Effective methods for solving the complex and noisy engineering problems using a finite sequence of instructions can be categorised into optimisation and meta-heuristics algorithms. The latter might be defined as an iterative search process that efficiently performs the exploration and exploitation in the solution space aiming to efficiently find near optimal solutions. Various natural intelligences and inspirations have been adopted into the iterative process. In this work, two types of meta-heuristics called Bees and Firefly algorithms were adapted to find optimal solutions of noisy non-linear continuous mathematical models. Considering the solution space in a specified region, some models contain global optimum and multiple local optimums. Bees algorithm is an optimisation algorithm inspired by the natural foraging behaviour of honey bees. Firefly algorithm is used to produce a near optimal solution under a consideration of the flashing characteristics of fireflies. A series of computational experiments using each algorithm were conducted. Experimental results were analysed in terms of best solutions found so far, mean and standard deviation on both the actual yields and execution time to converge to the optimum. The Firefly algorithm seems to be better when the noise levels increase. The Bees algorithm provides the better levels of computation time and the speed of convergence. In summary, the Firefly algorithm is more suitable to exploit a search space by improving individuals' experience and simultaneously obtaining a population of local optimal solutions.