Optimizing Dataframe Rows with PuLP and SciPy: A Guide to Linear Optimization

Discover how to effectively select rows in a dataframe using `PuLP` for linear optimization and alternative strategies with `SciPy` for complex problems.
---
This video is based on the question stackoverflow.com/q/71321221/ asked by the user 'user18352664' ( stackoverflow.com/u/18352664/ ) and on the answer stackoverflow.com/a/71360206/ provided by the user 'joni' ( stackoverflow.com/u/4745529/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

Visit these links for original content and any more details, such as alternate solutions, latest updates/developments on topic, comments, revision history etc. For example, the original title of the Question was: How do I select dataframe rows using PuLP for linear optimisation

Also, Content (except music) licensed under CC BY-SA meta.stackexchange.com/help/licensing
The original Question post is licensed under the 'CC BY-SA 4.0' ( creativecommons.org/licenses/by-sa/4.0/ ) license, and the original Answer post is licensed under the 'CC BY-SA 4.0' ( creativecommons.org/licenses/by-sa/4.0/ ) license.

If anything seems off to you, please feel free to write me at vlogize [AT] gmail [DOT] com.
---
Optimizing Dataframe Rows with PuLP and SciPy: A Guide to Linear Optimization

In the world of data science and optimization, finding the best parameters to maximize or minimize certain results is crucial. A common task is selecting rows from a pandas DataFrame based on specific constraints—in this case, using the PuLP library for linear optimization. Let’s dive into a specific problem where we aim to maximize a result using values a and b, based on constraints set on our DataFrame.

Introduction to the Problem

Consider you have a DataFrame df with columns x, y, and result. Your goal is to find values for a and b that will maximize the average of the result column, given certain conditions on x and y. Specifically, the conditions are:

Select rows where df['x'] >= a and df['y'] <= b

The bounds for a are 2.5 <= a <= 20

The bounds for b are 0.05 <= b <= 0.35

The difficulty arises from the fact that the objective function, defined as the mean of the result values for the selected rows, cannot be expressed directly as a linear programming problem due to the nature of the operation involving np.mean(). Let’s break down how to solve this effectively.

Step-by-Step Solution

1. Understanding Your Data

First, let’s take a look at a sample DataFrame:

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

2. Setting Up the Optimization Problem with PuLP

You might want to start with setting up the problem using PuLP. Here’s how you originally approached it:

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

Note: The issue arises here because the approach with lpSum and slicing the DataFrame is not valid in the context of linear programming with PuLP since you're trying to use the actual data rather than just expressions involving LpVariable.

3. Reformulate the Problem

Since the objective function isn't linear or expressible with LpVariable, we need a different approach. Two alternatives are available: reformulate using a mixed-integer program or leverage black-box optimization techniques.

a. Solution Using SciPy's dual_annealing

The second option involves using the dual_annealing method from SciPy to perform a global optimization over the defined space:

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

4. Analyzing the Results

The above code successfully finds optimal values for a and b, resulting in a summary output indicating the best selections found. Run this script, and you should end up with findings like a=6.55, b=0.13, leading to an optimal objective value for your intended process.

Conclusion

Optimization in data-centric tasks can often be complicated. We discovered that using libraries like PuLP is invaluable for linear programming but requires that the conditions must align with the library's capabilities. For more complex problems, tools like SciPy can provide powerful alternatives for non-linear optimizations.

Empowering yourself with these tools will enhance your ability to extract meaningful insights from your DataFrames efficiently. Happy optimizing!