Evolutionary multi-objective concurrent maximisation of process tolerances

Concurrent tolerancing which simultaneously optimises process tolerance based on constraints of both dimensional and geometrical tolerances (DGTs), and process accuracy with multi-objective functions is tedious to solve by a conventional optimisation technique like a linear programming approach. Concurrent tolerancing becomes an optimisation problem to determine optimum allotment of the process tolerances under the design function constraints. Optimum solution for this advanced tolerance design problem is difficult to obtain using traditional optimisation techniques. The proposed algorithms (elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE)) significantly outperform the previous algorithms for obtaining the optimum solution. The average fitness factor method and the normalised weighting objective function method are used to select the best optimal solution from Pareto optimal fronts. Two multi-objective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the strength of the Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find the computational effort of the NSGA-II and MODE algorithms. Comparison of the results establishes that the proposed algorithms are superior to the algorithms in the literature.