BINARY FRUIT FLY OPTIMIZATION ALGORITHM FOR COUNTING THE NUMBER OF SPANNING TREES IN NETWORKS

Abstract

The NP-hard problem of determining the number of spanning trees of graphs is examined in this paper. A spanning tree of a graph is a tree such that (i) it is a subgraph of (i.e., that includes only edges from ), and (ii) it includes every vertex of . The most classical interest concerning a spanning tree is the number of spanning trees or the complexity of the graph denoted by We propose the first attempt to use a binary version of the fruit fly optimization algorithm (BFFOA) to compute the minimal spanning tree of a graph in a heuristic manner. The fruit fly of BFFOA is binary encoded and used to represent which one of the vertices of the graph belongs to the spanning tree of . The feasibility is enforced by repairing the fruit fly such that an extra vertex created from vertices of is added to , and this repairing process is repeated until becomes the spanning tree of . Theoretically computed graph results are used to compare the proposed BFFOA against competing techniques. The proposed BFFOA performs better than the binary Grey Wolf Optimizer (BGWO), the binary Particle Swarm Optimizer (BPSO), the binary Whale Optimizer (BWO), and the binary Multi-verse Optimization (BMVO) algorithms, according to analysis and computational results.