# DEVELOPMENT OF AN IMPROVED CULTURAL ARTIFICIAL FISH SWARM ALGORITHM WITH CROSSOVER

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## DEVELOPMENT OF AN IMPROVED CULTURAL ARTIFICIAL FISH SWARM ALGORITHM WITH CROSSOVER

Chapter One:

Introduction

1.1 Background Of The Study

Optimisation is the study of minimising or maximising a specific function in a finite-dimensional space across a subset of that space, which is typically governed by functional inequalities (Wang & Li, 2015).

Over the last century, optimisation has evolved into a mature science with numerous branches, including linear conic optimisation, convex optimisation, global optimisation, discrete optimisation, and so on.

Each of these fields has a strong theoretical foundation and is supported by a large number of sophisticated algorithms and software. Optimisation is a strong modelling and problem-solving tool that has a broad range of applications in management science, industry, and engineering (Nashat et al., 2012).

There is no known single optimisation approach capable of handling all optimisation difficulties. Several optimisation algorithms have emerged in recent years.

These algorithms include Artificial Fish Swarm Algorithm (AFSA) (Li, 2002), Artificial Bee Colony Optimisation (ABC) (Karaboga, 2005), Particle Swarm Optimisation (PSO) (Eberhart & Kennedy, 1995), Genetic Algorithm (GA) (Holland, 1959), Ant Colony Optimisation (ACO) (Dorigo, 1996), Fire-Fly Algorithm (FFA) (Yang, 2010), Bacterial Foraging Algorithm (BFA) (Passino, 2002), and Cultural Algorithm (CA) (Reynolds, 1994).

Some of these optimisation methods, which mirror evolution, animal behaviour, natural ecology laws, and human cultural mechanisms in nature, were designed to handle particular categories of complex scientific, social, and engineering design problems (Chung, 1997).

i) Weak problems that need little or no domain expertise

ii) Non-deterministic Polynomial (NP) Complete Problems

2 iii) Problems where a near-optimal solution is acceptable

iv) Issues with non-smooth (discontinuous; not differentiable) and noisy search spaces.

v) Problems with uncertain or dynamic surroundings

This study looks into artificial fish swarm optimisation, a relatively new addition to the field of natural computational intelligence that draws inspiration from the social behaviours of natural swarms of fish.

Since its inception in 2002, AFSA has found significant use in complicated optimisation domains and is now a prominent research area, providing an alternative to more established evolutionary computational approaches that may be used in many of the same applications.

Li Xiao Lei (Li et al., 2002) was the first to introduce the AFSA algorithm, which was motivated by simulations of fish social behaviour. It is based on the natural mechanism of group communication to share individual information when a group (swarm) of fish look for food, despite the fact that not all fish are aware of the optimal food source.

However, due to the nature of social behaviour, if one person can identify a desirable path to take, the rest of the members will soon follow suit (Neshat et al., 2012). AFSA is based on three basic fish behaviours (preying, swarming, and chasing).

In this technique, each fish swarms over the multidimensional search space, adjusting its position in each step based on its own experience and the experience of surrounding fishes, until the entire swarm achieves an optimal solution (Li, 2002). Its next behaviour is determined by its current state as well as the status of the local environment.

AFSA is related to genetic algorithms (GA) in that it solves complicated nonlinear, high-dimensional problems without relying on the objective function’s gradient. Furthermore, they can reach faster convergence speeds with fewer parameters to change.

The system begins with a set of randomly generated alternative solutions and then searches for the optimal solution one interactively (Zhang et al. 2006). AFSA’s evolution, like human evolution, can be described as a Cultural Evolution Process (CEP).

Reynolds (Reynolds, 1994) created Cultural Algorithms to represent the evolution of the cultural component of an evolutionary computational system over time as it gained experience.

The cultural algorithm framework provides a mechanism for supporting the dual inheritance system that characterises both human culture at the macro evolutionary level and individual phenotypic evolution at the micro evolutionary level (Chung 1997).

It also provides a framework for isolating and leveraging cultural knowledge to accelerate issue solutions. This study focuses on changing the AFSA and leveraging cultural algorithm knowledge to speed up the problem-solving process during the evolution of AFSA.

1.2 Background on Optimal Control Theory.

Optimal control theory is a mathematical optimisation method that is an extension of calculus and has several applications in control engineering (Ata & Coban, 2015).

The fundamental objectives of an optimum control system are to verify the control signals that cause a process to fulfil the desired physical limitations

as well as to optimise (maximise or minimise) specific performance criteria. A linear quadruple optimal control issue is a subset of the general nonlinear optimal control problem in which the cost function is quadrupled and the system dynamics are characterised by a set of linear differential equations (Schildbach et al., 2015).

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