Multi-objective optimisation using learning automata and its applications in power systems

Learning automata are a major branch of machine learning designed to find the optimal action to a learning task in a random environment. Interactions with environment and repetitive learning of a number of individual units, which are independent and structurally simple, enable the learning automata to tackle complex learning problems. Systems built with learning automata have been successfully employed in many difficult learning situations over the years. They have also been investigated in solving optimisation problems. However, the performance of the learning automata in solving complex optimisation problems, such as high-dimensional optimisation problems and multi-objective optimisation problems, has not been fully investigated. Therefore, this thesis is devoted to exploring the potential of learning automata in solving complex optimisation problems. In the thesis, Function Optimisation by Learning Automata (FOLA) and Multi-objective Optimisation by Learning Automata (MOLA) have been developed for single and multi-objective complex optimisation problems respectively. In FOLA, the search domain of a complex optimisation problem is divided into cells and represented by cell values. Each automaton of FOLA conducts dimensional search actions according to the path values which are calculated based on the cell values situated on the searching path. During the optimisation process, cell values are continuously updated using the values of the automata states, and stored in memory. In this way, the information obtained prior to the current state can be collected and efficiently used. With these approaches, FOLA is able to undertake search in continuous states and achieve accurate solutions efficiently. To fully analyse the performance of FOLA, it has been tested based on twenty-two benchmark functions, which represent a wide range of challenging optimisation problems. FOLA has been compared with ten Evolutionary Algorithms (EAs), which are widely used for solving complex optimisation problems nowadays, and four newly-proposed EAs which have been reported to solve the same benchmark functions promisingly in literature. The experimental results have demonstrated the superiority of FOLA over the other EAs for most benchmark functions, in terms of the convergence rate and accuracy of finding optimal solutions. FOLA has shown its capability to solve high-dimensional multi-modal problems. The experiment also shows that FOLA is able to greatly reduce computation time, especially for high-dimensional functions. Most optimisation problems existing in the real world have more than one objective. These problems aim to find evenly distributed Pareto fronts which are the plots of the objective function values of the optimal solutions. They can be tackled by combining the multiple objectives into one single objective function that can be solved by a single-objective optimisation algorithm. However, this method suffers from the drawback of large computation load, and has difficulty in finding non-convex Pareto fronts. Therefore, it is important to develop alternative optimisers that can be used for complex multi-objective problems. Based on FOLA, MOLA is proposed to solve complex multi-objective optimisation problems. MOLA mainly comprises two processes: the process of searching and the process of learning from neighborhood. The process of searching is carried out through a tournament that is held between Pareto global search and Pareto local search. This tournament can lead to a better trade-off between exploitation and exploration, which is a critical factor in finding the optimal solution. In the process of learning, the relationship of neighborhood among the non-dominated solutions is investigated, as it is believed that useful information that can benefit the search is embeded in neighborhood. Based on the relationship, non-dominated solutions are updated based on their neighbors. Through these processes, MOLA is able to find evenly distributed Pareto fronts for complex optimisation problems. MOLA has been compared with two popular weighted-sum based algorithms, Multi-Objective Genetic Algorithm (MOGA) and Multi-Objective Particle Swarm Optimiser (MOPSO), on four multi-objective benchmark functions that comprise low and high-dimensional models, convex and non-convex models, and continuous and discontinuous models respectively. Besides, MOLA has been also compared with the latest developments of Pareto front-based multi-objective algorithms, Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) and Non-dominated Sorting Genetic Algorithm II (NSGA-II), on the basis of thirteen widely used multi-objective functions, which comprise complex Pareto set shapes. The simulation results have shown that MOLA greatly exhibits its superiority over the other algorithms, as it can find accurate and evenly distributed non-dominated solutions, and its Pareto fronts are wider than those obtained by the other algorithms. Besides, MOLA consumes less computation time, whilst finding more accurate non-dominated solutions. In the thesis, the application of FOLA and MOLA in solving optimal power flow problems of power systems has been investigated. Optimal power flow problems are very important in power system operation and planning, especially economic power system dispatch and voltage stability enhancement problems, which have attracted more and more attention around the world. FOLA has also been applied to solve the power flow problems which concern with fuel cost minimisation, voltage profile improvement and voltage stability enhancement, based on the IEEE 30-bus and IEEE 57-bus systems. FOLA is fully compared with improved Particle Swarm Optimisation (PSO) and Genetic Algorithm (GA). The simulation results have demonstrated that FOLA is able to offer more accurate solutions with shorter computation times, in comparison with the improved PSO and GA, particularly on the IEEE 57-bus system. FOLA is also applied to solve the optimal power flow problems in the power systems where the operation condition varies for a short period time. Although the varying operation condition is considered here, these problems are considered as static problems in a short period of time. In this case, the fluctuating power output will affect the power flow calculation, and it can cause instability which results in severe detriments in the power systems. In this case, an algorithm which can provide security to the power systems is highly demanded. Simulation studies have been carried out among FOLA, the improved PSO and GA, based on the modified IEEE 30-bus and 57-bus systems, which are embedded with time-varying power outputs. The simulation results have demonstrated that FOLA is able to track the changes of the power system configuration more rapidly and accurately than the improved PSO and GA, particularly when voltage stability is involved in the objective function. Besides, FOLA is able to offer more accurate solutions with shorter computation time, in comparison with PSO and GA. FOLA is also compared with two recently-proposed EAs, Comprehensive Learning Particle Swarm Optimiser (CLPSO) and Cooperative Particle Swarm Optimisation (CPSO), based on the IEEE 118-bus system. Advantages of FOLA have been demonstrated by the fact that FOLA reduces the fuel cost greatly and enhances the voltage stability of the power system. Nowadays, wind power is expected to be largely increased in power systems, due to its inexhaustible and nonpolluting merits. However, it brings new challenges to power system operation when wind power is connected to the grid of power systems. The study is undertaken on the modified IEEE 30-bus power system and new England test power system, which are incorporated with fixed-speed and variable-speed wind generators respectively. MOLA has been fully compared with MOEA/D and NSGA-II in solving the multi-objective optimisation problem, which aims to reduce the operational cost and enhance voltage stability simultaneously. The simulation results have demonstrated that MOLA performs better than MOEA/D and NSGA-II, as MOLA can find wider and evenly distributed Pareto fronts, and obtain more accurate Pareto optimal solutions efficiently. Additionally, MOLA consistently finds larger hypervolume and smaller diversity metric than MOEA/D and NSGA-II under different circumstances. MOLA has presented its superiority by finding wider Pareto fronts than MOEA/D and obtaining more accurate solutions than NSGA-II, while using much less function evaluations. MOLA has also been applied to solve the multi-objective optimisation problem in deregulated market, which aims to maximise the social benefit and enhance voltage stability in the IEEE 30-bus power system. MOLA greatly increases the social benefit and improves the voltage stability. It can find wide and evenly distributed Pareto fronts, and obtain accurate Pareto optimal solutions efficiently.