Nesting of regular and irregular shaped parts in a sheet metal having constrained boundary so as to maximize effective utilization of material with minimum wastage imposes a challenging task to the metal cutting industries. To resolve the problem, this paper presents the applications of six popular metaheuristics, i.e. artificial bee colony, ant colony optimization, particle swarm optimization, firefly algorithm, differential evolution and teaching-learning-based optimization (TLBO) algorithm with an objective to maximize effective utilization ratio during metal cutting operation. For all the metaheuristics, the considered parts are optimally allocated in the given sheet metal based on bottom left fill algorithm to minimize the corresponding nested height. It is observed that TLBO algorithm supersedes the others with respect to effective utilization ratio, nested height and computational effort. A comparative analysis using values of t-statistic also proves the uniqueness of this algorithm over the others in efficiently solving the nesting problems for regular and irregular shaped parts during sheet metal cutting operation.