Скачать или смотреть Resolving the Optimization Discrepancy between CPLEX and C+ +

Discover how to align the results of your optimization problems in C+ + with those produced by CPLEX by addressing common pitfalls and understanding the correct implementation.
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This video is based on the question https://stackoverflow.com/q/76883136/ asked by the user 'Arctic_Skill' ( https://stackoverflow.com/u/7185286/ ) and on the answer https://stackoverflow.com/a/76897602/ provided by the user 'TimChippingtonDerrick' ( https://stackoverflow.com/u/2108433/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

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Understanding the Optimization Discrepancy: CPLEX vs C+ +

Optimization problems are at the forefront of operations research and data analysis, allowing us to model complex real-world scenarios. Many professionals use tools like IBM ILOG CPLEX Optimization Studio to solve these problems effectively. However, when transitioning to C+ + and trying to replicate the solutions using the CPLEX API, discrepancies may arise. This guide explores why this happens and outlines the necessary steps to correct the issue.

The Problem Statement

While working with CPLEX to model optimization problems, one might decide to shift to C+ + for enhanced control or integration into larger systems. In the case discussed, a simple optimization problem was programmed in both CPLEX and C+ + . Although the CPLEX version produced a correct solution, the C+ + version returned an "optimization failed" message, leading to confusion.

Example of the Problem Setup

The problem was defined in CPLEX as follows:

Objective Function: Maximize -3*x[1] - 2*x[2] + 4*x[3] + y[1] - 3*y[2] - 2*y[3]

Constraints:

-2*x[1] + 4*x[2] - x[3] + 3*y[1] - 2*y[2] + 3*y[3] <= -4

-x[1] - 2*x[2] + 4*x[3] + 2*y[1] + 4*y[2] - 5*y[3] <= 2

Variables constraints: forall(i in i) x[i] <= 6

The corresponding C+ + code snippet attempted to replicate this setup but resulted in an infeasible solution.

Solution: Adjusting the C+ + Implementation

Key Changes Required

Variable Initialization: In the original C+ + code, the integer variables x1, x2, and x3 were initialized with an upper bound of IloInfinity, which may lead to unexpected behavior. Changing the declaration to set these variables' upper bounds directly in the initialization solves the issue:

[[See Video to Reveal this Text or Code Snippet]]

Modeling Constraints: The original code added an upper bound for x[i] using constraints after initializing the variables. While this can work, it is more straightforward and effective to enforce upper bounds (e.g., <= 6) within the variable initialization itself.

Revised C+ + Code Snippet

The corrected code, inclusive of changes, would look like this:

[[See Video to Reveal this Text or Code Snippet]]

Result Verification

After implementing these changes, the C+ + program should now successfully find a solution that aligns with the CPLEX output:

An objective value close to 2.429 and corresponding variable assignments for x1, x2, x3, y1, y2, y3.

Conclusion

Transitioning from CPLEX to a C+ + implementation using the CPLEX API can lead to challenges, notably when dealing with variable bounds and constraints. By carefully setting variable limits during initialization and leveraging the CPLEX API effectively, it is possible to replicate CPLEX results accurately. If you encounter persistent issues, consider reviewing variable declarations and constraints, or reach out to community forums or IBM support for specialized assistance.

Implementing these changes will not only help in resolving discrepancies but can also enhance your understanding of the optimization process within C+ + . Happy coding!