Probably the most popular algorithm for unconstrained minimization for problems of moderate dimension is the Nelder-Mead algorithm published in 1965. Despite its age only limited convergence results exist. Several counterexamples can be found in the literature for which the algorithm performs badly or even fails. A convergent variant derived from the original Nelder-Mead algorithm is presented. The proposed algorithm's convergence is based on the principle of grid restrainment and therefore does not require sufficient descent as the recent convergent variant proposed by Price, Coope, and Byatt. Convergence properties of the proposed grid-restrained algorithm are analysed. Results of numerical testing are also included and compared to the results of the algorithm proposed by Price et al. The results clearly demonstrate that the proposed grid-restrained algorithm is an efficient direct search method.

We used genetic programming to evolve a direct search optimization algorithm, similar to that of the standard downhill simplex optimization method proposed by Nelder and Mead ( 1965 ). In the training process, we used several ten-dimensional quadratic functions with randomly displaced parameters and different randomly generated starting simplices. The genetically obtained optimization algorithm showed overall better performance than the original Nelder-Mead method on a standard set of test functions. We observed that many parts of the genetically produced algorithm were seldom or never executed, which allowed us to greatly simplify the algorithm by removing the redundant parts. The resulting algorithm turns out to be considerably simpler than the original Nelder-Mead method while still performing better than the original method.

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Abstract:The ever-shorter time-to-market calls for efficient robust IC design algorithms. Robust circuits satisfy all design requirements across a range of operating conditions and manufacturing process variations. In the paper we propose an automated robust IC design and optimization process derived from the design algorithms utilized manually by experienced analog IC designers. We achieve this by transforming the robust design and optimization problem into a constrained optimization problem using tradeoff planes and penalty functions. We illustrate the method on a robust differential amplifier design problem. Circuits resulting from several different optimization runs show that a computer can not only improve existing circuit designs but it can also size a circuit with very little initial knowledge. The resulting circuits have comparable or even superior performance to humanly designed circuits. The method could easily take advantage of parallel processing but is still efficient enough to be run on a single computer.

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