# An Exploratory Landscape Analysis-Based Benchmark Suite
## 2 Background
### Benchmark Functions  
There are many commonly used single-objective boundary-constrained benchmark functions that have been defined in the literature. [PERSON] and [PERSON] [7] provide a comprehensive overview of commonly used benchmark functions, and along with the Al-Roomi repository [9], the smoof R package [20], and the CIIib benchmark repository [21], these resources provide the benchmark function definitions that the majority of researchers use to test their algorithms. Although the basic benchmark functions are described in the literature, it is common for researchers to make use of benchmark suites, which contain a collection of these benchmark functions, to compare the performances of their algorithms. Both the GECCO and CEC conferences hold annual competitions in which such benchmark suites are defined.  
The CEC benchmark suites are composed of three problem types: standard functions, hybrid functions, and composition functions. The standard functions make use of the standard function definitions of benchmark functions as they are described in the literature (called basic functions by the CEC organizers). However, input vectors are first rotated and shifted by predefined matrices and vectors. The hybrid functions are linear combinations of basic functions, where the input vector is divided up and each sub-vector becomes an input to a separate basic function. The composition functions are a weighted linear combination of both the basic, standard, and hybrid functions. Each year the benchmark suite used in the CEC competition changes. Despite this, there is an overlap in the functions used across the different benchmark suites. Nevertheless, the predefined rotation matrices and shift vectors differ for each competition and therefore the properties of the benchmarks can differ, despite having the same function definition. The study focuses on the CEC benchmark functions defined for the 2013, 2014, 2015, and 2017 competitions [2; 3; 4; 5]. The CEC'13 functions are defined in 10, 30, and 50 dimensions. The CEC'14, CEC'15 and CEC'17 functions are defined in 10, 30, 50, and 100 dimensions. For all the CEC benchmark suites, the functions are defined within the hypercube \([-100,100]^{D}\), where \(D\) is the dimensionality of the decision variable space. That is, the search space has a range of \([-100,100]\) in each dimension.  
The GECCO conference holds the Black-box Optimization Benchmarking (BBOB) workshop, in which several benchmarking suites are provided for different problem types. This study focuses on the BBOB benchmark suite [6] which contains 24 noiseless single-objective, boundary-constrained optimization problems. The BBOB benchmark suite has remained the same since its inception in 2009. In the BBOB benchmark suite, the optimization functions are categorized into five categories:  
* Separable functions
* Functions with low or moderate conditioning
* Functions with high conditioning and unimodal
* Multi-modal functions with an adequate global structure
* Multi-modal functions with a weak global structure  
The BBOB functions are defined in 2, 3, 5, 10, 20, and 40 dimensions. Furthermore, the functions are defined within the hypercube \([-5,5]^{D}\), where \(D\) is the dimensionality of the decision variable space.