Looking for Feedback and Benchmark Comparisons on an NP-Complete Optimization Framework

[np-douce]

Hi everyone,

I wanted to start a discussion about the main idea behind this project and what I’m hoping to learn from sharing it publicly.

The framework is based on calculating properties of the full solution space of a combinatorial problem, including the exact number of states, exact average, and exact variance, without directly enumerating every state. The same framework is then carried across different NP-complete problems through polynomial reductions, which is how the different solvers in the app are connected.

When the problem is treated as a thermal system, these exact quantities are used in a Taylor expansion to approximate the partition function. That approximation gives a probabilistic way to study the solution space and guide the search as constraints are added.

I’m currently interested in:

• Comparing the algorithms against established benchmark solvers and datasets.
• Finding weaknesses, incorrect assumptions, or cases where the approach performs poorly.
• Adding more NP-complete problems through polynomial reductions.
• Comparing the framework with methods such as ant colony optimization, simulated annealing, and other probabilistic or combinatorial optimization techniques.
• Finding existing methods or research projects that may be closely related to this approach.

Critical feedback is very welcome. If you see something that looks wrong, already known, inefficient, or worth testing more carefully, I’d especially like to hear about it.