In this paper, an application of the inverse method based on the artificial bee colony algorithm has been demonstrated for estimating unknown dimensions of a rectangular perforated fin. The analysis has been done to maximize the heat transfer rate for a given volume occupied by the fin. The perforated fin has been assumed to dissipate heat by virtue of natural convection and surface radiation. The least square mismatch between a given volume and an initially guessed one is used to define the objective function that in turn has been minimized using the artificial bee colony algorithm. A comparative study reveals the advantage of the artificial bee colony algorithm against other evolutionary and stochastic optimization methods for the present problem. Since, there exist multiple dimensions satisfying a given volume, so, the most optimal dimension has been identified on the basis of a heat transfer rate maximization criterion. The study reveals that a given amount of heat transfer rate can be achieved with multiple combinations of the fin surface area and even a particular value of surface area can result in different heat transfer rates.