Selection hyper-heuristics and job shop scheduling problems: How does instance size influence performance?

Selection hyper-heuristics are novel tools that combine low-level heuristics into robust solvers commonly used for tackling combinatorial optimization problems. However, the training cost is a drawback that hinders their applicability. In this work, we analyze the effect of training with different problem sizes to determine whether an effective simplification can be made. We select Job Shop Scheduling problems as an illustrative scenario to analyze and propose two hyper-heuristic approaches, based on Simulated Annealing (SA) and Unified Particle Swarm Optimization (UPSO), which use a defined set of simple priority dispatching rules as heuristics. Preliminary results suggest a relationship between instance size and hyper-heuristic performance. We conduct experiments training on two different instance sizes to understand such a relationship better. Our data show that hyper-heuristics trained in small-sized instances perform similarly to those trained in larger ones. However, the extent of such an effect changes depending on the approach followed. This effect was more substantial for the model powered by SA, and the resulting behavior for small and large-sized instances was very similar. Conversely, for the model powered by UPSO, data were more outspread. Even so, the phenomenon was noticeable as the median performance was similar between small and large-sized instances. In fact, through UPSO, we achieved hyper-heuristics that performed better on the training set. However, using small-sized instances seems to overspecialize, which results in spread-out testing performance. Hyper-heuristics resulting from training with small-sized instances can outperform a synthetic Oracle on large-sized testing instances in about 50% of the runs for SA and 25% for UPSO. This allows for significant time savings during the training procedure, thus representing a worthy approach.