Monitoring Objective Function Value During Solving in OR-Tools

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What will you learn?

In this tutorial, you will learn how to track the progression of the objective function’s value while solving mixed-integer programming problems using Google’s OR-Tools. You will explore the use of callbacks to monitor the solver’s progress and gain insights into your optimization model’s behavior.

Introduction to the Problem and Solution

When dealing with optimization problems, especially mixed-integer programming (MIP) models using Google’s OR-Tools, it is essential to monitor how our solutions evolve. Tracking the objective function value not only helps us gauge our progress towards an optimal solution but also provides valuable insights into our model’s performance and behavior.

To address this need, we can leverage callbacks in OR-Tools. Callbacks are functions that allow us to tap into the solving process at specific stages, enabling us to extract information like the current best objective function value. By incorporating callbacks into our code, we can enhance our understanding of how the solver operates and make informed decisions to improve our model.

Let’s delve into practical Python examples that demonstrate how callbacks can be utilized in OR-Tools to monitor and analyze the objective function value during the solving process.

Code

from ortools.linear_solver import pywraplp

def monitor_callback(solver):
    """Callback function to monitor solver progress."""
    print(f"Current Objective Value: {solver.Objective().Value()}")

# Create your solver instance.
solver = pywraplp.Solver.CreateSolver('SCIP')

# Example problem setup:
x = solver.IntVar(0, solver.infinity(), 'x')
y = solver.IntVar(0, solver.infinity(), 'y')
solver.Maximize(3 * x + y)
solver.Add(x + 2 * y <= 14)
solver.Add(3 * x - y >= 0)
solver.Add(x - y <= 2)

# Register callback.
solver.SetProgressMonitor(monitor_callback)

# Solve problem.
status = solver.Solve()

if status == pywraplp.Solver.OPTIMAL:
    print("Solution:")
    print("Objective value =", solver.Objective().Value())
else:
    print("The problem does not have an optimal solution.")

# Copyright PHD

Explanation

In this solution:

  1. Creating a Callback Function: The monitor_callback function is defined to accept a single argument�our solver. It prints out the current objective value by accessing solver.Objective().Value().

  2. Setting Up Our Solver and Problem: We initialize a MIP problem using SCIP through OR-Tools’ interface (pywraplp). A simple optimization problem with variables (x, y), an objective function, and constraints is set up for demonstration.

  3. Registering Our Callback: Before solving the problem, we register our callback using SetProgressMonitor. This instructs OR-Tools to call monitor_callback periodically during the solve process.

  4. Solving The Problem: Calling Solve() initiates the solving process where our callback fires periodically, providing updates on progress until completion or interruption.

This approach offers real-time insights into your model’s progression towards optimality, aiding in both development and analysis phases of modeling work.

  1. How do I customize what information gets reported by my callback?

  2. You can modify your callback function to access various properties from your solver object such as constraints satisfaction status or specific variable values at that point in time.

  3. Can I use callbacks with any OR-tools solvers?

  4. Callbacks functionality may vary across different solvers supported by OR-Tools; always refer back to specific documentation of your chosen solver within OR-tools framework for compatibility details.

  5. What are other uses of callbacks beyond monitoring?

  6. Callbacks can serve many purposes including dynamically adding constraints based on intermediate results (lazy constraints), modifying stopping criteria mid-solve based on custom logic among others offering great flexibility in controlling solve processes intricately.

  7. Is there performance overhead when using callbacks?

  8. Yes, invoking a Python-based callback introduces computational overhead due mainly to context switching between C++ core library code and Python layer�keep this in mind especially if performance is critical in your application scenario.

Conclusion

By utilizing callbacks in Google’s OR-Tools, you gain significant control over optimization processes and valuable insights into complex mixed-integral programming problems. Through experimentation and observation facilitated by these mechanisms, you can uncover innovative solutions and enhance efficiency in tackling challenging optimization tasks.

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