Genetic algorithm approach to generating the optimal development of a thin-walled object

The authors present a new method for generating the optimal development of a thin-walled object. The design of developments of thin-walled objects such as ventilation pipes is very important in the industry, where many complex development patterns are required. Although many CAD systems have been developed for this purpose, none to date has been able to satisfy this sort of practical demands because they are only applicable to limited patterns. For example, studies based on the flattening technique applicable to some developable figures have been reported. This may be the first report with respect to the optimal selection of bending lines for the development of an object. In this work, GA is adopted, where a new coding method and a fitness function are introduced that pool the experience of experts in the field and take into account all physical aspects of this domain. Additional conditions for generating only feasible developments are also considered. The phenotype of each solution is expressed in the form of a 0–1 matrix, which describes the conditions mentioned above, and the genotype is expressed as a starting point and a zigzag (right and down) path in the matrix. In addition, an ‘alternative path representation’ is proposed for the coding of GA. The fitness function is made up of two objective functions, the first of which describes the total length of bending lines that link two sample points surrounding the entrance and the exit, respectively; the second of which describes the smoothness of changes in directions of normal vectors of the generated side surface. The coding method of ‘alternative path representation’ is effective enough for speeding up the calculation. It has been confirmed through several experiments that the method presented here is sufficiently applicable to the generation of a variety of development-patterns required by the industry.