How to Efficiently Pick an Element from a Matrix in Python Using OR-Tools скачать в хорошем качестве

How to Efficiently Pick an Element from a Matrix in Python Using OR-Tools

Explore how to leverage the `AddElement` constraint in `OR-Tools` to select elements from a matrix based on decision variables in Python. Learn step-by-step what's needed to achieve this and resolve common issues. --- This video is based on the question https://stackoverflow.com/q/68706893/ asked by the user 'Bhartendu Awasthi' ( https://stackoverflow.com/u/12236429/ ) and on the answer https://stackoverflow.com/a/68709435/ provided by the user 'Laurent Perron' ( https://stackoverflow.com/u/9971759/ ) 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 to pick an element from matrix (list of list in python) based on decision variables (one for row, and one for column) | OR-Tools, Python Also, Content (except music) licensed under CC BY-SA https://meta.stackexchange.com/help/l... The original Question post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/... ) license, and the original Answer post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/... ) license. If anything seems off to you, please feel free to write me at vlogize [AT] gmail [DOT] com. --- How to Efficiently Pick an Element from a Matrix in Python Using OR-Tools Choosing elements from a matrix in programming can often pose a challenge, especially when utilizing constraint programming libraries like Google's OR-Tools. In this guide, we will break down how to select elements from a matrix (in this case, a list of lists in Python) based on decision variables. We’ll particularly focus on resolving a common error encountered by beginners when using the AddElement function within the CP-SAT (Constraint Programming for Satisfiability) model. The Problem: Selecting Elements Based on Decision Variables You’re working with a setup where there are multiple positions, and for each of these positions, you need to select moves from two different types—let's denote them as move_A and move_B. The objective is to maximize the value derived from the combination of these two moves at each position, using the decision variables for row and column selections. The confusion often arises when attempting to utilize the AddElement function to pick the right value based on these decision variables. Here's a simplified outline of your problem: Positions: 8 Moves of Type A: Rows Moves of Type B: Columns Objective: Maximize results from combinations of moves at positions using a matrix of values. The Approach to Solve the Problem Understanding the Matrix Structure We begin with a matrix representing the value combinations from different moves of type A and type B, for example: [[See Video to Reveal this Text or Code Snippet]] The Typical Error with AddElement When using the AddElement function in your model, you might encounter an error like the following: [[See Video to Reveal this Text or Code Snippet]] Why Does This Happen? The AddElement function is designed to work with 1D arrays. When attempting to access a 2D structure (like your value matrix) using decision variables, you encounter a type mismatch. This is a common pain point for those transitioning from different programming environments, like MiniZinc where the syntax may handle things more straightforwardly. The Solution: Leveraging Intermediate Variables The key to resolving this issue lies in creating intermediate variables. Instead of directly accessing the 2D array, you can flatten your matrix and use a single index variable to access elements. Here’s how to do it step by step: Flatten the Matrix: Create a linear representation (1D) of your matrix by combining row and column indices. Define Index Calculation: Use the formula p == index1 * max(index2) + index2: Here, index1 is the decision variable for rows (move_A). index2 is the decision variable for columns (move_B). max(index2) is the total number of columns. Use AddElement with 1D Access: Now, you can call AddElement with your flattened structure. [[See Video to Reveal this Text or Code Snippet]] Final Considerations and Best Practices Refer to Documentation: Always check the official OR-Tools documentation for updates and best practices. Test Incrementally: Validate each stage of your model incrementally to identify potential issues swiftly. Seek Community Help: Don’t hesitate to turn to online forums and communities for support when you get stuck. Conclusion For those beginning their journey into constraint programming with OR-Tools, making sense of how to access elements within a matrix using decision variables is crucial. By flattening your data and using intermediate variables for indexing, you can overcome common pitfalls and enhance your problem-solving capabilities.