Neutral networks, which occur in fitness landscapes containing neighboring points of equal fitness, have attracted much research interest in recent years. In our recent papers, we have shown that, in the case of simple test functions, the mutation rate of a genetic algorithm is an important factor for improving the speed at which a population moves along a neutral network. Our results also suggested that the benefits of the variable mutation rate strategy used by the operon-GA increase as the ruggedness of the landscapes increases. In this paper, we conducted a series of computer simulations with evolutionary robotics (ER) problems in order to investigate whether our previous results are applicable to this problem domain. The evolutionary dynamics we observed were consistent with those observed in our previous experiments, confirming that the variable mutation rate strategy is also beneficial to the ER problems.
In this paper, we propose a model reduction method by truncation of the balanced realization associated with the sine-wave response observability gramian and the controllability gramian. A feature of the present model reduction method is that the transfer function's value of the reduced-order model is equal to that of the original model at some frequency points. This method is also shown to provide the reduced-order model which minimizes an error norm of the model reduction.
Pass schedules for a tandem cold mill have been optimized using the chance constrained programming method. Variations of variables are evaluated from past data without assuming probability distributions. Discrete constraints are smoothed with the sigmoid functions, and the sequential quadratic programming method is applied. Furthermore, the constraints are relaxed individually on a priority basis so that a feasible and practical solution is obtained. Experimental results with high tensile strength steel strips showed 13 to 35% decreases in off-gage length.
We consider the problem of designing optimal smoothing spline curves by employing an approach based on linear control systems. First, the problem is formulated using continuous-time, time-invariant systems with piecewise constant inputs. Then by introducing discrete time-varying systems, the solutions for optimal splines including periodic splines are derived. The existence conditions for unique optimal solutions are established and linked to the concepts of controllability and observability. The computational procedures for the optimal splines are straightforward. The design method for periodic splines is applied to a shape synthesizing problem using jellyfish as the example.