# Initialisation Approaches for Population-Based Metaheuristic Algorithms: A Comprehensive Review
###### Abstract
Furthermore, there has been a corresponding claim of novelty and solid capability of the algorithms serving as powerful optimisation tools. Unfortunately, most algorithms do not seem to draw inspiration from nature or incorporate any successful methodology that mimics natural phenomena or systems [7]. From the concept of the theorem of No Free Lunch, many real-world optimisation problems still require new approaches or methods to be solved perfectly or optimally. The theorem proved that any method could solve a problem efficiently, but no single method can effectively solve all problems. Studies have shown the popularity and successes of proposing algorithms that mimic the behaviours of animals to solve optimisation problems with reasonable accuracy. The commonly used distribution for initialisation by most metaheuristic algorithms is the random number generator, which generates sequences (used as position vectors) that follow the uniform probability distribution. However, these sequences do not have low discrepancies, or are not equidistributed in a given search area, and do not efficiently cover the search space [8]. On the other hand, quasirandom numbers can be generated with low discrepancy; these have been proven to have optimal discrepancy because they tend to cover the search space better and are helpful in optimisation [9]. Low discrepancy sequences, like Van der Corput, Sobol, Faure, and Halton, are potent computational method tools and have been used to improve the performance of optimisation algorithms. Many other approaches exist in the literature, and these are presented in this paper. A situation where the set of initial solutions lies near the position of the true optimality by chance, can increase the probability of finding the true optimality and significantly reduce the search efforts. In optimisation problems, the location of the true optimality is unknown a priori, and initialisation is a stochastic process. Additionally, the population size is equally important and when considering problems with high dimensions, small population size may lie sparsely in unpromising regions, and can return suboptimal solutions with bias. In addition, the different distributions used as position vectors for the initial population may have a different sampling emphasis and hence different degrees of diversity. To demonstrate the importance of initialisation, consider the Bukin N. 6 function shown in Figure 1. We assumed a search space of \([-20,0]\times[-8,4]\). The advanced arithmetic optimization algorithm (nAOA) [10] was initialised with beta distribution, and the distribution of the population after the first iteration is shown in Figure 2. The blue dots represent the current location of the population, the red asterisk (*) represents the current best solution, and the red star (\(\bigstar\)) denotes the global optimal solution of the Bukin function. The nAOA converged towards the optimal solution after a few iterations, as shown in Figure 3. Similarly, the nAOA was initialised with the random number, and the distribution  
Although initialisation plays a significant role in the performance of most metaheuristic optimizers, few studies or surveys have been conducted on the subject area. A search using the keywords survey OR review, initialisation (initialization), and metaheuristics, yielded no comprehensive review or survey articles in the literature. However, in discussing PSO variants, ref. [11] provide a paragraph on attempts to improve PSO performance using different initialisation schemes. The authors discuss how low discrepancy sequences and variants of opposition-based learning enhance the initial swarm population. Another attempt using GA was presented by [12], where the effect of three initialisation functions, namely, nearest neighbour (NN), insertion (In), and [PERSON]'s heuristic, were studied. [PERSON], [PERSON], and [PERSON] [13] evaluated the effect of 22 different probability distribution initialisation methods on the convergence and accuracy of five optimisation algorithms.