Abstract: We have further developed our Stage 1 result, which was a series of algorithms with increasing accuracy and increasing running time, based on the local search method and the ant colony metaheuristic. The result of Stage 2 is a single algorithm that works reliably both on short and on long time budgets, on smaller sub-matrices as well as on the original matrix. This was achieved by optimizing the data structures, by caching the most frequently used functions, and by adaptively increasing the parameters of the algorithm during the run. The final result on the original matrix is 77.19% accuracy in one hour (our result of Stage 1 - 77.14% in 20 hours) and 77.35% in 24 hours. On random row samples, the one-hour accuracy ranges approximately from 78.3% on 0.3-matrices to 77.4% on 0.7-matrices (and up to 83.7% on very small samples, i.e., 0.05-matrices).

Cite: Khandeev V. , Mikhailova L. , Neshchadim S. , Panasenko A.
Challenge 2: Column Clustering Problem. Local Search + Ant Colony Optimization: Stage 2
Mathematical Optimization Theory and Operations Research 2026 06-11 Jul 2026