Section 6 - Eg 1 - Walkway of Fixed Width Given Finite Material - Intro to NLP

That is, there is a space of given dimensions. Now, build a walkway around it such that the space (linear) between the empty-space-edge and the walkway is constant and using only the available material to build the walkway.

Sounds like something we might have done in differential calculus class ages ago.

But, what makes this one different is that the Objective function involves w*l = meaning - it's non-linear.

He's good at solving optimization problems, but a very poor (undisciplined) coder. Doesn't think twice about sprinkling magic constants throughout the code :(

!pip install pyomo

!wget -N -q "https://ampl.com/dl/open/ipopt/ipopt-linux64.zip"

!unzip -o -q ipopt-linux64


Solver = SolverFactory( 'ipopt', executable = '/content/ipopt')

OK, the code nails it easily, and that's when (checking the width thing), I realized that this one can be done on the back of an envelope. 

And, then, I saw that it can't be - because he (they, maybe? Poler and Diaz-Madronero) did such a poor job in problem description and elucidation. A simple 3D sketch in 10 seconds would have helped.

Turns out, you don't even need calculus in this case. Just assume you use all the material - why wouldn't you?

2x1 + 2x2 - 56 = 250 (minus 56? Because you put a handrail around that "empty space" 😊

Then, the constant width gives you a 2nd equation and they give you x1 = 44.5 and you're done. How lame!


Comments

Post a Comment

Popular posts from this blog

Section 5 Challenge Problem: Traveling Salesman

Winston and Goldberg 2004 Pg 532 You *have* to visit all cities (demand). What order will minimized the cost (total distance)? Solve it using integer programming. You're give the table of distances between cities. Set up the problem so you don't return to Ci immediately after leaving Ci. And also, a workaround for sub-tours - 3-4-3 (started from 3 and only visited 4) is not acceptable. 3-4-1-2-5-3 is acceptable (though may not be lowest cost). I didn't follow the lesson, but, this is probably so well known that, if you had to do it, you could just use chatGPT to knock it out..
Read more

Integer Programming (Section 5) Introduces a Nice (Big "em") Coding Trick

You have a decision variable that can take a range of natural number values - including 0.  It's the number of items you decide to produce. You want to maximize profit. The catch is, there a fixed cost associated with the decision to produce an item at all. If you make 0 of it and make that decision, then you don't rent the machinery for it. Else, add a fixed cost. How do you add this to your constraints and your objective (cost) function that you're trying to maximize? Z = whatever + sum( Fi * yi) And then, xi <= M*yi where M is just some large number - this introduces the coupling between x and y that you'd otherwise only get with an if statement.. Really? y is (0,1) whole - only two possible values. What you are trying to do is ensure the optimizer doesn't set y to 0 by introducing the coupling. Now, with a non-zero xi, yi has to be 1. Choosing Mi? Pick the largest value xi can attain - given the known parameter values. here, we starting using domain = pyo.Int...
Read more