Hexaly study: native time-slice encoding scales to 16 threads, beats external callbacks

A new experimental report by Florian Rascoussier, posted on arXiv (2608.10079), examines how thread scaling in the Hexaly Optimizer behaves for the Time-Dependent Vehicle Routing Problem with Time Windows (TDVRPTW). The study compares two Python model encodings: one that evaluates continuous travel-time functions through external callbacks, and another that approximates them using native time slices evaluated directly by the solver. Across 18 pages with 6 figures and 12 tables, the author measures independent CPU performance and finds that the external-function interface serializes evaluation to a single worker, no matter how many threads are requested. This bottleneck prevents any meaningful parallel speedup in the callback-based model.

In contrast, the native time-slice encoding makes full use of allocated cores. Across the benchmark panel, wider native searches produced better solutions both at the end of the run and throughout the search, while also substantially reducing variation between random seeds. Nearly every paired run improved when going from 1 to 16 threads, and the choice of encoding had an even larger impact than the thread count itself. The authors conclude that multi-threading is a practical way to boost solution quality and stability when the model can exploit it, but the modeling approach is central to any thread-scaling conclusion. For practitioners, the native approximation must be sufficiently fine and independently validated to be safe, but the payoff in parallelism is clear.