integer-programming

I am trying to solve the Bin Packing Problem using the Integer Programming Formulation in Python PuLP. The model for the problem is as follows: I have written the following Python Code using the PuLP library from pulp import * #knapsack problem def knapsolve(bins, binweight, items, weight): prob = LpProblem('BinPacking', LpMinimize) y = [LpVariable("y{0}".format(i+1), cat="Binary") for i in range(bins)] xs = [LpVariable("x{0}{1}".format(i+1, j+1), cat="Binary") for i in range(items) for j in range(bins)] #minimize objective nbins = sum(y) prob += nbins print(nbins) #constraints prob += nbins >

I noticed that R doesn't use all of my CPU, and I want to increase that tremendously (upwards to 100%). I don't want it to just parallelize a few functions; I want R to use more of my CPU resources. I am trying to run a pure IP set packing program using the lp() function. Currently, I run windows and I have 4 cores on my computer. I have tried to experiment with snow, doParallel, and foreach (though I do not know what I am doing with them really). In my code I have this... library(foreach) library(doParallel) library(snowfall) cl <- makeCluster(4) registerDoParallel(cl) sfInit(parallel = TRUE,

This problem appeared in a challenge , but since it is now closed it should be OK to ask about it. The problem (not this question itself, this is just background information) can be visually described like this, borrowing their own image: I chose to solve it optimally. That's probably (for the decision variant) an NP-complete problem (it's certainly in NP, and it smells like an exact cover, though I haven't proven that a general exact cover problem can be reduced to it), but that's fine, it only has to be fast in practice, not necessarily in the worst case. In the context of this question, I'm