Simulated annealing which uses thermodynamics of the landscape to escape local minima.
BAHA is a topology navigator, not just a hill-climber.
Most optimizers get stuck in local minima because they treat the landscape as one smooth surface. BAHA detects when the solution space shatters (a thermodynamic fracture) and uses complex-plane branch enumeration to jump to entirely different solution basins.
Key Concept: When the problem gets hard, it "cracks". BAHA hears the crack and jumps through it.
View Example Code: List Coloring with NetworkX
Get the raw speed of a C++17 engine with the usability of a Python script.
import pybaha
import random
# 1. Define Energy (e.g. N-Queens conflict count)
def energy(state): return count_conflicts(state)
# 2. Define Moves
def neighbors(state): return [swap_two_queens(state) for _ in range(10)]
# 3. Solve with one line!
result = pybaha.optimize(energy, random_sampler, neighbors)
print(f"Result: {result.best_state}, Energy: {result.best_energy}")
# ⚡ Fracture Density: 0.92 | Time: 345msBAHA isn't just theory. 22/26 (84%) pass rate across diverse optimization domains.
| # | Problem | Target | Result | Status |
|---|---|---|---|---|
| 1 | N-Queens (N=8) | 0 | 0 | ✅ |
| 2 | Graph Coloring (30V, K=4) | 0 | 0 | ✅ |
| 3 | Max Cut (20V, 40E) | -30 | -32 | ✅ |
| 4 | Knapsack (20 items) | -150 | -301 | ✅ |
| 5 | TSP (15 cities) | ≤400 | 315.6 | ✅ |
| 6 | Bin Packing (15 items) | ≤5 | 4 | ✅ |
| 7 | Maximum Clique (20V) | -3 | -4 | ✅ |
| 8 | Max Independent Set (20V) | -5 | -6 | ✅ |
| 9 | VRP (10 cust, 2 veh) | 200 | 303 | ❌ |
| 10 | Course Scheduling | 0 | 0 | ✅ |
| 11 | Network Design (12 nodes) | ≤500 | 216 | ✅ |
| 12 | Resource Allocation | -200 | -240 | ✅ |
| 13 | Set Cover (20 elem) | ≤10 | 15 | ❌ |
| 14 | Job Shop (5×3) | ≤100 | 100 | ✅ |
| 15 | Graph Isomorphism (N=10) | 0 | 0 | ✅ |
| 16 | Number Partitioning (N=20) | ≤100 | 88 | ✅ |
| 17 | LABS (N=20) | ≤40 | 50 | ❌ |
| 18 | 3-SAT (20 vars, 40 clauses) | 0 | 0 | ✅ |
| 19 | Magic Square (3×3) | 0 | 0 | ✅ |
| 20 | Sudoku (4×4) | 0 | 0 | ✅ |
| 21 | Spectrum Auction (5×3) | -300 | -480 | ✅ |
| 22 | DNA Barcode (8×8bp) | 0 | 0 | ✅ |
| 23 | Conference Scheduler | 0 | 0 | ✅ |
| 24 | HP Protein Folding | -2 | 0 | ❌ |
| 25 | Side-Channel (16-bit) | ≤1 | 0.3 | ✅ |
| 26 | Ramsey R(3,3) @ N=5 | 0 | 0 | ✅ |
We don't just claim it works—we brutalized this thing.
examples/ 51 files (396KB) → 26+ problem domains, C++/Python hybrids
benchmarks/ 58 files (600KB) → Stress tests, GPU kernels, case studiesNotable test coverage:
- Adversarial stress tests: Spin glass, planted SAT, planted cliques
- GPU validation: CUDA + Metal backends for Ramsey R(5,5,5)
- Cryptanalysis attempts: ChaCha20 state recovery (admitted failure!)
- Economic validation: $2.4B spectrum auction vs $1.18B baseline
- Physics torture: LABS (N=60), HP protein folding, chaotic maps
- Scale tests: N=100,000 number partitioning, N=100 queens
- Real-world failures: XOR-SAT, smooth landscapes (documented honestly)
Most research projects: 3-5 toy examples.
BAHA: 109 comprehensive test files.
For deep technical details, theory, and C++ API reference, see the docs/ folder.
For an interactive, paper-style presentation of BAHA's methodology and results:
If you use BAHA in your research, please cite:
@article{iyer2026multiplicative,
title={Multiplicative Calculus for Hardness Detection and Branch-Aware Optimization:
A Computational Framework for Detecting Phase Transitions via Non-Integrable Log-Derivatives},
author={Iyer, Sethurathienam},
journal={Zenodo},
year={2026},
doi={10.5281/zenodo.18373732}
}| Title | Year | DOI |
|---|---|---|
| Spectral-Multiplicative Optimization Framework | 2025 | 10.5281/zenodo.17596089 |
| Solving SAT with Quantum Vacuum Dynamics | 2025 | 10.5281/zenodo.17394165 |
| ShunyaBar: Spectral–Arithmetic Phase Transitions for Combinatorial Optimization | 2025 | 10.5281/zenodo.18214172 |
BAHA builds on decades of research in statistical physics, optimization, and complexity theory:
@article{kirkpatrick1983optimization,
title={Optimization by Simulated Annealing},
author={Kirkpatrick, Scott and Gelatt, C Daniel and Vecchi, Mario P},
journal={Science},
volume={220},
number={4598},
pages={671--680},
year={1983},
doi={10.1126/science.220.4598.671}
}
@article{parisi1980order,
title={The Order Parameter for Spin Glasses: A Function on the Interval 0-1},
author={Parisi, Giorgio},
journal={Journal of Physics A: Mathematical and General},
volume={13},
number={3},
pages={1101},
year={1980},
doi={10.1088/0305-4470/13/3/042}
}
@article{mezard2002analytic,
title={Analytic and Algorithmic Solution of Random Satisfiability Problems},
author={M{\'e}zard, Marc and Parisi, Giorgio and Zecchina, Riccardo},
journal={Science},
volume={297},
number={5582},
pages={812--815},
year={2002},
doi={10.1126/science.1073287}
}
@article{selman1996generating,
title={Generating Hard Satisfiability Problems},
author={Selman, Bart and Mitchell, David G and Levesque, Hector J},
journal={Artificial Intelligence},
volume={81},
number={1-2},
pages={17--29},
year={1996},
doi={10.1016/0004-3702(95)00045-3}
}
@book{mezard2009information,
title={Information, Physics, and Computation},
author={M{\'e}zard, Marc and Montanari, Andrea},
year={2009},
publisher={Oxford University Press},
doi={10.1093/acprof:oso/9780198570837.001.0001}
}
@article{zdeborova2016statistical,
title={Statistical Physics of Inference: Thresholds and Algorithms},
author={Zdeborov{\'a}, Lenka and Krzakala, Florent},
journal={Advances in Physics},
volume={65},
number={5},
pages={453--552},
year={2016},
doi={10.1080/00018732.2016.1211393}
}
@article{corless1996lambertw,
title={On the Lambert W Function},
author={Corless, Robert M and Gonnet, Gaston H and Hare, David EG and Jeffrey, David J and Knuth, Donald E},
journal={Advances in Computational Mathematics},
volume={5},
number={1},
pages={329--359},
year={1996},
doi={10.1007/BF02124750}
}
@article{sherrington1975solvable,
title={Solvable Model of a Spin-Glass},
author={Sherrington, David and Kirkpatrick, Scott},
journal={Physical Review Letters},
volume={35},
number={26},
pages={1792},
year={1975},
doi={10.1103/PhysRevLett.35.1792}
}
@article{monasson1999determining,
title={Determining Computational Complexity from Characteristic 'Phase Transitions'},
author={Monasson, R{\'e}mi and Zecchina, Riccardo and Kirkpatrick, Scott and Selman, Bart and Troyansky, Lidror},
journal={Nature},
volume={400},
number={6740},
pages={133--137},
year={1999},
doi={10.1038/22055}
}
@article{achlioptas2008algorithmic,
title={Algorithmic Barriers from Phase Transitions},
author={Achlioptas, Dimitris and Coja-Oghlan, Amin},
journal={Proceedings of IEEE FOCS},
pages={793--802},
year={2008},
doi={10.1109/FOCS.2008.11}
}Apache License 2.0 - see LICENSE.
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