优化2D布局的算法

Question

Is there a Javascript algorithm for finding the optimal layouts?

There is a fixed width and finite number of rectangular shapes, the goal is to find the shortest length required to fit all the shapes in.

We need to answer the following sort of query.

The width is 4,000 units and the following shapes are required, 10 lots of 450 x 750, 6 lots of 2,500 x 1,200 and 5 lots of 900 x 1,500. What is the optimal layout of the shapes and the length required to fit them all in.

I'm not sure how best to approach this if starting from scratch and am hoping that there is something out there already so as to avoid simply doing this via brute force.

Answer 1

Is there a Javascript algorithm for finding the optimal layouts?

The question should rather be "Is there an (efficient) algorithm which happens to be available as JavaScript implementation". I personally would post it on Math SE or the professional Math site, you might add RPP for "Rectangle Packing Problem".

There is a fixed width and finite number of rectangular shapes, the goal is to find the shortest length required to fit all the shapes in.

The width is 4,000 units and the following shapes are required, 10 lots of 450 x 750, 6 lots of 2,500 x 1,200 and 5 lots of 900 x 1,500. What is the optimal layout of the shapes and the length required to fit them all in.

Are there constraints on the orientation of the rectangles? (Have a fun look here ).

The naive algorithm would be to try out all configurations which honor the constraints and pick an optimal one. This is usually not possible due to too many configurations.

So one sticks to heuristics (eg here ). You might end up with research level maths while I have the feeling you are looking for some "good enough" optimizer.