Many studies have been carried out using different metaheuristic algorithms on optimisation problems in various fields like engineering design, economics and routes planning. In the real world, resources and time are scarce. Thus the goals of optimisation algorithms are to optimise these available resources. Different metaheuristic algorithms are available. The firefly algorithm is one of the recent metaheuristic algorithms that is used in many applications; it is also modified and hybridised to improve its performance. In this paper, we compare the Standard Firefly Algorithm, the Elitist Firefly Algorithm, also called the Modified Firefly Algorithm with the Chaotic Firefly Algorithm, which embeds chaos maps in the Standard Firefly Algorithm. The Modified Firefly Algorithm differs from the Standard Firefly Algorithm in such a way that the global optimum solution at a particular iteration will not move randomly but in a direction that is chosen from randomly generated directions that can improve its performance. If none of these directions improves its performance, then the algorithm will not be updated. On the other hand, the Chaotic Firefly Algorithm tunes the parameters of the algorithms for the purpose of increasing the global search mobility i.e. to improve the attractiveness of fireflies. In our study, we found that the Chaotic Firefly Algorithms using three different chaotic maps do not perform as well as the Modified Firefly Algorithms; however, at least one or two of the Chaotic Firefly Algorithms outperform the Standard Firefly Algorithm under the given accuracy and efficiency tests.