, Taguchi developed a methodology for applying statistics to improve the quality of manufactured goods. Taguchi methods have been controversial among some conventional Western statisticians, ...

, a Japanese engineer, published his first book on

experimental design The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...

in 1958. The aim of the Taguchi design is to make a product or process more stable in the face of variations over which there is little or no control (for example, ensuring reliable performance of a car engine for different ambient temperatures).

Applications

The use of Optimus covers a wide range of applications, including
optimization of the production process of a center wing box (CWB) factory in function of production rate variations

identification of the best possible design trade-off between ease of swallowing and durability, based on finite element based analysis of food supplement tablet hardness and punch strength simulations

engineering of a hybrid electric vehicle (HEV) prototype for fuel economy
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References

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External links

Noesis Solutions website

Optimus integration with engineering software

Optimus integration with resource management systems

Optimus industry applications
Computer system optimization software Computer-aided engineering software Computer-aided design software Mathematical optimization software Simulation software