Standard Optimization Package

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The Standard Optimization Package is comprised of the following tools:

• Design Explorer SQP - Gradient-based optimizer
• Darwin - Evolutionary-based optimizer
• Variable Influence Profiler
• Prediction Profiler

Design Explorer SQP - Gradient-based optimizer

Design Explorer's SQP (Sequential Quadratic Programming) algorithm can be used to solve a wide variety of nonlinear optimization problems. The optimizer will change the input parameters of a model in order to minimize or maximize an objective, subject to constraints specified by the user. The final responses can be linear or nonlinear functions of the design variables and may be calculated as very simple analytical functions or they may be highly complicated implicit functions.

Design Explorer SQP is developed by Boeing's Mathematics and Computing Group.

Darwin - Evolutionary-based optimizer

Darwin is a genetic algorithm-based trade study tool designed specifically for solving "real world" engineering optimization problems. Darwin is capable of solving design problems with both discrete and continuously valued design variables, and any number of constraints. The algorithm is well suited for discontinuous, noisy, and/or multi-modal design spaces.

Darwin features an intuitive graphical user interface that allows the user to quickly define the design problem by dragging and dropping variables from ModelCenter's component tree, view optimization results in real time, and configure optimizer parameters.

Variable Influence Profiler

The Variable Influence Profiler is used to gain insight into key design parameters. It allows you to determine what design parameters are most important and to assess the impact of these parameters on product and process performance. The tool allows you to visualize your data in the following 3 ways:

Variable Importance Plot
The Variable Importance plot allows you to see which individual design parameters (main effects) and combinations of design parameters (interaction effects) have the most influence on the currently selected output variable. This plot helps you to quickly zero in on the most important design parameters for your problem.

The Variable Importance plot will display all the main effects and two-variable interaction effects that have an importance greater than 0.5%. Variables with an importance less than 0.5% will be grouped together under the category "Other". Higher order interaction effects (those involving more than two variables) will be grouped together under the category "Higher Order Effects". These higher order effects will only be displayed if their combined importance is greater than 0.5%.

Main Effects Plots
A separate Main Effects plot can be drawn for each design parameter in ModelCenter's Data Explorer. The Main Effects plot shows quantitatively how the selected output variable changes (on average) as the design parameter is varied from its lower bound to its upper bound. The influence of all of the other design parameters is averaged out.

The Main Effects plots can be displayed one at a time (the default), or all at once as shown here.

Interaction Effects Plots
A separate Interaction Effects plot can be drawn for any two design parameters in ModelCenter's Data Explorer. The Interaction Effects plot shows quantitatively how the selected output variable changes (on average) as each of the two design parameters is varied from its lower bound to its upper bound. The influence of all other design parameters is averaged out.

The Interaction Effects plots can be displayed one at a time (the default, shown here), or all at once.

Prediction Profiler

The Prediction Profiler is an interactive tool that dynamically shows how input variables affect output variables. The Prediction Profiler's graphical user interface allows users to manipulate "slider" bars to set values for input design parameters. As the slider bars are adjusted, graphical plots show the resulting affects on selected response quantities, design constraints, and/or design objectives. The Prediction Profiler allows you to interactively view your data using profile or contour plots, shown left to right below.

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