# Optimisation

Optimisation with FEKO
 Specification of optimisation goals. Mask for optimising the response of a microstrip filter. Frequency response of the optimised microstrip filter.

### Overview

Finding the optimal design is most often the primary objective of an engineer. The process can be summarised as follows:

• Define which design parameters can be varied.
• Set a range within which these can be changed.
• Define the desired goal(s).
• Select an optimisation method and then let FEKO find the optimal design.

### Optimisation Parameters

Any variable defined in CADFEKO may be used as an optimisation parameter e.g.

• Physical dimensions.
• Excitation (amplitude and phase). This could especially be relevant for arrays.
• Expressions may be used for boundary, start and grid settings.

### Optimisation Methods

The optimisation methods that are available in FEKO are:

• Grid search. Grid search is strictly speaking not an optimisation technique as it linearly scans the solution space, selecting the optimum value on completion. It is computationally expensive and is not recommended for use in solution spaces with more than 2 variables.
• Simplex Nelder-Mead. The Simplex Nelder-Mead Algorithm falls under the category of local or hill-climbing search methods where the final optimum can be significantly influenced by the starting value specified by the user.
• Genetic Algorithm (GA). GA optimisers are robust, stochastic search methods modelled on the Darwinian principles and concepts of natural selection and evolution. GA optimisation borrows from the natural world in a number of ways. Conceptually, during a GA optimisation, a set of trial solutions or individuals is chosen and then evolved toward an optimal solution under the selective pressure of the fitness/goal function. It is classified as a global optimiser.
• Particle Swarm (PSO). PSO is a population-based stochastic evolutionary computation technique based on the movement and intelligence of swarms. Individual particles start in random locations in the solution space with random velocity vectors. A particle's velocity vector is then adjusted relative to its knowledge of its own local optimum and the global optimum found by the entire swarm. As the name suggests, the population swarms toward the global optimum. PSO is also classified as a global optimiser.

### Goals

The following goals can be defined and each can have a different focus type, i.e. parameter to be optimised according to the user specification:

• Impedance goal (Input impedance, Input admittance, Reflection coefficient, Transmission coefficient, VSWR, Return losses)
• Near-field goal (E-field, H-field, Directional component, Coordinate system)
• Far-field goal (E-field, Gain, Directivity, RCS)
• S-parameter goal (Coupling, Reflection coefficient, Transmission coefficient, VSWR, Return losses)
• SAR goal

Goals can be defined for single output values (e.g. antenna directivity in a specified direction), or over ranges of values (e.g. input impedance as a function of frequency). In the latter case masks are used.

### Combination of Several Goals

In some advanced cases it might be required to specify more than one goal and to weigh their relative importance in a single goal that is then optimised. An example might be where a designer wants to optimise both the input impedance bandwidth and directivity of an antenna and sets up a goal function that takes both these aims into account. A GUI wizard assist users in specifying goal functions and combining them into combined optimisation requirements.

### Parallelisation Features

• Each solution during the optimisation process may be parallelised as in the case of any normal FEKO solution.
• Optimisation runs may be farmed out (i.e. parallel processes each handle a solution specified by the optimizer).

### Processing of Results

Visual feedback on all the optimisation Parameters (variables) and the Goal(s) is provided in POSTFEKO during the optimisation process.

### Example

A bent dipole with variable bend angle (#alpha) is placed at a variable distance (#d) in front of a flat reflector plate. The operation frequency is 300MHz. Find the angle, #alpha, and dipole to plate separation distance, #d, that will give the maximum broadside gain (i.e. in the X-direction).