Solve problem of choice of resistor

I'm trying to learn the Optimization Toolkit by trying solve a very simple optimization problem:

I have a a simple LED circuit consisting of three elements: a power source, LED and resistor.

Each element has own operational constraints. I want to choose a resistor from a list of available resistors, which provides highest current to LED while fitting into the constraints.

Constants/known values

% Power source
source_V = 5        % voltage of the power source
source_I_max = 0.04 % max current draw from the power source

% Resistors
resistor_R = [100 220 330 1000 10000 100000 1000000] % available resistors

% LED
led_V_forward = 1.85 % forward volage of the LED
led_I_max = 0.02     % max current for the LED

Objective

% Find resistor_idx, index of the desired resistor from the list resistor_R
% integer, discrete
resistor_idx = optimvar('resistor_idx') 

% LED current, optimization variable which we need to iterate
% real number
% we need max value
led_I = optimvar('led_I')
led_I = (source_V - led_V_forward) / resistor_R(resistor_idx)

Constraints

led_I <= source_I_max % LED should draw current below limitation of the power source
led_I <= led_I_max % LED should draw current below own limiation
resistor_idx % is discrete variable, index of resistor_R value

Please help me define this problem in MATLAB. I'm getting confused what is my objective (resistor_idx or led_I) and how to defined discrete constraint of resistor_idx and what kind of optimization should I use.

Answer 1

[Alan Weiss]

To allow this code to work, I copy over your data.

% Power source
source_V = 5;        % voltage of the power source
source_I_max = 0.04; % max current draw from the power source
% Resistors
resistor_R = [100 220 330 1000 10000 100000 1000000]; % available resistors
% LED
led_V_forward = 1.85; % forward volage of the LED
led_I_max = 0.02;     % max current for the LED

I think that you need to be more careful in defining your optimization variable:

resistor_idx = optimvar('resistor_idx',"Type","integer","LowerBound",1,"UpperBound",7);

Also, I don't think that led_I is an optimization variable. So remove the line

% led_I = optimvar('led_I') % Remove this line

You need to create an optimization problem for maximization.

prob = optimproblem("ObjectiveSense","max");

You need to use fcn2optimexpr to create your objective, because you cannot use an optimization variable as an index.

fun = fcn2optimexpr(@(x)(source_V - led_V_forward) /resistor_R(x),resistor_idx);
prob.Objective = fun;

Put the constraints in the problem.

prob.Constraints.led = fun <= source_I_max; % LED should draw current below limitation of the power source
prob.Constraints.led2 = fun <= led_I_max;

Solve the problem like this:

[sol,fval] = solve(prob)

Solving problem using ga.
Optimization terminated: average change in the penalty fitness value less than options.FunctionTolerance
and constraint violation is less than options.ConstraintTolerance.

sol = struct with fields:
    resistor_idx: 2

fval = 0.0143

You see that integer-constrained problems are not so simple to set up. But you can do it if you are careful to follow the limitations.

Alan Weiss

MATLAB mathematical toolbox documentation

[Sergey Kostrukov]

Thank you!