optimizer

Optimizer is a wrapper function for fmincon and the SOM-Toolbox. It's primary goal is to make optimization easily accesible and intuitive for everyone.

The function gets its all its input from a simple excel spreadsheet where you layout your design variables with initial values and bounds, constants, auxilary equations (equations that might make up your constraints or objective function), your constraint functions, and your objective function. There is a blank template included, and a sample file to show how things work.

If you're human, and are unsure where to start your initial values, there is a handy discrete mode, which will solve all your constraint equations and your objective function over your bounds over a discrete matrix, so you can get an idea of where to start.

If you're still human, and staring at a large matrix of numbers leaves you stumped, you can make use of the Self-Organizing Maps toolbox written by Esa Alhoniemi, Johan Himberg, Jukka Parviainen and Juha Vesanto. This will visually direct you to a good set of initial conditions, or even a "good enough" solution.

Quick Start - Excel Input Sheet Example

name	value	type	LL	UL	description
A	4	con			Some Constant Value
B	3	var	1	6	A Design Variable Value with lower and upper bounds
C	2	var		10	A Design Variable with only one bound
D2	C+B	cst		2*A	A Constraint Equation with an equation as a bound
Ei	B-C^2	cst	-1		An additional Constraint Equation
Fo	A^2-D	aux			An auxilary equation (these should not have bounds)
Gm	A*Fo-B^2+D2	obj	1		The objective function**
** NOTE: The bound(s) on the objective function is(are) optional in discrete mode, this can help you narrow in on your solution. It will be ignored in optimize mode. Also, objective functions are always minimized in optimize mode, so if you need it maximized, multiply the whole equation by -1. Be careful to remove that for discrete mode if you have a bound, or make your bounds negative as well. I'm working on a fix...

Quick Start - Matlab Code

This is the quickest way to get started. It will run in discrete mode and give you a table of possible values for your solution.

[Table] = optimizer();

To run the fmincon optimization on your problem, use the below command. The data output is your input data from the excel spreadsheet in a Structure, x is the actual optimized design variables, and eqn is a structure with all your constraint, auxilary, and objective functions, as matlab functions of the design variables x(1), x(2)...

[data,x,eqn] = optimizer();

Name-Value Input Options

• Name [Default Value] - (Alternate Values)
• fname ['input_data.xlsx'] - ('C:\Some Full Path\file.xlsx')
  • This supplies the full path to your input excel file.
• verbose [false] - (true)
  • This turns on and off verbose mode, which will show you your equation substitutions and will show you which design varible bounds are removing the most solutions.
• update [false] - (true)
  • In discrete mode, update will create the matrix of unique solutions found (values to constraint and objective functions) to sheet 2 in your input data sheet.
  • In optimize mode, update will update the initial conditions in your input data sheet with the optimal values it finds.
• iterations [false] - (true)
  • This will show each iteration in optimize mode
• mode ['discrete'] - ('optimize')
  • This is where you choose whether your want to use the discrete or optimize modes. Discrete is helpful for finding initial conditions "by hand" while optimize will "do it for you" to the best of it's ability.
• disc_size [1e5] - (Any Integer)
  • This is the maximum size of your discrete matrix. rⁿ = disc_size where r is the range between your bounds for each variable, and n is the number of variables. The greater this number, the more discrete values between your variable bounds, but the more memory intensive the operation. I suggest not exceeding 1e7.
• SOM [false] - (true)
  • This will use the SOM-Toolbox to show component planes with your discrete solutions self organized. Basically, that means it will make color maps for each constraint, your objective, and each design variable. Each unique solution is mapped to the same position on each plane or map, and the color shows you its value in that plane. I've found this incredibly useful for finding solid initial conditions or for "hand picking" optimal values.

Example

[Table] = optimizer('fname',fname,'SOM',true,'disc_size',1e6,'verbose',true,'update',true);