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/purpose: The newly developed probability-based multi - objective optimization (MOO) has introduced a novel concept of preferable probability to represent a preferability degree of a candidate in optimization in order to overcome the inherent shortcomings of subjective and "additive" factors in the previous MOO methods. In this paper, the new method is extended to include robust optimization for material engineering. Furthermore, energy consumption in a melting process with orthogonal array design and the robust optimization of four different process schemes in machining an electric globe valve body are taken as examples. Methods: The arithmetic mean value of each performance utility indicator of the candidate contributes to one part of the partial preferable probability, while the deviation of each performance utility indicator from its arithmetic mean value of the candidate contributes to the other part of the partial preferable probability quantitatively. Furthermore, following the procedures of the newly developed probability-based multi-objective optimization (PMOO), the total preferable probability of a candidate is obtained, which thus transfers a multi-objective optimization problem into a single objective optimization problem. Results: The optimal control factors of lower electric energy consumption with robustness are bundled steel, loose steel, and uncleaned steel of 12.5%, 50% and 37.5% by weight, respectively, in this steel melting process. This case is closely followed by the scenario of 50 wt% bundled steel, 50 wt% loose steel, and 0 wt% uncleaned steel. The robust optimization of four different process schemes for machining an electric globe valve body is scheme No. 1. Conclusion: The extension of probability-based multi-objective optimization while considering robustness is successful, which can be easily used to deal with the optimal problem with dispersion of data to get objectively an optimal result with robustness in material engineering. The extension of probability-based multi-objective optimization while considering robustness will be beneficial to relevant research and process optimization.

An approach of probability based multi-objective optimization considering robustness for material engineering