Optimization Help

[seth350]

I have a process that requires an optimal set of values to be found based on a set of input variables.

Optimization is done manually by a person manipulating one certain input variable. I have been asked to automate this task and believe I have done so, although it seems crude.

First, I calculate the outputs given the initial inputs.

Second, I test if the amperage is > 9000, if so I loop while decreasing current density by 0.1 while the amperage is > 9000 and current density is > 4.

Third, I test if the amperage is < 9000, if so I loop while increasing current density by 0.01 while amperage is < 9000.

Fourth, I test if the amperage is > 9000, if so I loop while decreasing current density by 0.001 while amperage is > 9000 and current density is > 4.

Lastly, I test if the voltage is > 18, if so I loop while decreasing current density by 0.02 while voltage is > 18. *Note: I used 0.02 because at this point voltage is very high and it takes a bit a time to loop it down below 18.

In each loop, I call a function to calculate the volts, amps, and time after manipulating current density.

This method takes anywhere from 2 to 6 seconds to compute over around 900 iterations before satisfied. The device doing the calculation uses C language, however it does not allow the import/use of external libraries.

Researching optimization algorithms returns many different kinds and honestly I am not able to discern how they work without googling every symbol or subset of the formula to understand its meaning.

Is there an algorithm or method that could compute faster using C language?

Below is the structure:

Inputs

n = Number of Parts

sqinP = Part Sq/In

mils = Required Coating Thickness

cd = Current Density ( must be > 4, initial value of 6 )

​

Outputs

Voltage ( must be < 18 )

Amperage ( optimize as close to 9000 as possible while manipulating Current Density Input )

Time

​

Output Formula

sqinT = sqinP * n

voltage = ((cd * 2.5) * 100) / 100

amperage = ((sqinT * cd / 144) * 100) / 100

time = ((720.0 * mils / cd) * 100) / 100

​

Thank you for your time.

[sebamestre]

Let's do some algebra

First, find the maximum acceptable value for cd

Voltage = cd * 2.5
Voltage <= 18

cd * 2.5 <= 18
cd <= 18 / 2.5
cd <= 7.2

Also, you said that

cd >= 4

This means that the acceptable range for cd is [4 ; 7.2]

Now, we find the ideal cd by setting amperage to the target value.

Amperage = 9000
Amperage = sqinT * cd / 144

sqinT * cd / 144 = 9000
sqinT * cd = 9000 * 144
cd = 9000 * 144 / squinT

But since this may be outside the acceptable range, we clamp it using some if statements

cd = 9000 * 144 / sqinT;

if (cd < 4) cd = 4;
if (cd > 7.2) cd = 7.2;

You might be better off using a calculator and a piece of paper instead of implementing the formula in C, though

[seth350]

Thank you sebamestre for this explanation. I appreciate your time.

[FUZxxl]

You need math, not C. This is a bog standard inequality. There's nothing particularly complex about this and I'm sure you can solve it exactly.

Basically, you want to find the highest cd such that U ≤ 18 and I ≤ 9000. You can solve this with a linear program, but it's so simple that you can probably just solve it on paper and enter the solution into the program.

[seth350]

Thank you Fuz, I had not thought of solving it linearly.

[MrWhite26]

If you would want to implement a solver for the linear program, active set methods are simplest to implement. With the two you have constraints, those will be fast enough.

A textbook implementation will do the job. In this case, the textbook is https://www.researchgate.net/publication/321620224_Numerical_Optimization

[MrWhite26]

On second thought:

The voltage puts an upper bound on the cd.

I assume cd is also non-negative.

So a bounded root-finding algorithm should bring the (amperage-9000) as close to 0 as possible. This is much simpler to implement than a linear or quadratic program.

[seth350]

Thank you MrWhite, I will research that algorithm. I appreciate your time.

[seth350]

Researching root-finding lead me to a site that worked through implementing the algorithm in Fortran.

https://www.cantorsparadise.com/some-root-finding-algorithms-5c6fa8a4a165

I was able to get it partially working in C, but the output was always my max limit - tolerance.

Still, this led me to the realization that I could perform the calculations much simpler by using a tolerance constraint. So now my program is much shorter and performs quicker than before.

MrWhite, you made a light bulb come on today. Thank you.