Comparing Open-Source and Commercial Solvers in Mathematical Optimization

Understanding the Strengths and Limitations of Different Options

If we overlook OpenAI’s ChatGPT 4’s current edge over open-source alternatives (at least as of this writing), many data science professionals rely on open-source packages like TensorFlow and PyTorch for their needs. These tools are not only powerful but also widely accessible. This naturally leads to a question for those with a background in data science: For solving mathematical optimization models, should one lean towards commercial solvers, or are open-source alternatives just as viable?

To address this, let's explore the key differences between open-source and commercial solvers, focusing on Mixed Integer Programming – a widely used technology in mathematical optimization. The insights shared here, while informed by my personal experiences, predominantly summarize the collective wisdom of experts, as discussed in this OR Stack Exchange thread.

Commercial Solvers: Strengths and Advantages

Commercial solvers are known for their robust algorithms, which have been continuously refined over the years. Their ability to efficiently utilize a model's structure is a key strength. This manifests in several areas:

1. Performance

The speed at which solvers address problems varies. Sometimes, the difference is marginal – a matter of a minute or two. Other times, it's more pronounced – perhaps a few seconds versus half an hour. Commercial solvers often lead in terms of speed.

2. Ability To Solve

It’s not solely about speed. There's the crucial question of whether your model can be solved at all. Open-source solvers may struggle with certain problem types that commercial solvers handle easily. The Mittelmann benchmarks provide a comparative analysis of various solvers’ performances.

3. Ease of Use and Functionality

Commercial solvers typically offer more features and advanced functionalities like support for various platforms, APIs, and cloud computing, which might not be available with open-source options.

4. Reliable Support

Thanks to dedicated full-time developers and a vast customer base, commercial vendors often provide faster and more comprehensive support.

Open-Source Solvers: When Are They Suitable?

Open-source solvers are a viable choice for straightforward problems that do not require the advanced functionalities of commercial solvers. They are free and can be quite effective for specific scenarios. Note that the sheer size of a model, defined by the number of variables and constraints, doesn't automatically imply that it's beyond the capabilities of open-source solvers. A model with millions of variables or constraints might be solved in a reasonable amount of time, whereas a smaller model with only hundreds of variables and a few constraints could prove more challenging.

Additionally, for those embarking on their mathematical optimization journey with limited resources, especially outside of academia, open-source solvers offer a valuable starting point. Using these tools to showcase the impact of mathematical optimization can create a compelling story, even if the speed is less than ideal. Successfully solving problems with open-source tools can provide persuasive narratives, increasing the chances of gaining buy-in from senior leadership for further investment in mathematical optimization. For a guide on when to choose mathematical optimization over heuristics, be sure to check out this blog.

Takeaway

The choice between commercial and open-source solvers depends on your specific needs. For simple, well-defined problems, open-source solvers are sufficient and cost-effective. However, for more complex problems, commercial solvers often provide superior performance, broader functionality, and more reliable support.

However, if you find an open-source solver struggling with a problem, avoid jumping to the conclusion that the problem is unsolvable. Before turning to alternative solutions such as heuristics, consider exploring commercial solvers. Many vendors offer free evaluation licenses, allowing a risk-free initial assessment. Combining both personal and expert insights ensures selecting the most effective option for your optimization problems.