A Multidimensional Approach for Solving Multi-Objective Linear Programming Problems
Abstract
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 his ability to decide. Multi-dimensional scaling (MDS) gives this capability to 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 on R^2. Start by building a matrix from a collection of points and then use clustering to optimize the matrix dimensions and configure the points in R^2. The matrix has (k_1*2) dimensions, where k_1 is the big cluster of the points. Also, a center of points was used to find the scaling points, and then the center of 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: multi-dimensional scaling; multi-objective linear programming; comprise solution; optimal advanced; quadratic average; optimal 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 R^2: dimulai dengan membangun matriks dari kumpulan titik, lalu gunakan pengelompokan untuk mengoptimalkan dimensi matriks dan mengonfigurasi titik-titik di R^2. Matriks memiliki dimensi (k_1*2), dimana k_1 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: skala multidimensi; pemrograman linier multiobjektif; solusi terpadu; lanjutan optimal, rata-rata kuadratik, rata-rata optimal.
2020MSC: 90C29, 90C90.
Keywords
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DOI: 10.15408/inprime.v7i1.45661
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