## 3 Literature Review and Related Work
### Metaheuristics and Parameter Tuning
Moreover, this also implies that parameter tuning is not a one-time task, meaning that researchers and users need to address the parameter tuning problem again and again when facing new problems [3]. Given this, several approaches have been proposed to solve the metaheuristics parameter tuning problem. In the literature, one can find approaches that attempt to findthe best parameters for a given configuration issue [20; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37]. All these techniques aim to find a parameter definition to optimize an objective function that covers all instances of a problem. If the instances are homogeneous, that approach behaves well. However, if the instances have a heterogeneous distribution or even unrelated application areas, then the best parameter settings can vary from instance to instance. There are two different approaches to the parameter tuning of metaheuristics [15]: offline and online (Figure 1). In the offline parameter tuning, the values of various parameters are defined before the execution of the metaheuristic. On the other hand, in online approaches, parameters are controlled and updated dynamically or adaptively during the execution of the technique. These approaches are also known by parameter tuning and control, respectively [21; 38; 39; 40; 41; 42]. The purpose of offline parameter tuning is to obtain parameter values that may be useful for the resolution of a large number of instances, which requires several experimental evaluations [39]. Usually, metaheuristics are tuned one parameter at a time, and their best values are empirically determined. Thus, the interaction between the parameters is generally not studied. To overcome this problem, Design of Experiments (DOE) is often used [43; 44; 45]. Before being able to use a DOE approach, it is necessary to take into account the factors representing the variations of parameters and the levels representing different values for the parameters (which may be quantitative or qualitative), which means that it is a very time-consuming task [21]. [PERSON] [46] discussed different aspects of the DOE specification and analysis with stochastic optimization algorithms. The great disadvantage of using a DOE approach is the high computational cost when there are a large number of parameters and where the domains of the respective values are high, since a large number of experiments are need [47]. In offline parameter tuning, a meta-optimization approach can be done by any (meta)heuristic, resulting in a meta-metaheuristic [15]. Meta-optimization consists of two levels [15]: the meta-level and the base level. In the meta-level, solutions represent the parameters to optimize, such as the size of the tabu list in Tabu search, the cooling rate in simulated annealing and the crossover and mutation rates of genetic algorithms. At this level, the objective function of a solution corresponds to the best solution found (or another performance indicator) for metaheuristics with the specified parameters. Thus, each solution at the meta-level corresponds to an independent metaheuristic at the base level. Meta-optimization is largely used in evolutionary computation [48]. In problems with heterogeneous distributions, the best parameter settings can vary from instance to instance. [PERSON] et al. [20] demonstrated that machine learning models  
Figure 1: Metaheuristic parameter tuning strategies (adapted from [15]). can make amazingly accurate predictions of runtime distributions of random and incomplete research methods such as metaheuristics, and how these models can be used to automatically adjust the parameters for each instance of a problem in order to optimize the performance, without requiring human intervention. A review on learning approaches for parameter tuning is presented in the next subsection. Some authors argue that leaving the parameters' values fixed during the execution of an algorithm seems to be inappropriate [21].