Using Design Sensitivities

Design sensitivities are a measure of how much an objective or constraint response varies due to a small change in a design variable. Based on this definition, they are sometimes referred to as sensitivity derivatives. Let’s discuss how to use them properly, as well as how not to use them.

First, note that the design sensitivities we refer to here are calculated for a particular design, not for a design space. Statistical methods of sensitivity analysis can provide useful information about a design space, but not the type of information we seek here.

Since a design represents a point in the design space, it is clear that sensitivities are defined at a point, as are mathematical derivatives. Two distinct designs within a design space will probably have different sensitivities unless the design space is linear, which is seldom the case for engineering problems. Continue reading

How to Handle Software License Unavailability during a Design Exploration Study

If a valid license is not available for any of your modeling and simulation software during a HEEDS study, the default response is for that design to be classified as an error design. But this behavior can be modified using a pre-analysis command to check for the availability of a license before HEEDS launches each analysis. This simple process can help to avoid many such error designs, making your exploration studies more effective. Let’s review how to do this for FLEXlm based licenses.

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How to Accelerate Your Design Exploration Studies

We all feel the “need for speed” when trying to find better design solutions through simulation. What can we do to speed up our design exploration studies? Let’s discuss all the options here, including one that may not be obvious.

In a typical study, the total CPU time needed to perform a design exploration study is determined using this simple formula:


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Using Constraints to Limit the Range of the Pareto Front

Sometimes we have more than one output response that needs to be either minimized or maximized, so we need some way to encourage multiple responses to be as small as possible or as large as possible at the same time. These are called multi-objective design exploration problems.

One of the most common reasons for using multiple objectives is to assess the trade-off between two or more competing responses. In other words, what is the cost to improve one response in terms of making another response worseContinue reading

Is it OK if Some Simulations Fail during a HEEDS Design Study?

error-designsDuring a design exploration study, HEEDS makes many calls to your simulation model to evaluate potential designs. This means that your model needs to accurately predict design performance values (objectives and constraints) over a wide range of inputs (design variables). Most modern simulation models satisfy this requirement without difficulty.

But in some cases, it is too much to ask that a model be perfect for all combinations of variable values. For example:

  • In a shape optimization problem, some combinations of shape parameter values might produce invalid geometries, making it impossible to generate a CAD model for those designs. Ideally, shape parameters should be defined in a way that ensures all geometries are valid, but that is not always a realistic expectation.
  • Nonlinear or dynamic CAE models occasionally experience problems with convergence or other kinds of numerical errors. Hopefully your models are robust, but it is more difficult to predict the behavior of some designs than others, so numerical errors will occur now and then.

Of course there are many other reasons why a simulation model might terminate prematurely or predict incorrect results. Because many of these cases are unavoidable, HEEDS has been designed to be robust against these model failures. We refer to these as error designsContinue reading


We often need for a design or a model to perform in a specified way. For example, the parameters in a nonlinear material model should be selected to best match the experimental stress-strain response. The geometrical parameters of a rubber bushing should be designed so that its force-deflection response matches the desired nonlinear stiffness behavior.

Optimization problems like these arise frequently. We refer to them as curve-fitting problems, because the goal is to minimize the difference between the specified target curve and the actual response curve
of our design or model.

Figure 1.

Figure 1. The difference between a target curve and a design curve is minimized in a curve fitting optimization problem.

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Using Variable Resolution to Enhance Design Space Exploration

A nice feature in HEEDS is the ability to define the resolution of a continuous variable. Assigning a resolution to a continuous variable seems contradictory, as this essentially transforms the continuous variable into a discrete variable. We often refer to these as “discretized continuous variables,” and there are several advantages to representing variables this way in an optimization search. Let’s explore how you can use variable resolution to enhance your design studies.

What is a variable resolution?

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Using Semi-Independent Variables to Generate More Feasible Designs and Improve Search Process

Sometimes we intend for a set of design variables to be independent, but then realize that these variables need to satisfy a given relationship. How can a variable be both independent and dependent at the same time? We call these semi-independent variables.

Let’s illustrate this concept with two separate examples.

In our first example, the goal is to optimize the thickness of each layer in a three-layer laminated composite plate, as shown below. The thickness of the ith layer is ti. But the total thickness of the laminated plate must remain equal to a specified value T, so we have three design variables: t1, t2, t3 and a required relationship:

t1 + t2 + t= T                                                                                (1)

Figure 1. A three-layer laminated composite plate

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Reducing the Accidental Coupling of Variables

One of the challenges to finding optimal solutions is the coupling of variables. If we could change one variable at a time, the search process would be so much easier. But in most problems the variables are strongly coupled, so the best value for one variable depends on the values of many other variables.2variables

Often, we have no control over this variable coupling, since it is inherent in the physics model that defines our objectives and constraints. In these cases, we need a powerful optimization search strategy like SHERPA to figure out the complexities of the design landscape and to produce an optimized solution.

But in some cases we make this task harder than it needs to be because of how we represent the problem. That is, sometimes the way we define the problem creates unnecessary coupling or increases the complexity of existing coupling among variables. This makes the optimization search harder, and may decrease the chance of finding the optimal solution within our limited optimization search budget. The good news is that we can often alleviate this situation with a different representation.  Continue reading

Optimizing the Number and Location of Design Features (without using a CAD model)

Recent advances in process automation and optimization search technology have made it easier than ever to perform automated design studies and discover innovative solutions. But we still have to define the problem we want to solve and then decide how to represent that problem in our models. These two tasks are sometimes challenging, and they rely heavily on experience and intuition. In this article, as well as some future ones, we will share some of our experience in defining and representing various types of optimization problems. Hopefully you will find some of these techniques useful in your applications.

Numbers and locationsA common design scenario is to optimize the number and location of certain design features to satisfy performance goals and requirements. For the sake of discussion, let’s consider a specific example of this type of problem. Continue reading