In this paper, a special nonlinear bilevel programming problem (nonlinear BLPP) is transformed into an equivalent single objective nonlinear programming problem. To solve the equivalent problem effectively, we first construct a specific optimization problem with two objectives. By solving the specific problem, we can decrease the leader’s objective value, identify the quality of any feasible solution from infeasible solutions and the quality of two feasible solutions for the equivalent single objective optimization problem, force the infeasible solutions moving toward the feasible region, and improve the feasible solutions gradually. We then propose a new constraint-handling scheme and a specific-design crossover operator. The new constraint-handling scheme can make the individuals satisfy all linear constraints exactly and the nonlinear constraints approximately. The crossover operator can generate high quality potential offspring. Based on the constraint-handling scheme and the crossover operator, we propose a new evolutionary algorithm and prove its global convergence. A distinguishing feature of the algorithm is that it can be used to handle nonlinear BLPPs with nondifferentiable leader’s objective functions. Finally, simulations on 31 benchmark problems, 12 of which have nondifferentiable leader’s objective functions, are made and the results demonstrate the effectiveness of the proposed algorithm.

An optimal allocation model for the subprocessing-element (sub-PE) level redundancy is developed, which is solved by the genetic algorithms. In the allocation model, the average defect density D and the parameter δ are also considered in order to accurately analyze the element yield, where δ is defined as the ratio of the support circuit area to the total area of a PE. When the PE’s area is imposed on the constraint, the optimal solutions of the model with different D and δ are calculated. The simulation results indicate that, for any fixed average defect density D, both the number of the optimal redundant sub-circuit added into a PE and the PE’s yield decrease as δ increases. Moreover, for any fixed parameter δ, the number of the optimal redundant sub-circuit increases, while the optimal yield of the PE decreases, as D increases.

A new reflector shaping technique to improve the beam scanning capability of hybrid antennas (i.e., a reflector system illuminated by a phased array) is presented. Errors between the desired scan directions and the outgoing rays’ directions in the scanning range are minimized by adjusting the reflector shape. This technique can be used to decrease the active element number of the feed array during the antenna scans, or reduce the gain loss caused by beam scanning when the number of active elements is given. An offset reflector antenna system is designed and analyzed, through which the validity of the technique is demonstrated.

The application of the new nonlinear optimization algorithms to arrays design is demonstrated by the low-side-lobe pattern synthesis of conformal arrays. By adopting the information of array element realized gain patterns (RGP’s), we formulate synthesis problems as nonlinearly constrained optimization problems, and propose a new direct method to solve them. The technique allows one to find a new direct method to solve them. The technique allows one to find a set of array coefficients that yield a pattern meeting a specified side-lobe level and achieving the maximum directivity, if such a set of array coefficients exists. If the side-lobe specifications cannot be met with the given array, the technique will result in a set of coefficients that yield a pattern meeting the best attainable side-lobe level and having directivity as high as possible. Also, simplified synthesis problems for an axial dipole array in an infinite, perfectly conducting cylinder are discussed, and numerical synthesis results are given. Our synthesis technique works for general array patterns.

In this paper, a hybrid genetic algorithm for solving constrained optimization problems is addressed. First, a real-coded genetic algorithm is presented. The simplified quadratic interpolation method is then integrated into the genetic algorithm to improve its local search ability and the accuracy of the minimum function value. Simulation results on 13 benchmark problems show that the proposed hybrid algorithm is able to avoid the premature convergence and find much better solutions with high speed compared to other existing algorithms.