## 4 Methodology  
For this manuscript, we used Python 3.7 and a Dell Inc. PowerEdge R840 Rack Server with 16 Intel Xeon Gold 5122 CPUs @ 3.60 GHz, 125 GB RAM, and CentOS Linux release 7.6.1810-64 bit system for running our experiments. Moreover, we employed the framework CUSTOMPHyS v1.0 to test the proposed model with ease. This open-access framework can be found at [[https://github.com/jcrvz/customphys](https://github.com/jcrvz/customphys)]([https://github.com/jcrvz/customphys](https://github.com/jcrvz/customphys)), accessed on 10 May 2021, and it is documented in [31]. Thus, we needed to specify two domains at different levels of abstraction for testing and implementing the idea. Table 1 illustrates these domains, as well as their level of abstraction and role. The symbols and terminology from this table follow those from previous sections. Plus, each domain is detailed below. At the lowest level, we selected a total of 107 benchmark functions as continuous optimisation problem domains. We considered a different number of dimensions \(D\) such as 2, 5, 10, 20, 30, 40, and 50. Plus, we categorised these problems by using their qualitative characteristics such as differentiability and unimodality in four duads of binary-encoded features, i.e., DU. With this information, we followed three manners of grouping the functions for analysing the obtained results. First, we regarded the whole set of functions, i.e., without discriminating categories, for procuring an overview of the behaviour. Then, we studied the functions grouped by feature duads: DU equals 11 (Differentiable and Unimodal problems), 10, 01, and 00 (Non-differentiable and Multimodal problems). Third, we performed a similar procedure as before, but only considering a marginal grouping, i.e., differentiability or unimodality. For example, we got differentiable and not differentiable problems neglecting the unimodality feature; a similar case applies for marginalising unimodality. At the highest level, we utilised the population-based heuristics provided by CUSTOMPHyS and also included others based on single-agent operations. Both collections belong to the heuristic space and are employed from a metaheuristic point of view. Although, the former is specialised population-based operations over a continuous problem domain with a fixed dimensionality, say, Population-based Fixed-dimension (PF) heuristics. Otherwise, the latter set corresponds to the single-agent operations, sometimes called actions, applied over a domain with variable dimensionality, say, Single-agent Variable-dimension (SV) heuristics. In this work, this particular domain is discrete, and the dimensionality is aliased to cardinality. These two sets of operators are closely related to the MCOP that we  
Figure 2: Graphical representation of a metaheuristic and how it becomes an unfolded metaheuristic (or a heterogeneous heuristic sequence) passing through a homogeneous heuristic sequence, which is obtained by considering an additional degree of freedom (the iteration axis) when observing the standard model. solved. Table 2 summarises the simple heuristics collected for this work, and further details are provided in Appendix A. We divided them into three groups: SV perturbation, PF perturbation, and selection heuristics as aforementioned. The SV perturbators were designed conforming several works reported in the literature [32,33]. They were extracted from ten well-known metaheuristics: Random Search [34], Simulated Annealing [35], Genetic Algorithm [36], Cuckoo Search [37], Differential Evolution [38], Particle Swarm Optimisation [39], Firefly Algorithm [40], Stochastic Spiral Optimisaiton Algorithm [41], Central Force Optimisation [42], and Gravitational Search Algorithm [43]. We also included the random sample because it is the most straightforward manner of performing a search in an arbitrary domain. This simple heuristic also serves as the initialiser in all the implemented heuristic sequences.