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I am new to LP and have only briefly used PuLP in Python.

  1. Why is there a speed difference between SCIP 3.2.1 - CPLEX 12.63 and CPLEX 12.6.3? Doesn't SCIP still use CPLEX for solving?

  2. Why will someone use SCIP with CPLEX solver, instead of using CPLEX directly?

enter image description here

Nyxynyx
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    Some remark: [cbc](https://projects.coin-or.org/Cbc) (one of the best open-source MIP-solvers) will be typically the default-solver for [pulp](https://github.com/coin-or/pulp). At least within the windows-distribution. – sascha Oct 07 '16 at 19:40

1 Answers1

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What is this difference about

This plot is not showing a LP-benchmark, but a Mixed-integer programming benchmark.

Mixed-integer programming solvers typically use a branch-and-cut-based algorithm (including heuristics and co.), where a lot of relaxations are solved (in sequence; treating binary-/integer-variables as continuous resulting in an LP-problem).

One decision then is to choose how to solve these relaxed subproblems. The most simple decision (there are many more; e.g. tuning the Simplex-algorithm's parameters; it get's even more complex when solving problems with nonlinear-conic objectives) is to choose the LP-solver.

SoPlex is a LP-solver implementation by the SCIP-team. Meaning:

  • SCIP - SoPlex will use SCIP's algorithm for MIP (handling branching, cut-generation and co.) using SoPlex as solver for the internal LP-subproblems
  • SCIP - CPLEX will use SCIP's algorithm for MIP using CPLEX as solver for the internal LP-subproblems

Why using SCIP with CPLEX (instead of using a pure CPLEX approach)

The why is not that easy to explain.

  • Keep in mind, that all MIP-solvers are heuristics-based and on some problems SCIP will be faster than CPLEX (despite the underlying LP-solver selected).

    Keywords for some theory: NP-hardness (of MIP) and the No free lunch theorem

    • Faster could mean: faster due to the MIP-based strategies, not the speed of the underlying LP-solver so that you may even gain an overall speedup using CPLEX on the subproblems!

  • The two solvers (MIP-solvers) are probably also much different in regards to parameters & accessibility (of internal algorithmic components). It's obvious, that you can tune SCIP in a much more general way than CPLEX (because it's open source)

  • As mattmilten mentioned in the comments: SCIP and CPLEX are also different in regards to the support of problem-classes which can be solved. One example of this might be the possibility for some special nonlinear-constraints (resulting in a MINLP). Using SCIP for these kind of problems, can still use CPLEX' LP-solver internally (same arguments as above)

sascha
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    Worth noting is that SCIP can solve a wide variety of problem classes - more than CPLEX - and sometimes it may be of advantage to still use CPLEX as LP solver while solving a nonconvex MINLP for instance. – mattmilten Oct 07 '16 at 19:28
  • @mattmilten I just added one remark, that sometimes the MIP-based algorithm is faster and an additional speedup could be obtained by using CPLEX' LP-solver for the subproblems. I agree with everything you said. – sascha Oct 07 '16 at 19:30