Optimisation Introduction

Optimization of a design requires three ingredients:

An objective function which you want to minimize or maximize. For instance, you may wish to maximize the performance; minimize the cost of materials; or maximize the strength of a component. In some problems you may have multiple objective functions - for instance you may wish to maximize the strength of a component whilst simultaneously minimizing its weight.

A set of variables or parameters which, when changed, affect the value of the objective function. For instance the aerodynamic performance of a wing will be affected by its shape and that shape is described by a set of parameters. Similarly the strength of a structure will be affected by the materials used and the dimensions and thicknesses of its component parts.

A set of constraints within which the unknown parameters or quantities derived from them must lie. For instance there would be no meaning for any part of a design to have a length less than zero; or a particular component might be constrained to fit inside another - these are constraints on the input variables. You might also constrain output variables, for instance your design might have to be able to be strong enough to withstand maximum loads at certain places; or you might wish to improve the vibrational response of a structure subject to it having a fixed size.

The dezineforce suite of optimisation tools covers each of the three main approaches to optimisation

hill-climbers and gradient-based methods

evolutionary methods

design of experiment and response surface methods

Very often these methods are combined together in hybrid algorithms which assist the designer by initially casting a wide view over an objective function which might be expensive to calculate; helping to focus in on particular parameter values that improve the design significantly; and then zeroing in to locate the best design in that region. At each stage you gain further insight into your design and the tools help you make further choices to improve it. Such hybrid methods can also yield considerable insight into the robustness of your design where each of the dimensions might be subject to manufacturing tolerances. Hybrid optimisation approaches are available from dezineforce.