Parameter tuning is a challenging and time-consuming task, crucial to obtaining improved metaheuristic performance. There is growing interest in cross-domain search methods, which consider a range of optimisation problems rather than being specialised for a single domain. Metaheuristics and hyper-heuristics are typically used as high-level cross-domain search methods, utilising problem-specific low-level heuristics for each problem domain to modify a solution. Such methods have a number of parameters to control their behaviour, whose initial settings can influence their search behaviour significantly. Previous methods in the literature either fix these parameters based on previous experience, or set them specifically for particular problem instances. There is a lack of extensive research investigating the tuning of these parameters systematically. In this paper, F-Race is deployed as an automated cross-domain parameter tuning approach. The parameters of a steady-state memetic algorithm and the low-level heuristics used by this algorithm are tuned across nine single-objective problem domains, using different training strategies and budgets to investigate whether F-Race is capable of effectively tuning parameters for cross-domain search. The empirical results show that the proposed methods manage to find good parameter settings, outperforming many methods from the literature, with different configurations identified as the best depending upon the training approach used.

Selection hyper-heuristics have emerged as high level general-purpose search methodologies that mix and control a set of low-level (meta)heuristics. Previous empirical studies over a range of single objective optimisation problems have shown that the number and type of low-level (meta)heuristics used are influential to the performance of selection hyper-heuristics. In addition, move acceptance strategies play an important role and can significantly affect the overall performance of a hyper-heuristic. In this paper, we introduce an adapted variant of an existing learning automata based multiobjective hyper-heuristic from the literature. We investigate the performance and generality level of the proposed method, and another learning automata based selection hyper-heuristic, operating over a search space of multiobjective evolutionary algorithms (MOEAs) across two well-known multiobjective optimisation benchmarks. The experimental results demonstrate that, regardless of the number and type of low-level metaheuristics available, the learning automata based hyper-heuristics outperform each constituent MOEA individually, and an online learning and random choice selection hyper-heuristic from the literature. This performance and generality is shown to be consistent across a number of different move acceptance strategies.