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Hybrid ant colony optimization algorithm with binary gray wolf optimization for detour metric dimension and bi-metric dimension problem | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 05 اردیبهشت 1404 | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.29133.1855 | ||
| نویسندگان | ||
| H. Hendy1، 2؛ Mohammad Isa Irawan* 1؛ Imam Mukhlash1؛ R. Rinurwati1 | ||
| 1Department of Mathematics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia | ||
| 2Faculty of Engineering, Universitas Kadiri, Kediri, Indonesia | ||
| چکیده | ||
| In this work, two class NP-hard optimization problems on the graph are discussed: the detour metric dimension and the bi-metric dimension. Both are used in many distinct areas, as well as pattern recognition, keeping track of the movement of robots on a network, and reviewing the structural properties of chemical structures. The metric dimension $dim(G)$ of graph $G$ is the minimum number of vertices such that every vertex of $G$ is uniquely assigned by its vector of distances to the selected vertices. This concept was expanded into the detour metric dimension $D\beta(G)$ and the bi-metric dimension $\beta_{b}(G)$ by considering the detour distance of two vertices. A computational approach is needed to solve these two problems on large graphs. In this research, we propose the BGWO algorithm to determine the metric dimension of some generalized antiprism graphs. In addition, we develop a probabilistic-based metaheuristic algorithm, namely ant colony optimization, to find the detour distance and then modify the binary gray wolf optimization (BGWO) algorithm to solve the detour metric dimension and the bi-metric dimension on some families of graphs. The simulation shows that the BGWO algorithm gives better results for the generalized antiprism graphs. Also, the hybrid ACO-BGWO algorithm gives the same detour dimension result as in the literature. We show that the bi-metric dimension of the generalized antiprism graph is the same as its metric dimension. | ||
| کلیدواژهها | ||
| distance in graph؛ computational intelligence؛ metaheuristic algorithm؛ resolving set | ||
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