# Initialisation Approaches for Population-Based Metaheuristic Algorithms: A Comprehensive Review
## 3 Major Initialisation Methods
### Chaos Theory  
Chaos theory describes the unpredictability of systems, and over the years, many advances have been made in this area. Chaotic sequences follow these properties: sensitive to initial conditions, ergodicity, and randomicity. This type of sequence has the advantages of introducing chaos or unpredictability into the optimisation, increasing the range of chaotic motion, and using these chaotic induced variables to search the space effectively [69].  
Using the logistic chaotic function, ref. [70] proposed novel improvements on the CS, and one of these improvements is the use of the logistic chaotic function to initialise the population. While their results are promising, they suffer from high computational complexity. The same scheme was used in the work of [71] to improve BA, where the bat population was initialised using chaotic sequences, instead of the random number generator. In addition, the bacterial population of BFO was initialised using chaotic sequences that were generated using logistic mapping [72]. Similarly, the butterflies in the work of [73] were initialised using the homogenous chaotic sequence which were adapted  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Reference** & **Year** & \multicolumn{2}{c}{**Initialisation Scheme**} & **Optimisation Problem** \\ \hline
[51] & 2014 & PSO & Image segmentation \\ \hline
[53] & 2015 & GRASP & Far from most string problem (FFMSP) \\ \hline
[55] & 2020 & Competitive swarm optimizer (CSO) & Train single hidden layer feed forward \\  & & Networks (SLFN) \\ \hline
[56] & 2019 & K-Means clustering algorithm & Band selection of hyperspectral images \\ \hline
[60] & 2018 & Firefly algorithm & Greyscale image segmentation \\ \hline
[52] & 2013 & PSO & Mahalanobis distance and post-segmentationCorrection \\ \hline
[46] & 2014 & ABC & Geo-demographic analysis \\ \hline
[62] & 2017 & Firefly algorithm & Wavelet neural networks (WNNs) \\ \hline
[49] & 2019 & Metaheuristic algorithm & Dynamic Data Streams \\ \hline
[63] & 2017 & Hyper-heuristic & Benchmark test functions \\ \hline
[64] & 2020 & Hybrid of fuzzy metaheuristics (e.g., FATPSO) and the base TsC algorithms & Different areas \\ \hline
[65] & 2015 & Heuristic initialization strategies & Dynamic flexible job shop scheduling problems \\ \hline
[66] & 2014 & Opposition-based learning & Benchmark test function \\ \hline
[42] & 2015 & VNS & Task Scheduling \\ \hline
[48] & 2015 & Opposition-based learning & Benchmark function \\ \hline
[43] & 2018 & Quasi-opposition based learning (QOBL) & Parameter estimation of photovoltaic (PV) models \\ \hline
[57] & 2012 & Crown jewel defense (CJD) & Benchmark test functions \\ \hline
[58] & 2020 & DE combined with local search & Hybrid flow-shop scheduling problem \\ \hline
[41] & 2017 & Pairwise linear optimization & Takagi-Sugeno fuzzy systems \\ \hline
[67] & 2018 & Greedy algorithm & Multi-skill resource-constrained project scheduling problem \\ \hline
[68] & 2020 & Nawaz-Enscore-Ham (NEH) algorithm & Slabs and beams manufacturing \\ \hline \hline \end{tabular}
\end{table}
Table 4: Summary of hybrid methods.  
to the ultraviolet changes. Among other improvements proposed in the work of [74], the chaotic initialisation strategy was used to initialise the whales in the multi-strategy ensemble whale optimization algorithm (MSWOA).  
The chaos theory was used to initialise the moth-flame optimization (MFO) [75], firefly algorithm (FA) [76], artificial bee colony (ABC) [77], biogeography based optimization (BBO) [78]), krill herd (KH) [79], water cycle algorithm (WCA) [80], and grey wolf optimizer (GWO) [81]. In all, the authors claimed superiority of their results over other algorithms; however, high computational complexity remains an issue for this category, and we provide a summary of efforts in Table 5.