A Multidimensional Approach for Solving Multi-Objective Linear Programming Problems
DOI:
https://doi.org/10.15408/tc5hws29Keywords:
Comprise solution, Multi-dimensional scaling, multi-objective linear programming, Optimal advanced transformation, Optimal average., Quadratic averageAbstract
Solving multi-objective linear programming problems (MOLPP) is a great challenge because it is essential in many real-life problems, especially manufacturing. Choosing the best solution is the goal of the decision-maker to produce a possibility to improve their ability to decide. Multi-dimensional scaling (MDS) gives this capability to make the right decision. In this study, we develop the MDS method for (MOLPP) in the work of Mrakhan et al. (2020). The method depends on embedding points in R2. Start by building a matrix from a collection of points, and then use clustering to optimize the matrix dimensions and configure the points in R2. The matrix has (k1*2) dimensions, where k1 is the big cluster of the points. Also, a center of points was used to find the scaling points, and then the center of the generated points was used to find a distance from the origin (0,0). Our proposed algorithm offers a structured, efficient compromise solution for MOLPPs, outperforming traditional scalarization-based methods.
Keywords: Comprise solution; Multi-dimensional scaling; Multi-objective linear programming; Optimal advanced; Optimal average; Quadratic average.
Abstrak
Menyelesaikan masalah pemrograman linier multiobjektif (MOLPP) merupakan tantangan besar karena sangat penting dalam banyak masalah kehidupan nyata, terutama manufaktur. Memilih solusi terbaik adalah tujuan pembuat keputusan untuk menciptakan kemungkinan guna meningkatkan kemampuan mereka dalam mengambil keputusan. Penskalaan multidimensi (MDS) memberikan kemampuan ini untuk keputusan yang tepat. Pada studi ini, akan dikembangkan metode MDS untuk (MOLPP) dalam karya Mrakhan et al. (2020). Metode ini bergantung pada penyematan titik-titik di R2: dimulai dengan membangun matriks dari kumpulan titik, lalu gunakan pengelompokan untuk mengoptimalkan dimensi matriks dan mengonfigurasi titik-titik di R2. Matriks memiliki dimensi (k1*2), dimana k1 adalah klaster besar titik-titik. Selain itu, titik pusat digunakan untuk menemukan titik penskalaan, kemudian titik pusat tersebut digunakan untuk menemukan jarak dari titik asal (0,0). Algoritma yang kami usulkan menawarkan solusi kompromi yang terstruktur dan efisien untuk MOLPP, yang mengungguli metode berbasis skalarisasi tradisional.
Kata Kunci: Solusi terpadu; Skala multidimensi; Pemrograman linier multiobjektif; Lanjutan optimal; Rata-rata optimal; Rata-rata kuadratik.
2020MSC: 90C29, 90C90
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