Abstract

Optimisation, in the mathematical sense, is the process of finding solutions to a problem such that one or many objectives are minimised or maximised. Optimisation problems are diverse in form, necessitating the need for many different optimisation algorithms. These algorithms can be defined in two categories: deterministic and non-deterministic algorithms. Deterministic algorithms usually have set execution schedules and are fairly exhaustive search methods. Non-deterministic algorithms use randomness and prove useful for problems where it may not be possible to execute a deterministic algorithm due to the size, or nature of the problem search space. In these cases a deterministic algorithm may take days or months to find an optimal solution, whereas a non-deterministic algorithm can usually find an approximate but still near-optimal solution in a matter of minutes or seconds. Ant Colony Optimisation (ACO), a non-deterministic algorithm class, aims to mimic (and exploit) the behaviours of real ant colonies to solve real-world optimisation problems. ACO algorithms are a class of constructive heuristic algorithms, which build solutions to a given optimisation problem, one solution component at a time, according to a defined set of rules (heuristics), i.e. starting with an ‘empty’ solution add solution components until a complete solution is built. ACO algorithms are unique in this class by their use of past solutions in manipulating an artificial ‘pheromone’. The pheromone being a measure associated to every unique solution component which reflects the estimated utility of this solution component. These pheromone values are used to bias solution construction by influencing the probability of a solution component being added to a growing solution based on the amount of pheromone it contains. The Population-based Ant Colony Optimisation (PACO) algorithm is a recently developed antinspired algorithm which, unlike traditional ACO algorithms, maintains a finite population of solutions as well as pheromone information. It has been demonstrated to be an efficient optimisation algorithm when applied to a range of difficult single-objective, multi-objective and dynamic problem instances. In this thesis a review of existing PACO algorithms is offered and an identification of common features is used in the development of a Population-based ACO framework. Using the new Population-based ACO framework, several new PACO algorithms imbued with a diversity preservation technique known as niching are defined. Niching has been used extensively in the field of Evolutionary Computation, but to the best knowledge of the author, has never been explicitly applied to an ACO algorithm per se. An empirical analysis of these novel implementations is presented using a variety of single and multiple objective continuous function and combinatorial optimisation problems. These optimisation problems have been chosen since they demonstrate the advantages and disadvantages of adding niching to a PACO algorithm. To conclude, two of these new PACO algorithms are applied to a real-world optimisation problem.