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I have a very specific Integer Linear Programming problem to tackle:-

https://math.stackexchange.com/questions/1724708/efficient-time-complexity-algorithm-for-linear-programming-problems

I did ask this question on the math forum but I think its more relevant here in the programming section. Can someone please suggest some (possibly Monte Carlo) algorithm which is easily implementable ? Wikipedia page on integer programming:- https://en.wikipedia.org/wiki/Integer_programming states that tabu search is applicable in general to ILP. However it is not completely clear how to go about implementing this for my specific problem.

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  • Montecarlo won't be efficient, and won't be optimal. It's between both. Heuristics are efficient but not optimal. What's your specific problem? – xvan Apr 03 '16 at 20:25
  • Well, that was not what i meant. the specific problem which is at hand (math.stackexchange link provided) is an optimization problem. The very purpose of Monte Carlo algos is to provide efficient near optimal solutions. Please explain your statement that Monte Carlo wont be efficient. – kurtgodel95 Apr 04 '16 at 03:25
  • Monte Carlo accuracy depends on the amount of simulations. So as accuracy increases, you may find methods of less computational cost for an specific problem. Monte Carlo will always work, but won't always maximise efficiency for a target accuracy. – xvan Apr 04 '16 at 03:48
  • I suggest solving the underlying LP to get a (probably fractional) solution. This is fast even for thousands of variables. You can then try rounding the variables up and down randomly, and checking whether the resulting integer solutions are feasible. Even if they are, they aren't guaranteed to be optimal, but they're likely to be good, especially if they were mostly close to 0 or 1 before. – j_random_hacker Apr 04 '16 at 12:15
  • This sounds reasonable,great! thanks!. However if you can think of some local search based solutions please let me know. – kurtgodel95 Apr 04 '16 at 13:56

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