New Mean and Median Techniques to Solve Multiobjective Linear Fractional Programming Problem and Comparison with Other Techniques

IF 1 Q3 ENGINEERING, MULTIDISCIPLINARY
Getaye Fentaw, Adane Akate
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引用次数: 0

Abstract

In the field of operation research, both linear and fractional programming problems have been more encountered in recent years because they are more realistic in expressing real-life problems. Fractional programming problem is used when several rates need to be optimized simultaneously such as resource allocation planning, financial and corporate planning, healthcare, and hospital planning. There are several techniques to solve the multiobjective linear fractional programming problem. However, because of the use of scalarization, these techniques have some limitations. This paper proposed two new mean and median techniques to solve the multiobjective linear fractional programming problem by overcoming the limitations. After utilizing mean and median techniques, the problem is converted into an equivalent linear fractional programming problem; then, the linear fractional programming problem is transformed into linear programming problem and solved by the conventional simplex method or mathematical software. Some numerical examples have been illustrated to show the efficiency of the proposed techniques and algorithm. The performance of these solutions was evaluated by comparing their results with other existing methods. The numerical results have shown that the proposed techniques are better than other techniques. Furthermore, the proposed techniques solve a pure multiobjective maximization problem, which is even impossible with some existing techniques. The present investigation can be improved further, which is left for future research.
解决多目标线性分式编程问题的新平均值和中值技术及其与其他技术的比较
在运筹学领域,线性规划问题和分式规划问题都是近年来比较常见的问题,因为它们在表达现实问题时更加真实。当需要同时优化多个比率时,如资源分配规划、财务和企业规划、医疗保健和医院规划等,就会用到分数规划问题。有多种技术可以解决多目标线性分式编程问题。然而,由于使用了标量化,这些技术都有一些局限性。本文提出了两种新的均值和中值技术来解决多目标线性分式编程问题,克服了这些局限性。利用均值和中值技术后,问题被转化为等效的线性分式编程问题;然后,线性分式编程问题被转化为线性编程问题,并通过传统的单纯形法或数学软件求解。一些数值示例说明了所提技术和算法的效率。通过与其他现有方法进行比较,对这些解决方案的性能进行了评估。数值结果表明,建议的技术优于其他技术。此外,所提出的技术还能解决纯粹的多目标最大化问题,而这在某些现有技术中甚至是不可能实现的。目前的研究还可以进一步改进,这有待于今后的研究。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Optimization
Journal of Optimization ENGINEERING, MULTIDISCIPLINARY-
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