The respect of the machined piece quality and productivity is closely related to the mastery of uncertain factors. Indeed, the efficient solutions obtained from the machining parameter optimization based on classical methods are assigned of uncertain deviations which affect the cutting process. In the present paper, we propose multi-and monoobjective optimization approach of parameter turning with taking into account both production constraints related to piece quality, to machine power, or to tool life, than uncertainty factors related to the tool wear and to piece geometry defaults. To this end, we developed and implemented an efficient genetic algorithm, based on an evaluation mechanism of "objective" functions, which integrate the Monte Carlo simulations to calculate the robustness of objective function and different constraints. Our approach has been validated by two applications implemented with Matlab™ for the minimization of cost and machining time, which has allowed obtaining simultaneously efficient and robust results and offering the possibility to choose beforehand a compromise between efficiency and robustness of solutions.

Abstract. In this contribution, a bi-objective robust optimization of cutting parameters, with the taking into account uncertainties inherent in the tool wear and the tool deflection for a turning operation is presented. In a first step, we proceed to the construction of substitution models that connect the cutting parameters to the variables of interest based on design of experiments. Our two objectives are the best machined surface quality and the maximum productivity under consideration of limitations related to the vibrations and the range of the three cutting parameters. Then, using the developed genetic algorithm that based on a robust evaluation mechanism of chromosomes by Monte-Carlo simulations, the influence and interest of the uncertainties integration in the machining optimization is demonstrated. After comparing the classical and robust Pareto fronts, A surface quality less efficient but robust can be obtained with the consideration of uncontrollable factors or uncertainties unlike that provides the deterministic and classical optimization for the same values of productivity.

In this paper, a contribution to the determination of reliable cutting parameters is presented, which is minimizing the expected machining cost and maximizing the expected production rate, with taking into account the uncertainties of uncontrollable factors. The concept of failure probability of stochastic production limitations is integrated into constrained and unconstrained formulations of multi-objective optimization problems. New probabilistic version of the nondominated sorting genetic algorithm P-NSGA-II, which incorporates the Monte Carlo simulations for accurate assessment of cumulative distribution functions, was developed and applied in two numerical examples based on similar and anterior work. In the first case, it is a question of the search space that is completely 'closed' by high natural variability related to the multi-pass roughing operation: in this case, the failure risk of technological limitations are considered as objectives to minimize with economic objectives. The second case is related to deformed search space due to the uncertainties specific to finishing operation; therefore, the economic objectives are minimized under imposed maximum probabilities of failure. In both situations, the efficiency and robustness of optimal solutions generated by the P-NSGA-II algorithm are analysed, discussed and compared with sequence of unconstrained minimization technique (SUMT) method. Keywords Failure probability . Monte Carlo simulations . Pareto optimal solutions . Optimization . NSGA-II . Reliable machining parameters Nomenclature R max The maximum roughness (μm) T max The maximum tool life (min) F max The maximum cutting force (kg) P max Power on the spindle (kW) L Length to be machined for a single pass (mm) d Diameter of workpiece (mm) t m Cutting time (min) t l Nonproductive and handling time (min) t r Tool changing time (min/edge) a Depth of cut (mm) t Total depth of metal to be cut in roughing operation (mm) n Number of passes in rough machining (an integer) p 0Direct labour cost added to overhead (paise/min) p 0 *t m Machining cost by actual time in cut (paise/pc) p 0 *t l Machine idle cost due to loading and unloading operations (paise) p l *(t m /T) Tool cost per unit piece (paise/pc) p lThe cost of a cutting edge (paise/edge) p 0 *(t r *t m / T) Tool replacement cost (paise/pc) r ε Nominal nose radius (mm) ηNominal machine efficiency (%) EThe expectation measurement

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