1. Context and Objectives of the Project

The optimization module of the SOGAE project was developed to automate the generation of efficient structural solutions in the construction of slabs, both concrete and porcelain. The main motivation was to replace manual or CAD-assisted design with an automated process that, while respecting structural and regulatory constraints, minimizes the total cost of forging.

Specific objectives:

• Automatically generate the distribution of joists and blocks on architectural plans.
• Comply with all installation and structural strength regulations.
• Minimize the overall cost of the forging project.
• Ensure viable, traceable and reproducible solutions in real industrial environments.

2. Technical Problem Addressed

It was a matter of solving a complex problem of entire optimization: given an architectural plan and certain structural metadata (load areas, obstacles, type of opening, etc.), finding the optimal distribution of joists and blocks that cover each area without overlaps or violation of restrictions, while also respecting criteria of constructability and economy.

This problem has multiple discrete variables and combinatorial constraints, which places it within the class of NP-complete problems, with a high computational load.

3. Developed Technical Solution

3.1. Problem Modeling

• It was formulated as an integer optimization problem (Integer Programming), using discrete variables to represent position, type and orientation of each component.
• Multiple geometric, structural and constructive constraints were incorporated depending on the type of slab.

3.2. Algorithmic Resolution

• The solver was selected CP-SAT from Google OrTools, for its competitive performance against commercial tools.
• Due to the complexity of the entire problem, a decomposition strategy, solving each gap separately through sub-problems and reconstructing a global solution.

3.3. Heuristic Techniques

• Heuristics were applied based on previous information (e.g. prioritizing gaps with obstacles or critical loads).
• An evolutionary strategy based on genetic algorithms to determine the most favorable resolution order between the spans.
• We studied the use of Bayesian optimization (BOHB) to minimize costly evaluations.

4. Built-in Technical and Operational Restrictions

More than 30 specific constraints were modeled, including:

• No overlapping of elements (blocks, joists, obstacles).
• Point and linear load conditions.
• Support restrictions on shared walls.
• Differential treatment depending on the type of slab (concrete/porexpan).
• Preference for solutions with standard blocks over cutouts or adjustments.
• Geometric considerations of orientation, rest and extension of joists.

5. Optimality Criteria

The objective function prioritized:

• Minimization of the total cost, considering joist lengths and block types.
• Minimizing the number of penalizing conditions, such as the use of custom blocks, unwanted starts or additional cuts.
• Maintaining structural viability and regulatory compliance.

6. Results and Conclusions

• A system capable of automatically generating detailed structural plans with a breakdown of materials and costs was achieved.
• Partial vain resolution made it possible to transform a globally intractable problem into a computationally viable one.
• A significant improvement in design efficiency and a reduction in human errors were achieved.
• The system is extensible to future types of slabs, adaptable to regulatory variations and scalable in new projects.

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