Fast genetic algorithm for roundness evaluation by the minimum zone tolerance (MZT) method

Abstract

The main goal of the minimum zone tolerance (MZT) method is to achieve the best estimation of the roundness error, but it is computationally intensive. This paper describes the application of a genetic algorithm (GA) to minimize the computation time in the evaluation of CMM roundness errors of a large cloud of sampled datapoints (0.2° equally spaced datapoints). Computational experiments have shown that by selecting the optimal GA parameters, namely a combination of the four genetic parameters related to population size, crossover, mutation, and stop conditions, the computation time can be reduced by up to one order of magnitude, allowing realtime operation. Optimization has been tested using seven CMM datasets, obtained from different machining features, and compared with the LSQ method. The performance of the optimized algorithm has been validated with GA from the literature using four benchmark datasets.

Multi-Level Search Algorithm for Roundness Error Evaluation by the Minimum Zone Circle Method

“…The measurement dataset 1 come from literature [12], using this dataset as an example, there are part of algorithm for roundness error assessment: Genetic Algorithm(GA) [1], Effective Genetic Algorithm(EGA) [2], Fast Genetic Algorithm(FGA) [3], Particle Swarm Optimization(PSO) [4], Curvature Technique Strategy(CTS) [5], Hybrid Improved Artificial Fish Swarm Algorithm(HI-AFSA) [6], Differential Evolutionary Algorithm(DEA) [7], et al The above algorithmic assessment results as the table 1 shows.…”

“…Step δ ≤ [12] --0.008 5 -GA [1] 0.035 61 -0.052 92 0.008 5 -EGA [2] 0.035 6 -0.052 9 0.008 5 0.28 FGA [3] --0.008 5 0.05 PSO [4] 0.035 61 -0.053 11 0.008 5 -CTS [5] 0.035 6 -0.052 9 0.008 5 -HI-AFSA [6] 0.035 61 -0.052 93 0.008 5 0.36 DEA [7] --0. 008 Ref.…”

“…Among them, only MZC method conforms to define, but it will be hard to solve due to the nonlinear problem. Generally all adopt different kinds of optimistic algorithm [1][2][3][4][5][6][7] search least global optimum point (following short "optimum point") of roundness error. Most of these algorithms are tedious and not intuitionistic.…”

Optimum Dataset Size and Search Space for Minimum Zone Roundness Evaluation by Genetic Algorithm

“…Among optimization techniques are Chebyshev approximation [4] and simplex search [5]. Metaheuristics approaches are also available in the literature, such as particle swarm optimization (PSO) [6], linear approximation [7], and genetic algorithms (GAs) [3], [8], [9], [10] and [11]. Performance of methods has been reviewed in [12].…”

“…the MZ center. The center of the rectangular area is an estimation of the MZ center evaluated as the mean value of the x i and y i coordinates of the sampled points [3], [8], [9], [10] and [11]. In [8] the search space is a square of fixed 0.2 mm side, in [11] it is 5% of the circle diameter.…”