I have been working on a combinatorial optimization problem which can be modeled as an integer linear programming. I implemented it as a c++ project in visual studio 2017 and CPLEX1271. With the hope that my program would run faster, I use MIPStart to provide cplex a feasible solution. But the running time changed from 49s to 140s. All I did is providing a feasible solution to cplex, according to the answer, it cannot hurt the running time. Can anyone explain it?

UPDATE1: The log shows that cplex accept the solution.

UPDATE2: I've tested on hundreds of instances. It turned out that a warm start sometimes slows down cplex and at other times it accelerates cplex.

  • $\begingroup$ Can you post the log that cplex prints before and after? $\endgroup$ – user3680510 Jul 7 '20 at 7:44
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    $\begingroup$ @prubin has addressed this here : or.stackexchange.com/questions/2931/… $\endgroup$ – Kuifje Jul 7 '20 at 9:52
  • $\begingroup$ @Kuifje I didn't add the time to generate a feasible solution. I only count the time consumed by cplex. $\endgroup$ – Mengfan Ma Jul 7 '20 at 9:58
  • $\begingroup$ @MengfanMa Read prubin's answer carefully : he explains why warm starting may result in a longer running time. $\endgroup$ – Kuifje Jul 7 '20 at 10:19
  • $\begingroup$ @Kuifje I got it. But I think the answer is too short to get a full understanding. I was wondering if there is any other material on this topic? $\endgroup$ – Mengfan Ma Jul 7 '20 at 14:09

If the solution you provided is not very good (i.e., it's far from the global optimum), it often leads the branch-and-bound algorithm down a different path, which ends up slowing down the overall solution time.

MIP solvers are very good in figuring this stuff out by themselves, so the best use of warm-start nowadays is when we solve many similar problems sequentially.

  • $\begingroup$ What do you mean by “use of warm start when we solve many similar problems”? $\endgroup$ – Mengfan Ma Jul 16 '20 at 6:41
  • $\begingroup$ This is part of many algorithms, e.g., a feasibility pump, where we only change the objective, or we fix some variables, or add a couple of constraints per iteration. In that case, the solution of problem $i+1$ is very likely to be very similar to the one of problem $i$. $\endgroup$ – Nikos Kazazakis Jul 16 '20 at 10:15

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