Algorithm design: can you provide a solution to the multiple knapsack problem?

Question

I am looking for a pseudo-code solution to what is effectively the Multiple Knapsack Problem (optimisation statement is halfway down the page). I think this problem

Answer 1

You need http://www.or.deis.unibo.it/knapsack.html, chapter 6.6 "Multiple knapscack problem - Approximate algorithms". There is pseudo-code (Pascal style) in the text and Fortran implementations (yes, it's an old book) as a ZIP file.

Answer 2

As far as I know, the problem is NP complete (Wikipedia confirms), so there's probably not much sense in attempting to solve it exactly. However, any number of approaches might be good enough for you: greedy, genetic algorithms, simulate annealing...greedy is probably the easiest to implement:

while (time available in block greater than smallest task duration)
  find the longest fitting task
  add it

...you get the idea.