Solving the example

While solving a problem, the Interactive Optimizer executes the optimize command.

The optimize command tells CPLEX to solve the LP problem. CPLEX uses the dual simplex optimizer, unless another method has been specified by setting the LPMETHOD parameter (explained more fully in the CPLEX User’s Manual).

Entering the optimize command

At the CPLEX> prompt, type the command:


optimize

Preprocessing

First, CPLEX tries to simplify or reduce the problem using its presolver and aggregator. If any reductions are made, a message will appear. However, in our small example, no reductions are possible.

Monitoring the iteration log

Next, an iteration log appears on the screen. CPLEX reports its progress as it solves the problem. The solution process involves two stages:

  • during Phase I, CPLEX searches for a feasible solution

  • in Phase II, CPLEX searches for the optimal feasible solution.

The iteration log periodically displays the current iteration number and either the current scaled infeasibility during Phase I, or the objective function value during Phase II. After the optimal solution has been found, the objective function value, solution time, and iteration count (total, with Phase I in parentheses) are displayed. This information can be useful for monitoring the rate of progress.

The iteration log display can be modified by the command set simplex display to display differing amounts of data while the problem is being solved.

Reporting the solution

After it finds the optimal solution, CPLEX reports:

  • the objective function value

  • the problem solution time in seconds

  • the total iteration count

  • the Phase I iteration count (in parentheses)

Optimizing our example problem produces a report like the following one (although the solution times vary with each computer): 


Tried aggregator 1 time.
No LP presolve or aggregator reductions.
Presolve Time = 0.00 sec. (0.00 ticks)

Iteration Log . . .
Iteration:     1  Dual infeasibility =             0.000000
Iteration:     2  Dual objective     =           202.500000

Dual simplex - Optimal:  Objective =    2.0250000000e+02
Solution Time =    0.00 sec.  Iterations = 2 (1)
Deterministic time = 0.00 ticks  (3.38 ticks/sec)

CPLEX>

In our example, CPLEX finds an optimal solution with an objective value of 202.5 in two iterations. For this simple problem, 1 Phase I iteration was required.

Summary

To solve an LP problem, use the command:


optimize