An efficient CMM inspection process implemented in industry gives significant productivity improvements. A key part of this improvement is the optimization of the inspection sequences. To ensure quality of the inspection the sequences are often constrained with respect to the order of the measurements. This gives rise to so called precedence constraints when modelling the inspection sequence as a variation of the travelling salesperson problem (TSP). Two heuristic solution approaches and a generic optimizing algorithm are considered. A generation based stochastic algorithm is found to reduce cycle time by as much as 12% in comparison to the currently used algorithm.