Robust and accurate evaluation of form tolerances is of paramount importance in today’s world of precision engineering. Present-day Coordinate Measuring Machines (CMMs) operate at high speed and have a high degree of accuracy and repeatability which are capable of meeting the stringent measurement requirements. However, the evaluation algorithms used in conjunction with them are not robust and accurate enough, because of the highly non-linear nature of the minimum-zone circularity formulation. Evolutionary algorithms have proved effective in solving constrained non-linear optimization problems. In this paper, Particle Swarm Optimization (PSO), which is one of the most recent and popular evolutionary algorithms, is employed to evaluate the minimum-zone circularity. The PSO approach imitates the social behavior of organisms such as bird flocking and fish schooling. It differs from other well-known Evolutionary Algorithms (EA) in that each particle of the population, called the swarm, adjusts its trajectory toward its own previous best position, and toward the previous best position attained by any member of its topological neighborhood. The constrained nonlinear model is rewritten as an unconstrained non-linear model using the penalty-function approach. The methodology is validated by testing on several simulated and experimental datasets and yields better results than other existing minimum-zone algorithms.

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