Variable Decomposition for Large-Scale Constrained Optimization Problems Using a Grouping Genetic Algorithm

Abstract

Several real optimization problems are very difficult, and their optimal solutions cannot be found with a traditional method. Moreover, for some of these problems, the large number of decision variables is a major contributing factor to their complexity; they are known as Large-Scale Optimization Problems, and various strategies have been proposed to deal with them. One of the most popular tools is called Cooperative Co-Evolution, which works through a decomposition of the decision variables into smaller subproblems or variables subgroups, which are optimized separately and cooperate to finally create a complete solution of the original problem. This kind of decomposition can be handled as a combinatorial optimization problem where we want to group variables that interact with each other. In this work, we propose a Grouping Genetic Algorithm to optimize the variable decomposition by reducing their interaction. Although the Cooperative Co-Evolution approach is widely used to deal with unconstrained optimization problems, there are few works related to constrained problems. Therefore, our experiments were performed on a test benchmark of 18 constrained functions under 100, 500, and 1000 variables. The results obtained indicate that a Grouping Genetic Algorithm is an appropriate tool to optimize the variable decomposition for Large-Scale Constrained Optimization Problems, outperforming the decomposition obtained by a state-of-the-art genetic algorithm.

Implementasi Algoritma Genetika untuk Aplikasi Penjadwalan Sistem Kerja Shift

“…Kinerja algoritma genetika berkerja dalam bentuk kode sekumpulan parameter [11], Untuk menyelesaikan masalah yang lebih rumit, algoritma genetika terintegrasi menggunakan metode hibridisasi untuk meningkatkan efektivitas kinerjanya [12]. Pencarian dilakukan dengan populasi dari masalah penjadwalan di representasikan menjadi string kromosom [13,14] serta berinterkasi dalam sub komponen [15] .…”

Numerical and Evolutionary Optimization 2021

“…In [8], Carmona-Arroyo et al propose a grouping genetic algorithm (GGA) to deal with the decomposition of decision variables in order to efficiently tackle large-scale optimization problems. Although the cooperative co-evolution approach is widely used to deal with unconstrained optimization problems, there are few works related to constrained problems.…”