Target shape design optimization by evolving splines

Target shape design optimization problem (TS-DOP) is a miniature model for real world design optimization problems. It is proposed as a test bed to design and analyze optimization approaches for design optimization with tremendously reducing the running period of optimization process, while, the merit can be only achieved by correctly approximating the real design situation and satisfying the causality of design and evaluation. The representation of the designed object is mostly described by parameterization techniques. To realize the design optimization, is to vary the parameterized object by means of operating the relevant parameters. The solution of design optimization often involved the choice of suitable description for the designed object, which can be obtained by expanding the design freedom. When changing the description length, the original parameters of the designed object will then varied. This bring about the requirements for optimization algorithms to self-adapt their strategy parameters and related variables to perform consistently searching. We first put forwards a revised fitness evaluation mechanism for the TSDOP in order to more reasonably check the designed shape and direct optimization procedures. Based on the revised TSDOP framework, we further discuss the parameter setting problem for algorithms, especially evolution strategies, to adapt and initial their search strategy parameters. A solution method is proposed with solving a linear equations by a recursive way with linear time complexity. All discussions are limited with the B-spline parameterization framework, but may generally suit other parameterization techniques. Experiments are used to verify the causality of the revised fitness evaluation mechanism and to study the significance of the proposed method for suitable parameter settings of optimization algorithms during the adaptation of the description length for design optimization.