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Numerical Solvers

by Martin Staadecker

Introduction

Numerical solvers, such as Gurobi, are tools used to solve linear programs.

This document is a record of what I've learnt about using numerical solvers while working with Switch, Pyomo and Gurobi.

Gurobi resources

The best resource when working with Gurobi is Gurobi's reference manual.

A few especially useful pages are:

Specifying parameters

To specify a Gurobi parameter use the following format:

switch solve --solver gurobi --solver-options-string "Parameter1=Value Parameter2=Value".

We recommend always using "method=2 BarHomogeneous=1 FeasibilityTol=1e-5 crossover=0" as your base parameters (this is what switch solve --recommended does).

Solving Methods

There are two methods that exist when solving a linear program. The first is the Simplex Method and the second is the Barrier solve method also known as interior-point method (IPM).

  • The Simplex Method is more robust than IPM (it can find an optimal solution even with numerically challenging problems).

  • The Simplex Method uses only 1 thread while the Barrier method can leverage multiple threads.

  • The Barrier method is significantly faster for our model sizes.

  • Running switch solve --recommended selects the Barrier method.

  • By default, when the Barrier method finishes it converts its solution to a simplex solution in what is called the crossover phase (see details). This crossover phase takes the most time and is not necessary. Therefore is gets disabled by the --recommended flag.

  • The crossover phase is important if the barrier method produces a sub-optimal solution. In this case use --recommended-robust to enable the crossover.