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1.1       Background on Heuristics Optimization
1.2       Background on Optimal Control Theory
1.3       Aim and Objectives
1.4       Statement of Problem
1.5       Methodology
1.6       Significant Contributions
1.7       Thesis Organization

2.1       Introduction
2.2       Review of Fundamental Concepts on Heuristic Methods
2.2.1 Artificial fish swarm algorithm
2.2.2 Cultural algorithm
2.2.3 Genetic algorithm
2.2.4 Particle swarm optimization
2.2.5 Artificial bee colony optimization algorithm
2.2.6 Standard optimization test functions Ackley function function DeJongF4 function Expfun function Griewangk function Hyperelliptic function and Montelvo first function Levy and Montelvo second function Neumaier3 function Rastrigin function Rosenbrock function Sal Function Schwefel function Schaffer function Sphere function Bukin N.6 function
2.2.7 Determination of optimal values of weighting matrices in LQR problems Design choice for determination of LQR weighting matrices

3.1 Introduction
3.2 Modified artificial fish swarm algorithm
3.2.1 Modified preying behaviour
3.2.2 Modified swarming behaviour
3.2.3 Modified chasing behaviour
3.3 Modified Cultural Artificial Fish Swarm Algorithm with Crossover
3.3.1 mCAFAC Knowledge adjustment
3.4 Design Choices for the mCAFAC Influence Function
3.4.1 mCAFAC_Ns: mCAFAC Using normative knowledge
3.4.2 mCAFAC_Sd: mCAFAC using situational knowledge
3.4.3 mCAFAC_NsSd: mCAFAC using normative knowledge and situational knowledge
3.4.4 mCAFAC_NsNd: mCAFAC using normative knowledge for step size, visual distance and the direction of evolution
3.5       Recombination Operator
3.6       Determination of Weighting Matrices Using mCAFAC
3.6.1quadruple inverted pendulum stabilization

4.1       Introduction
4.2       Visualization of the Optimization Test Function
4.2.1 Ackley function
4.2.2 CM function
4.2.3 DeJongF4 function
4.2.4 Expfun function
4.2.5 Griewangk function
4.2.6 Hyperelliptic function
4.2.7 Levy and Montelvo first function
4.2.8 Levy and Montelvo second functions
4.2.9 Neumaier3 function
4.2.10 Rastrigin test function
4.2.11 Rosenbrock test fuction
4.2.12 Sal test function
4.2.13 Schwefel test function
4.2.14 Schaffer test function
4.2.15 Sphere test function
4.2.16 Bukin N.6 test function
4.3       Performance Evaluation of Proposed AFSA Algorithms
4.3.1 Performance evaluation of AFSA (With and Without Inertial Weight)
4.3.2 Performance evaluation of mCAFAC_Ns using normative knowledge.
4.3.3 Performance evaluation of mCAFAC_Sd using situational knowledge
4.3.4 Performance evaluation of mCAFAC_NsSd using situational knowledge.
4.3.5 Performance evaluation of mCAFAC_NsNd using situational knowledge.
4.3.6 Performance evaluation of artificial bee colony (ABC) algorithm
4.4       Parameter Settings for the Proposed Algorithm
4.5       Artificial Bee Colony Parameters
4.6       Computer System Specification
4.7       Application of the Proposed Controller for Optimal Determination of Controller Parameters

5.1       Introduction
5.2       Summary of Findings
5.3       Conclusion
5.3       Limitations
5.4       Recommendations for Further Work


This research was aimed at the development of an improved artificial fish swarm optimization algorithm based on knowledge (normative and situational) in cultural algorithm and crossover operator called the modified Cultural Artificial Fish Swarm Algorithm with Crossover (mCAFAC). The Normative and Situational knowledge inherent in cultural algorithm were utilized to guide the step size as well as the direction of evolution of AFSA at different configurations, in order to combat the ease at which AFSA falls into local minima. An inertial weight selection is adopted such that the algorithm can adaptively select its parameters (visual and step size) when searching for global solution. Crossover operator was applied to fuse the AFSA and the modified Cultural Artificial Fish Swarm Algorithm called the mCAFAC, in order to enhance its convergence to a global minimal. Four variations of mCAFAC (mCAFAC_Ns, mCAFAC_Sd, mCAFAC_NsSd and mCAFAC_NsNd) were implemented in Matlab R2013b using different configurations of the cultural knowledge. A total of sixteen test functions (Ackley, Cosine Mixture, Rastrigirn etc.) were employed to evaluate the performance of each mCAFAC variant. Simulation results showed that the mCAFAC outperformed the original AFSA with the mCAFAC_NsSd having superior performance over all the other variants.mCAFAC_NsSd produced the best result in 9 out of the 16 test cases (56.25%) while mCAFAC_NsNd produced the best result in 1 out of the 16 test cases (6.25%), mCAFAC_Ns produced the best result in 3 out of the 16 test cases (18.75%) and mCAFAC_Sd produced the best result in 1 out of the 16 test cases (6.25%). All the variants, including the standard AFSA, the modified AFSA and the replicated ABC produced the same result in 2 out of the 16 test cases (12.5%).mCAFAC_NsSd was then applied to determine the optimal values of the weighting matrices (Q and R) of linear quadruple regulator (LQR) controller.This was validated on the quadrupleInverted Pendulum (QIP) model where the obtained LQR was able to stabilize the model in 7.4161s as against 7.5162s when using the conventional trial-and-error LQR method. This showed a convergence of the solution space using both approaches with the LQR (mCAFAC) having a more optimal time-to-solution.



1.1 Background on Heuristics Optimization

Optimization is a subject that deals with the problem of minimizing or maximizing a certain function in a finite dimensional space over a subset of that space, which is usually determined by functional inequalities (Wang & Li, 2015). During the past century, optimization has been developed into a mature field that includes many branches, such as linear conic optimization, convex optimization, global optimization, discrete optimization, etc. Each of such branches has a sound theoretical foundation and is featured by an extensive collection of sophisticated algorithms and software. Optimization, as a powerful modelling and problem solving methodology, has a broad range of applications in management science, industry and engineering (Nashat et al., 2012)

There is no known single optimization method available for solving all optimization problems. Several Optimization Algorithms have been developed in recent years. These Algorithms includes, Artificial Fish Swarm Algorithm (AFSA) (Li, 2002), Artificial Bee Colony Optimization (ABC) (Karaboga, 2005), Particle Swarm Optimization (PSO) (Eberhart & Kennedy, 1995), Genetic Algorithm (GA) (Holland, 1959), Ant Colony Optimization (ACO) (Dorigo, 1996), Fire-Fly Algorithm (FFA) (Yang, 2010), Bacterial Foraging Algorithm (BFA) (Passino, 2002) and Cultural Algorithm (CA) (Reynolds, 1994).

Some of these optimization methods mimicking evolution, animal behaviour, rules of natural ecology and mechanisms of human culture in nature were developed in order to solve certain categories of complicated scientific, Social and engineering design problem.......

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