Abstract-Minimum Routing Cost Spanning Tree (MRCT) is one of spanning tree optimization problems having several applications in network design. In general case, the problem is proved to be NP-hard. The paper uses genetic (GA) approach to solve MRCT problem. Computational experiment results show that GA approach outperforms current approximation algorithms.
Abstract-Minimum routing cost spanning tree -MRCT is one of spanning tree optimization problems having many applications in network design. In general cases, the problem is proved as NP-hard. This paper is going to propose 2 heuristic-based algorithms used for MRCT. The general idea of those algorithms is to start at a spanning tree and step by step improve edges to obtain better spanning tree. We conducted experiment implemetations for these proposals and obtained better result than the result of current approximate algorithms.Index Terms-Routing cost spanning tree, heuristic algorithm, gradually edge-removal algorithm, gradually edgereplacement algorithm.
I. MINIMUM ROUTING-COST SPANNING TREE PROBLEMIn this section, we are going to represent some main terms related to MRCT problem, traditional approachs and their drawbacks.Given G = (V,E,w) is an undirected connected graph having non-negative edge weights (costs); in which V is the node set, E is the edge set, w is the cost matrix. Suppose T is a spanning tree in G, the routing cost of T, denoted by C(T), is the total routing costs of all vertex pairs in T, in which the routing cost of a vertex pair (u,v) in T, denoted by d T (u,v), is the sum over edge costs on the path connecting vertex u and vertex v in T. So, by definitions, we have:
Minimum Routing Cost Spanning Tree problem — MRCT is one of the spanning tree problems having several applications in network designing; this problem belongs to class of NP—hard. In this paper, we will apply Particle Swarm Optimization algorithm — PSO into MCRT problem, compare the effectivity of Genetic algorithm and PSO for MRCT problem and concurrently exploit the combining of PSO with other metaheuristic algorithms.
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