## 4 Methodology
To alleviate the influence of dimensionality and problem characteristics, we plan to loosen the constraints imposed on the cardinality and steps, and include other relevant parameters, such as the population size. In the same way, we believe that improving the hyper-heuristic algorithm (i.e., SAHH) must increase the overall performance of the resulting uMHs. An alternative and faster approach requires considering a non-heuristic-based algorithm such as a Machine Learning methodology. Plus, we are going to consider additional benchmark problems, including those utilised in algorithm competitions, e.g., CEC and GECCO. Lastly, we plan to implement this approach in a practical engineering scenario to test its feasibility to achieve low-budget heuristic sequences. We considered it a relevant topic for future works. Conceptualisation, J.M.C.-D., I.A., J.C.O.-B., and N.P. ; methodology and software, J.M.C.-D., I.A., J.C.O.-B., and N.P. ; validation, J.M.C.-D., I.A., J.C.O.-B., and N.P. ; formal analysis and investigation, J.M.C.-D., I.A., J.C.O.-B., and N.P. ; resources, J.M.C.-D., I.A., J.C.O.-B., and N.P. ; data curation, J.M.C.-D., I.A., J.C.O.-B., and N.P. ; writing-original draft preparation, J.M.C.-D., I.A., J.C.O.-B., and N.P. ; writing-review and editing, J.M.C.-D., I.A., J.C.O.-B., and N.P. ; visualisation, J.M.C.-D., I.A., J.C.O.-B., and N.P. ; supervision, J.M.C.-D., I.A., J.C.O.-B., and N.P. ; project administration, J.M.C.-D., I.A., J.C.O.-B., and N.P. ; funding acquisition, I.A. All authors have read and agreed to the published version of the manuscript. The research was supported by the CONACyT Basic Science Project with grant number 287479. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. ## Abbreviations

The following abbreviations are used in this manuscript: \begin{tabular}{l l} CF & Central Force \\ CFO & Central Force Optimisation \\ CS & Cuckoo Search \\ DC & Differential Crossover \\ DE & Differential Evolution \\ DM & Differential Mutation \\ FA & Firefly Algorithm \\ FD & Firefly Dynamic \\ GA & Genetic Algorithm \\ GC & Genetic Crossover \\ GM & Genetic Mutation \\ GS & Gravitational Search \\ GSA & Gravitational Search Algorithm \\ HH & Hyper-Heuristic \\ NFL & No-Free-Lunch \\ MCOP & Metaheuristic Composition Optimisaiton Problem \\ MH & Metaheuristic \\ PS & Particle Swarm Dynamic \\ PSO & Particle Swarm Optimisation \\ RF & Random Flight \\ RS & Random Search \\ RW & Local Random Walk \\ RX & Random Sample \\ SA & Simulated Annealing \\ SAHH & Hyper-Heuristic based on Simulated Annealing \\ SD & Spiral Dynamic \\ SH & Simple Heuristic \\ SO & Search Operator \\ SSO & Stochastic Spiral Optimisation Algorithm \\ uMH & Unfolded Metaheuristic \\ \end{tabular} 

## Appendix A Simple Heuristics

In this section, we detail the simple heuristics extracted from the following 10 well-known MHs: Random Search (RS) [48], Simulated Annealing (SA) [3], Genetic Algorithm (GA) [49], Cuckoo Search (CS) [50], Differential Evolution (DE) [38], Particle Swarm Optimisation (PSO) [39, 51], Firefly Algorithm (FA) [52], Stochastic Spiral Optimisation Algorithm (SSOA) [41], Central Force Optimisation (CFO) [53], and Gravitational Search Algorithm (GSA) [43]. These heuristics are presented and organised using the same nomenclature and terminology of Section 2. Furthermore, they also correspond to those listed in Table 2.

### Initialisers

This simple heuristics are pretty simple in their implementation because they are in charge of drawing the initial solution(s) for a subsequent searching process. In many practical implementations, the initialisers are just random samplers using a well-defined feasible domain. In others words, this work is performed by a practitioner with certain degree of expertise on the problem under solution.