3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item A comparative study of different Meta-Heuristic methods for scheduling the CAF Champions League(2020) Dithebe, KeletsoThe Confederation of African Football (CAF) Champions League, is an annual continental football tournament organised by CAF. The CAF Champions League has the capacity to feature 68 African teams, but on average only 57 teams participate in this league. Some of the reasons for teams and their affiliated football associations not participating, include excessive travel costs. In this dissertation, we highlight and tackle two problems which arise when generating fixtures for the CAF Champions League. These include the scheduling of football matches such that the total distance travelled by teams and match officials is minimized. These problems can be formulated as constrained optimization problems, where the constraints are dictated by the Confederation of African Football and other relevant stakeholders. We carry out a comparative study of the performance of three meta-heuristic methods, to solve the constrained problem. The methods under consideration are the Genetic Algorithm, Tabu search and Simulated Annealing. We then compare the results of the best performing meta-heuristic with that of existing CAF Champions League schedulesItem Line balancing using metaheuristic methods in BMW South Africa(2017) Hart, RichardThis study documents a project to investigate the possibility of achieving savings in BMW South Africa’s Rosslyn assembly plant through the use of metaheuristics to optimise line balancing methods. Through this project, a customised Ant Colony Optimisation algorithm was developed for the optimisation of the frontend assembly line in this plant. This algorithm is one which was designed to take into account many of the constraints which are found in an automotive manufacturing environment such as work areas, shared processes and sequence constraints. Through the use of the algorithm, a solution was developed which shows improvements to the line balancing in the area. These improvements show a 17% reduction in labour costs in the area, an improvement of 13.12% in the area’s average work loading and an increase in the average work stability of 17.81%. Additionally, improvements were found which would allow this algorithm to be used in other lines in the assembly plant for further savings and improvements.Item A new hybrid meta-heuristic algorithm for solving single machine scheduling problems(2017) Zlobinsky, NatashaNumerous applications in a wide variety of elds has resulted in a rich history of research into optimisation for scheduling. Although it is a fundamental form of the problem, the single machine scheduling problem with two or more objectives is known to be NP-hard. For this reason we consider the single machine problem a good test bed for solution algorithms. While there is a plethora of research into various aspects of scheduling problems, little has been done in evaluating the performance of the Simulated Annealing algorithm for the fundamental problem, or using it in combination with other techniques. Speci cally, this has not been done for minimising total weighted earliness and tardiness, which is the optimisation objective of this work. If we consider a mere ten jobs for scheduling, this results in over 3.6 million possible solution schedules. It is thus of de nite practical necessity to reduce the search space in order to nd an optimal or acceptable suboptimal solution in a shorter time, especially when scaling up the problem size. This is of particular importance in the application area of packet scheduling in wireless communications networks where the tolerance for computational delays is very low. The main contribution of this work is to investigate the hypothesis that inserting a step of pre-sampling by Markov Chain Monte Carlo methods before running the Simulated Annealing algorithm on the pruned search space can result in overall reduced running times. The search space is divided into a number of sections and Metropolis-Hastings Markov Chain Monte Carlo is performed over the sections in order to reduce the search space for Simulated Annealing by a factor of 20 to 100. Trade-o s are found between the run time and number of sections of the pre-sampling algorithm, and the run time of Simulated Annealing for minimising the percentage deviation of the nal result from the optimal solution cost. Algorithm performance is determined both by computational complexity and the quality of the solution (i.e. the percentage deviation from the optimal). We nd that the running time can be reduced by a factor of 4.5 to ensure a 2% deviation from the optimal, as compared to the basic Simulated Annealing algorithm on the full search space. More importantly, we are able to reduce the complexity of nding the optimal from O(n:n!) for a complete search to O(nNS) for Simulated Annealing to O(n(NMr +NS)+m) for the input variables n jobs, NS SA iterations, NM Metropolis- Hastings iterations, r inner samples and m sections.Item Research into a method of crew scheduling for suburban rail transport using heuristic and linear programming techniques(2015-01-14) Comrie, Andrew NevilleCrew schedules on the South African Transport Services are done by roster compilers at depots. A method that uses heuristic and mathematical programming algorithms was developed to replace existing hand methods. It is a two stage method that will use a microcomputer to assist roster compilers to draw up crew schedules. Initially timetables are subdivided into shifts and then they are combined into crew schedules. The solution, which produces a significant improvement compared with an existing crew schedule and an existing method, has been accepted in principle and computer programming has begun. In Appendix E another heuristic for the scheduling of league matches is described.