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This paper presents a technique for applying genetic algorithms for the two dimensional packing problem. The approach is applicable to not only convex shaped objects, but, can also accommodate any type of concave and complex shaped objects including objects with holes. In this approach, a new concept of a two dimensional genetic chromosome is introduced. The total layout space is divided into a finite number of cells for mapping it into this 2-D genetic algorithm chromosome. The mutation and crossover operators have been modified and are applied in conjunction with connectivity analysis for the objects to reduce the creation of faulty generations. A new feature has been added to the genetic algorithm(GA) in the form of a new operator called compaction. Several examples of GA based layout are presented.