The linear solver comparison

The graph below shows the processing time of each linear solver for three different instances, quite large(Instance21 from Scheduling Benchmarks), large(n120w8 from INRCⅡ）, and nominal(Instance8 from Scheduling Benchmarks).

 When the instance size is quite large, the First Order Method has an overwhelming advantage. In contrast, the Simplex is dominant for light instances. In the middle graph, Interior Point Solver is dominant. As you can see, there is no single, all-purpose linear solver, so your best bet is to choose the best linear solver for your instance. In practical use, CLP will be the default linear solver since our nominal instance is less than 100 staffs per month. However, for long-term and large-scale applications such as 3 or 6 months, we should consider using Interior Point Solver or First Order Method.