Watch an Edge COIN model learn directed transitions between chessboard squares. The experiment runs in a verified NumPy/Numba engine and reports compact progress without sending entire populations to your browser.
Knight’s Tour has constructive, heuristic, backtracking, evolutionary, neural, and ant-colony solutions. Their reported times are not directly interchangeable: some construct one tour using chess-specific knowledge, while others learn from candidate populations or enumerate diverse tours.
Warnsdorff chooses the legal continuation with the smallest onward degree. Parberry later presented an O(n²) divide-and-conquer construction for closed tours. These approaches are exceptionally fast, but they answer a different question: they embed Knight’s Tour structure rather than asking a reusable permutation learner to discover it.
Parberry, 1997 ↗Gordon and Slocum evaluated 1,000,000 repaired strings over 20,000 generations per run. Their GA found tours in 94% of runs and averaged 89 distinct tours. Repair was essential: without it, the reported GA found no complete tour. COIN differs materially because it uses neither repair nor local search.
Gordon & Slocum, 2004 ↗Hingston and Kendall reported an average 488,245 unique tours, including 9,192 closed tours, from 100,000 cycles of 64 ants. This is a strong solution-bank baseline. However, each ant is constrained to legal, unvisited destinations, whereas COIN samples a complete permutation first and receives legality only through fitness.
Hingston & Kendall, 2004 ↗Takefuji and Lee formulated a parallel neural network for closed tours. It is historically important, but its neural dynamics, hardware assumptions, and stopping measurements are not equivalent to population evaluations in COIN; wall-clock claims should therefore not be compared without a common implementation.
Takefuji & Lee, 1992 ↗In our tested configuration (population 400), COIN achieved a 100% observed success rate, with the first complete tour always appearing before generation 300 and the earliest observed at generation 102—approximately 40,800 to fewer than 120,000 candidate evaluations. Runs also discovered closed tours, and continuing to 1,000 generations contributed multiple distinct records to the persistent solution bank.
Scope note: these are observed results from our current runs, not a claim that COIN is the universally fastest Knight’s Tour algorithm. A definitive comparison requires the same hardware, seeds, stopping rule, open/closed definition, and evaluation budget.
Every stored solution can leave the laboratory and become motion, light, colour, camera work, and sound. COIN Art reads the persistent solution bank and stages each Knight’s Tour as a continuous three-dimensional performance; the algorithm’s output is no longer only a score, but material for computational art.