Basics of the Command Line Interface for MILPs

Table of Contents

• Input File Format
  • Example (.lp and .mps)
• Solving Your First MILP

Describes the basic usage of idol_cl for MILPs, including the expected input file format.

Input File Format

For MILPs, idol_cl accepts .mps and .lp files.

These are standard formats used by solvers such as Gurobi, Cplex, GLPK, and HiGHS.

In most cases, the file parsing is performed by the underlying solver used by idol.

For more details, refer to the IBM page on the .lp format or the lpsolve page on the .mps format.

Example (.lp and .mps)

Example of a simple MILP:

\[\begin{align} \min_{x,y} \quad & 3x + 4y \\ \text{s.t.} \quad & 2x + y \ge 5 \\ & x + 2y \ge 6 \\ & x, y \in \mathbb{Z}_{\ge 0} \end{align} \]

Corresponding .lp file:

Minimize
 obj: 3 x + 4 y
 
Subject To
 c1: 2 x + y >= 5
 c2: x + 2 y >= 6
 
Bounds
 x >= 0
 y >= 0
 
Generals
 x
 y
 
End

Equivalent .mps file:

NAME          example
ROWS
 N  obj
 G  c1
 G  c2
COLUMNS
    x       obj     3
    x       c1      2
    x       c2      1
    y       obj     4
    y       c1      1
    y       c2      2
RHS
    rhs     c1      5
    rhs     c2      6
BOUNDS
 LO bnd     x       0
 LO bnd     y       0
ENDATA

Solving Your First MILP

To solve a given MILP stored in an .lp file, all you need to do is

idol_cl solve milp model.lp

If you want to set a time limit and use a specific method, run

idol_cl solve milp model.lp --time-limit 3600 --method GLPK

To see which solution methods are available for a given problem, use the list-methods subcommand.

idol_cl list milp model.lp

Sampled Output:

-- No configuration file loaded
-- The main input file is model.lp
-- Detected: problem type is MILP
-- Detected: applicable methods are [GUROBI, CPLEX, HIGHS, GLPK, JUMP]
 
Details (all methods):
 
 - HIGHS: High Performance Software for Linear Optimization [https://highs.dev/]
 - JUMP: Calls the Julia package JuMP [https://jump.dev/]
 - GLPK: GLPK (GNU Linear Programming Kit) [https://www.gnu.org/software/glpk/]
 - CPLEX: IBM ILOG CPLEX Optimization Studio [https://www.ibm.com/fr-fr/products/ilog-cplex-optimization-studio]
 - GUROBI: Gurobi Optimizer [https://www.gurobi.com/]

If no method is specified, idol_cl automatically selects a suitable solver for the detected problem type.