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In layout design problems including blank nesting, the positions and directions of layout elements must be determined so as to minimize the total space. It is difficult and computationally time-consuming to find the optimal solution for such layout problems, because they include a lot of underlying combinational conditions. In this paper, we present an approach for optimal nesting by combining a genetic algorithm and a local minimization algorithm. In the approach, the genetic algorithm is used for handling the combinations which are represented in the string, and the local minimization algorithm is used for determining the embodiment layout under the fixed combinations so as to minimize the scrap volume which is corresponding to the fitness value in the genetic algorithm. And we present an example for showing the effective nesting result produced by this approach.

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ABSTRACT

This paper proposes a mini-max type formulation for strict robust design optimization under correlative variation based on design variation hyper sphere and quadratic polynomial approximation. While various types of formulations and techniques have been developed for computational robust design, they confront the compromise among modeling of parameter variation, feasibility assessment, definition of optimality such as sensitivity, and computational cost. The formulation of this paper aims that all points within the distribution region are thoroughly optimized. For this purpose, the design space with correlative variation is diagonalized and isoparameterized into a hyper sphere, and the functions of nominal constraints and the nominal objective are modeled as quadratic polynomials. These transformation and approximation enable the analytical discrimination of inner or boundary type on the worst design and its quantified values with less computation cost under a certain condition, and bring the procedural definition of the strictly robust optimality of a design as a maximization problem. The minimization of this formulation, that is, mini-max type optimization, can find the robust design under the above meaning. Its validity is ascertained through numerical examples.