Using PHP ML - Machine Learning library, to generate solutions based on a single input value

Question

Problem:

I have a door of 2000mm height.

I have 2 types of panels to build the door:

615mm standard panels and 495mm standard panels.

For the above height, my optimal solution would have to be:

1 x 615mm panel standard

2 x 495mm panel standard

1 x 495mm panel from which I cut 100mm to reach the 2000mm height. Here is the best solution to cut from 495 instead of 615mm because it would be a lost of too much material.

Example: 1845mm height -

Optimal solution is:

3 x 615mm panels ( 3x 615mm = 1845mm).

Another example:

3000mm height -

Optimal solution:

4 x 615mm panels

1 x 540mm panel (default 615mm from which is cut 75mm to fill the 3000mm height)

My question is, can I use any algorythm from PHP-ML library to train and predict solutions for input given (height, in my case). If the answer is yes, which algorithm is best suitable for my case?

Classification

SVC or k-Nearest Neighbors or Naive Bayes

Please see the pic i attached. You will understand what I want to say.

I want to use that Library so it can return me several solutions for given height, and an optimal one.

Please explain any downvotes, in order to improve my explanations. Thank you! — Bogdan C, Jan 25 '18 at 20:23

terales · Accepted Answer · 2018-01-26T15:59:02.080

3

Your specific task is could be easily brute forced, check it online: https://3v4l.org/dQmdb

Here is a code:

<?php

// Examples:
// Door           2000    1845    3000
// 615mm panel    1       3       5
// 495mm panel    3       0       0
// panel loss     100     0       75

function calcOptimalPanels ($doorHeight) {
  $bigHeight = 615;
  $smallHeight = 495;

  $bigFit = floor($doorHeight / $bigHeight);
  $smallFit = floor($doorHeight / $smallHeight);

  $options = [];

  for ($big = 0; $big <= $bigFit; $big++) {
    for ($small = 0; $small <= $smallFit; $small++) {
      $waste = $bigHeight * $big + $smallHeight * $small - $doorHeight;

      if ($waste === 0) // Get first combination without waste
        return getFormattedResult($big, $small, $waste);

      if ($waste > 0)  // Omit combinations smaller then door
        continue;

      $options[$waste] = getFormattedResult($big, $small, $waste);
    }
  }

  $minWaste = min(array_keys($options));

  return $options[$minWaste];
}

function getFormattedResult($big, $small, $waste) {
  return ['615mm' => $big, '495mm' => $small, 'waste' => $waste];
}

echo '2000: ' . json_encode(calcOptimalPanels(2000)) . "\n";
echo '1845: ' . json_encode(calcOptimalPanels(1845)) . "\n";
echo '2340: ' . json_encode(calcOptimalPanels(1845 + 495)) . "\n";
echo '3000: ' . json_encode(calcOptimalPanels(3000)) . "\n";

// Result:
// 2000: {"615mm":1,"495mm":3,"waste":100}
// 1845: {"615mm":3,"495mm":0,"waste":0}
// 2340: {"615mm":3,"495mm":1,"waste":0}
// 3000: {"615mm":1,"495mm":5,"waste":90}

My previous answer is not correct but I leave it as an example of our love to overcomplicate things.

Old answer

This is a classic 1D Cutting stock problem which can be formulated as an integer linear programming problem.

You should be aware that this is an NP-complete problem:

This basically means that their is no way of being guaranteed the best solution without checking every possible solution. This is not to say that a solution reached by one of the following algorithms is not optimal, it may be.

With given info in mind, you have to implement an algorithm yourself: https://neos-guide.org/content/cutting-stock-problem

and video: https://www.youtube.com/watch?v=NoiPrt4OsQA

If you desperately want to leverage machine learning then check genetic algorithm: https://github.com/ffsantos92/2d-cutting-stock-problem

edited Jan 26 '18 at 15:59

answered Jan 25 '18 at 20:28

terales

3,116
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1

Very nice answer. I know you worked a lot to provide me this answer. Thank you very much. I will see if I can somehow transform into a php algorithm from cutting stock or adapt that genetic algorithm (which would be insane if I would succeed). – Bogdan C Jan 25 '18 at 21:08
And if you succeed either way try to open source it to help others and receive feedback from community – terales Jan 25 '18 at 21:14
So far you are the only who understood what I want. You pointed me in the best direction so far, better than anyone else. – Bogdan C Jan 25 '18 at 21:19
Added simpler solution – terales Jan 25 '18 at 23:49
This can be modified to return more than one solution per given height? Example, for 2000, your solution returns 4 x 495mm. Other solution is 3 x 495 + 1 x 615mm. I can`t have a solution where the sum of panel heights is less than my height, because it would remain an empty space. – Bogdan C Jan 26 '18 at 09:10
It won't return solution with sum of panel heights less then door height. Did you try it? – terales Jan 26 '18 at 09:29
Yes. 495 x 4 = 1980. Height is 2000. There is a gap of 20mm. – Bogdan C Jan 26 '18 at 09:29
I must ignore the solutions where `$waste > 0`; I dont get it why it returns me solutions with panels sum under the height. – Bogdan C Jan 26 '18 at 11:33
Ah, missed the sign. Good catch! – terales Jan 26 '18 at 14:51
Fixed. See an updated answer – terales Jan 26 '18 at 15:59
Thank you. One minor observation. Instead of returning me 0 panels, it should recalculate and offer other solution. This code returns 0 panels used on height 2000. But there can be used 1 x 615 and 3 x 495 (from which I cut 100mm to reach 2000). – Bogdan C Jan 26 '18 at 16:03
Checked: https://3v4l.org/dQmdb It returns exactly 1 x 615 and 3 x 495. Am I missing something? – terales Jan 26 '18 at 16:05
Let us [continue this discussion in chat](http://chat.stackoverflow.com/rooms/163963/discussion-between-bogdan-c-and-terales). – Bogdan C Jan 26 '18 at 16:09

Using PHP ML - Machine Learning library, to generate solutions based on a single input value

1 Answers1

Old answer