Lexi-Search algorithm to solve the minimum spanning connectivity of clustered cities to the headquarter city

Abstract

In this paper we present a variant minimum spanning problem called “Minimum Spanning Connectivity of Clustered Cities to the Headquarter City. This problem is a generalization of the Minimum Spanning Tree Problem (MST). In this sequel we developed a Lexi-Search algorithm based “Pattern Recognition Technique” to solve this problem which takes care of simple combinatorial structure of the problem and computational results are reported. In this conversation, we presented an exact algorithm called Lexi-Search algorithm using pattern recognition technique to solve the MINIMUM SPANNING CONNECTIVITY OF CLUSTERED CITIES TO THE HEADQUARTER CITY. Lexi-Search algorithms are proved to be more efficient in many combinatorial problems. First the model is formulated into a zero-one programming problem. A Lexi-Search Algorithm based on Pattern Recognition Technique is developed for getting an optimal solution. The problem is illustrated with help of suitable numerical example in detail. We planned the proposed algorithm using C-language. The computational details are reported and compare the existing results with the published paper. As an observation the CPU run time is reasonably less for higher values of the problem to obtain an optimal solution than the published model. Based on this experience we strongly consider that this algorithm can perform larger size problems.