I am trying to solve a problem in an optimal way. The problem is as follows:
- We have an n-dimensional space
- In this space, we have a "finish" point with n coordinates, all non-negative
- We have a set of vectors, each having a non-zero length, and extending in at least one dimension. The vectors never extend to negative values (you can have a vector of xy coordinates 1, 2, but not -1, 2)
- There is at least one vector that extends in every of the n dimensions
- Each vector has a cost associated with using it
The objective is:
- To get from the start of the space beyond the finish point in all dimensions (dimensions of the sum of the vectors used has to be greater than that of the finish point)
- We can use any combination of the vectors and use multiple of the same vector
- The solution should have the lowest cost possible
So for example, in 3D space we could have a finish point of (1000, 250, 600), and vectors (10, 0, 0) costing 1, (1, 1, 5) costing 1.3 and (0, 2, 2) costing 2. The objective is to add enough vectors to get at least 1000, 250, 600 in the end and "spend" as little as possible.