# Study of optimization for material processing parameters by means of probabilistic methodology for multi‑objective optimization

Selection and use of proper processing parameters are quite important for material machining. In the present paper, the probabilistic methodology is employed to perform the designs of materials processing for improving quality and cost saving at the same time.
Published in Mathematics

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Previously, optimization analysis involves either adding all weighting responses into a single objective or Pareto solution set or grey relational analysis for Taguchi orthogonal array. However, the reliability of these kind of algorithms is problematic with uncertainty.

The optimization of thin-wall machining was once performed by using Pareto-optimal solution with crucial requirements of enhanced energy efficiency, product quality, and productivity as objectives. However, its result is problematic due to the uncertainty of Pareto-optimal solution set, which could not give a definitive consequence. In fact, the inherent essence of optimization of multiple objectives is the “simultaneous optimization of multiple objectives” in a system inevitably. However, the previous methods (algorthms) of multi-objective optimization (MOO) and multi-criteria decision - making (MCDM) in the past took the “additive” algorithm as the actual algorithm for indexes in parameterization with weighting factors, or Pareto solution set with uncertainty, or grey relational analysis, etc.

Till now, the commonly used methods include, VIKOR (VIšekriterijumsko KOmpromisno Rangiranje), TOPSIS (Technique of ranking Preferences by Similarity to the Ideal Solution), MOORA (Multi-Objective Optimization on the basis of Ratio Analysis), and AHP (Analytical Hierarchy Process), etc., are not be considered as fully quantitative, which all include uncertainties actually.

In fact, the “additive” algorithm for evaluating multiple indexes is equivalent to the “union” in the spirits of probability theory and set theory, which is definitely inconsistent with the essence of “simultaneous optimization of multiple indexes”. Appropriately, in the respect of probability theory, “simultaneous optimization of multiple indexes” is to take the form of “joint probability” of the corresponding multiple events actually.

Additionally, in the additive algorithm there is a problem of choosing the scaled factor (denominator) of the normalization procedure of different objective, different scaled factors could often lead to quite different consequences. Therefore, the previous algorithms could not be considered as rational approaches in some sense due to their uncertainty and misusing of “union” in the spirits of probability theory and set theory.

Considering above situation, a probabilistic methodology was proposed. In the new methodology, each attribute/objective of the multi-objective optimization problem was taken as an independent event from the perspective of probability theory, furthermore the entire thing of the multi-objective optimization was taken as a “joint event” of all individual events, thus the overall / total probability of “joint event” was the product of each individual event in the entire thing. This methodology has the advantages of taking the simultaneous optimization of multiple objectives in the spirit of probability theory, which results in a definitive solution and an overall planning approach entirely. In this paper, the probabilistic methodology for multi-objective optimization (PMOO) is used to perform the optimal designs of materials processing of quality improvement and cost saving. The laser welding process of ANSI 304 austenitic stainless steel by using a pulsed Nd: YAG laser welding system and thin-wall machining of milling aluminum alloy 2024-T351 are taken as two examples. By performing the assessment of preferable probability of each scheme, the quantitative optimum designs of materials processing are thus completed equitably.

The importance of this paper is to present a reasonable approach which enables the influence of the process variables on the producibility, product quality and energy efficiency, and the evaluations of these responses in industrial environment to be conducted properly. The innovation of the work is the assessment of these process parameters and responses are using the probabilistic multi-objective methodology.

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Discrete Optimization
Mathematics and Computing > Mathematics > Optimization > Discrete Optimization