Initialisation Approaches for Population-Based Metaheuristic Algorithms: A Comprehensive Review

Abstract

A situation where the set of initial solutions lies near the position of the true optimality (most favourable or desirable solution) by chance can increase the probability of finding the true optimality and significantly reduce the search efforts. In optimisation problems, the location of the global optimum solution is unknown a priori, and initialisation is a stochastic process. In addition, the population size is equally important; if there are problems with high dimensions, a small population size may lie sparsely in unpromising regions, and may return suboptimal solutions with bias. In addition, the different distributions used as position vectors for the initial population may have different sampling emphasis; hence, different degrees of diversity. The initialisation control parameters of population-based metaheuristic algorithms play a significant role in improving the performance of the algorithms. Researchers have identified this significance, and they have put much effort into finding various distribution schemes that will enhance the diversity of the initial populations of the algorithms, and obtain the correct balance of the population size and number of iterations which will guarantee optimal solutions for a given problem set. Despite the affirmation of the role initialisation plays, to our knowledge few studies or surveys have been conducted on this subject area. Therefore, this paper presents a comprehensive survey of different initialisation schemes to improve the quality of solutions obtained by most metaheuristic optimisers for a given problem set. Popular schemes used to improve the diversity of the population can be categorised into random numbers, quasirandom sequences, chaos theory, probability distributions, hybrids of other heuristic or metaheuristic algorithms, Lévy, and others. We discuss the different levels of success of these schemes and identify their limitations. Similarly, we identify gaps and present useful insights for future research directions. Finally, we present a comparison of the effect of population size, the maximum number of iterations, and ten (10) different initialisation methods on the performance of three (3) population-based metaheuristic optimizers: bat algorithm (BA), Grey Wolf Optimizer (GWO), and butterfly optimization algorithm (BOA).