| Summary: | Optimization algorithm plays an important role in solving many complex and real-world problems. Solution offers by the algorithm has high accuracy and reliable. Moreover, with the fast development in computing technology, application of optimization algorithm in solving problems is easier and becomes more practical. Optimization algorithm is also known as a metaheuristic algorithm which is originally come from heuristic approach. It is a heuristic algorithm that is integrated with an advance strategy inspired from many natural phenomena found on earth. The algorithms can be categorized into a single objective and a multi-objective type. Single objective type optimization algorithm can be applied to solve a problem with a single objective. On the other hand, multi-objective algorithm is applicable to solve a problem with two or more objectives. A more complex problem in which has two conflicting objectives where it is not solvable by the single objective type algorithm is the right type of problem for the multi-objective algorithm. Solution produced by the multi-objective algorithm is always presented in Pareto front curve representation. The produced Pareto front curve is a measure of how good the solution produced by the algorithm is. The main measurement criteria include the accuracy of the solution to the actual Pareto curve and the distribution of the found solution on the actual Pareto curve. Yet the performance of many multi-objective algorithms in terms of the accuracy and the distributed solution is not achieved at the highest performance level. There are still rooms for improvement the algorithm performance by manipulating the algorithm strategy. This thesis presents two variants of multi-objective type algorithms based on a Spiral Dynamic Algorithm (SDA) with application to optimize a Proportional-Derivative (PD) controller for an Inverted Pendulum System. The first variant is known as a Nondominated Sorting Multi-objective Spiral Dynamic Algorithm (MOSDA-NS). It is a strategy which combines a Nondominated Sorting and Crowding distance approaches with the SDA. The second variant is known as Archived-based Multi-objective Spiral Dynamic Algorithm (MOSDA-A). It is a strategy combining an Archived approach with the SDA. All the developed algorithms were tested with a set of benchmark functions comprising of 10 different functions covering various fitness landscapes and features. Both accuracy performance and distribution of the found solution on the obtained Pareto front are recorded. A statistical analysis is then conducted via a Wilcoxon Sign Rank test and a Friedman test. Both tests are conducted to verify the significant improvement of the solution obtained via the proposed algorithms to the Multi-objective Particle Swarm Optimization (MOPSO) and Multi-objective Nondominated Sorting Genetic Algorithm II (NSGAII). Result from the test shows that the proposed MOSDA-NS achieved the best accuracy and distribution performances compared to all other algorithms. In terms of solving a real-world problem, the proposed algorithms are applied to optimize two different Proportional-Derivative (PD) controllers for an Inverted Pendulum system attached on a moving cart. The first PD controller attenuates error for a linear movement of the moving cart. The second PD controller eliminates error for a rotating angle of the inverted pendulum. Transient responses of both pendulum angle and cart position in time-domain representation are recorded. An analysis on the transient responses is then conducted which measuring steady-state error, percentage overshoot, rise time and settling time. Finding of the analysis indicates that the proposed algorithms have resulted in a better control performance compared to the MOPSO and NSGAII.
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