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Determining approximate efficient solutions of multiobjective optimization problems using the combined constrained scalarization method | ||
Journal of New Researches in Mathematics | ||
مقاله 8، دوره 6، شماره 25، آذر و دی 2020، صفحه 113-128 اصل مقاله (427.7 K) | ||
نوع مقاله: research paper | ||
نویسندگان | ||
Mehrdad Ghaznavi 1؛ Fereshteh Akbari2؛ Esmaile Khorram3 | ||
1Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran | ||
2Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, ‎Iran | ||
3Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No.424, Hafez Avenue, Tehran, Iran | ||
چکیده | ||
In this paper, approximate efficient ( -efficient) solutions of multiobjective optimization problems are investigated. One of the most important methods for solving multiobjective optimization problems is to use scalarization techniques. In these methods, a single objective optimization problem corresponding to the multiobjective problem is solved, and the relationship between optimal solutions of the single objective problem and (weakly, properly) efficient solutions of the multiobjective problem is investigated. In this paper, a combination of the modified constrained and elastic constrained scalarization methods is considered, which will provide necessary and sufficient conditions for generating approximate (weakly, properly) efficient solutions. We compare the results with the necessary and sufficient conditions obtained from the modified constrained and the elastic constrained methods. The presented results can be applied for every multiobjective optimization problem without any convexity assumption for the objective functions. Unlike many of the previous methods, the obtained results are also consistent with multiobjective problems with unbounded criterion space. | ||
کلیدواژهها | ||
Multiobjective optimization؛ Scalarization method. Approximate efficient solutions؛ Proper efficiency؛ Approximate optimality. | ||
مراجع | ||
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