3d bin packing algorithm [closed]

Question

I am looking for a deterministic implementation for any 3d bin packing algorithm, i.e. for packing many small and different cuboids inside one or many bigger ones. The solution could vary from the optimal one.

It should be written in C, C++, Java, C#, IronPython, IronRuby or any other language an can bin to from .Net code.

I found this C algorithm http://www.diku.dk/hjemmesider/ansatte/pisinger/3dbpp.c , but it doesn’t rotate the cuboids to find the best fit. I am ok with not rotating them upside down, but horizontal rotation should be possible.

Pinky

You claim you are looking for an algorithm, but you then list programming languages. Are you looking for a generic algorithm or an implementation? – Comanchean

Do you want the optimal solution, or one that's pretty good? Are the cuboids all the same? When you say rotation, do you mean 90 degrees, or any angle? – Permafrost

@Beta: If he is packing cuboids into a cuboid, surely anything other than integer multiples of 90 degrees will lead to a sub-optimal solution. – Coughlin

@Asaph: Of couse,not! Just because I mentioned "algorithm" doesn't mean it's a homework. – Pinky

@Beta, well it should be deterministic and a good solution is enough ( as I read optimal solutions are very hard to find) The cuboids are not all the same, and I guess, as Kinopiko said, any rotation other than by 90 degrees will not be helpful. – Pinky

@Mads-Elvheim: Sorry for the ambiguity. I need a concrete implementation, that I can directly call. I found a lot of papers solving this problem using integer linear programming or genetic algorithms. But I thought, for such a common problem there must be an exisitng implementation. – Pinky

@Kinopiko and Mouk, try putting 5 unit squares into a square of width 2.708, then tell me again about non-90-degree angles. – Permafrost

@Permafrost Convinced. Do have such an Algorithm? 90 degrees rotations are just enough for me. – Pinky

Answer 1

I have written an approximate algorithm for the case you describe i.e. 3D rectangular boxes, with orthogonal rotation, in C++. You can find the results and algorithm in the published paper: http://www.cs.ukzn.ac.za/publications/erick_dube_507-034.pdf

Hemihedral

Is the source or c++ app available online anywhere? – Winifred

This is good for a simple solution but really doesn't work all that well. For anyone wanting a explanation and help writing one I suggest this book: Knapsack Problems, by Martello and Toth, ISBN: 0471924202 – Aciculum

I can't find results in the linked page? is this still the correct url? – Geode

@AmrElgarhy From the name in original url, I guess this is the same paper. – Secondclass

Answer 2

I converted wknechtel/3d-bin-pack C code to javascript. Can be easily port to C#.

https://github.com/keremdemirer/3dbinpackingjs

You can run example calculations from index.html file and review the generated report. pack1.js file contains the app and algorithm. I'm not sure how the algorithm works but the results are satisfying for packaging calculations.

Selfemployed

Answer 3

This problem is NP-hard. Your best bet is an approximation algorithm (until a genius person solves any NP problem, or a very lucky fellow stumbles across a solution.) I do not know of any well know approximation algorithms for this problem unfortunately.

Volsung

Solving an NP-complete problem in polynomial time will still not give you a polynomial-solution to NP-hard problems :) – Montemontefiascone

Well for small packages, the required time is not that high. So brute force is a fair alternative for quite a few online shopping shipments. – Nick

@Nick if you are willing to go brute-force, you will most likely get the best bang for your buck by using a corresponding ILP to represent the problem and feeding it into something like gurobi. – Volsung

Thanks @idog, however I've already written a custom implementation which does a few application-specific optimizations like accounting for multiple boxes of the same size and such. – Nick