Optimality conditions via a unified direction approach for (approximate) efficiency in multiobjective optimization
Optimality conditions via a unified direction approach for (approximate) efficiency in multiobjective optimization
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DOI：
10.1080/10556788.2019.1571589
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发表时间：
2019-02
影响因子：
2.2
通讯作者：
M. Ghaznavi;F. Akbari;E. Khorram
中科院分区：
文献类型：
--
作者：
M. Ghaznavi;F. Akbari;E. Khorram
本文讨论了多目标优化问题的标量化技术。提出了一种求解一般多目标优化问题的新标量化方法。这种标量化方法被称为统一方向方法，因为它推广了帕斯科莱蒂-塞拉菲尼方法（方向方法）。建立了与所建议的标量化技术相关的一些理论结果，特别是显示了该方法生成（正确、弱）有效解的能力。此外，所提出的单目标问题的近似最优解和多目标优化问题的近似（弱，适当）有效解之间的关系进行了研究。事实上，易于检查，必要和充分条件的弱（弱，正常）有效性。最后，通过算例说明了该方法的有效性。
The presented paper addresses scalarization techniques for multiobjective optimization problems. A new scalarization technique for solving a general multiobjective optimization problem is proposed. This scalarization method is called the unified direction method, because it generalizes the Pascoletti–Serafini approach (direction approach). Some theoretical results related to the suggested scalarization technique are established, especially the ability of the method for generating (properly, weakly) efficient solutions is shown. Moreover, the relation between approximate optimal solutions of the proposed single objective problem and approximate (weakly, properly) efficient solutions of the multiobjective optimization problem is investigated. In fact, easy-to-check, necessary and sufficient conditions for ϵ-(weak, proper) efficiency are obtained. Moreover, the effectiveness of the proposed approach is illustrated with some illustrative computational examples.