In this paper, we propose a new combined scalarization method of multi-objective optimization problems by using the surplus variables and the generalized Tchebycheff norm and then use it to obtain some equivalent scalarization characterizations of (weakly, strictly, properly) efficient solutions by adjusting the range of parameters. These scalarization results do not need any convexity assumption conditions of objective functions. Furthermore, we establish some scalarization results of approximate solutions by means of the method. Moreover, we also present some examples to illustrate the main results.

中文翻译：

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一种多目标优化问题的组合标量化方法

在本文中，我们通过使用剩余变量和广义 Tchebycheff 范数提出了一种新的多目标优化问题的组合标化方法，然后通过调整参数范围。这些标化结果不需要任何目标函数的凸性假设条件。此外，我们还通过该方法建立了一些近似解的标化结果。此外，我们还提供了一些示例来说明主要结果。