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Network Design is very common problem which contributes key role in many real life applications which arose directly from everyday practice in engineering and management: determining shortest or most reliable paths in traffic or communication networks, maximal or compatible flows or shortest tours; planning connections in traffic networks; coordinating projects; and solving supply and demand problems, electricity distribution, designing of digital circuit, designing of gas pipeline, layout planning of roads and railway track, transportation and many many more. Because of vast real life application, network design has become the crucial problem in such real life applications. With the advancement of information technology our society is rapidly converting as an information society. The conversion of a society to information society means that extension of network and in this complex society, Network Design Problems are becoming increasingly critical & complex as all the types of networks are expanded and upgraded in response to consumer's information needs. The primary objective of this study is to develop a robust method based on genetic algorithm to solve this problem.