Optimization of parameters for binary genetic algorithms.

In the GA framework, a species or population is a collection of individuals or chromosomes, usually initially generated randomly. A predefined fitness function guides selection while operators like crossover and mutation are used probabilistically in order to emulate reproduction.Genetic Algorithms (GAs) belong to the field of evolutionary computation which is inspired by biological evolution. From an engineering perspective, a GA is an heuristic tool that can approximately solve problems in which the search space is huge in the sense that an exhaustive search is not tractable. The appeal of GAs is that they can be parallelized and can give us "good" solutions to hard problems.One of the difficulties in working with GAs is choosing the parameters---the population size, the crossover and mutation probabilities, the number of generations, the selection mechanism, the fitness function---appropriate to solve a particular problem. Besides the difficulty of the application problem to be solved, an additional difficulty arises because the quality of the solution found, or the sum total of computational resources required to find it, depends on the selection of the parameters of the GA; that is, finding a correct fitness function and appropriate operators and other parameters to solve a problem with GAs is itself a difficult problem. The contributions of this dissertation, then, are: to show that there is not a linear correlation between diversity in the initial population and the performance of GAs; to show that fitness functions that use information from the problem itself are better than fitness functions that need external tuning; and to propose a relationship between selection pressure and the probabilities of crossover and mutation that improve the performance of GAs in the context of of two extreme schema: small schema, where the building block in consideration is small (each bit individually can be considered as part of the general solution), and long schema, where the building block in consideration is long (a set of interrelated bits conform part of the general solution).Theoretical and practical problems like the one-max problem and the intrusion detection problem (considered as problems with small schema) and the snake-in-the-box problem (considered as a problem with long schema) are tested under the specific hypotheses of the Dissertation.The Dissertation proposes three general hypotheses. The first one, in an attempt to measure the impact of the input over the output, study that there is not a linear correlation between diversity in the initial population and performance of GAs. The second one, proposes the use of parameters that belong to the problem itself to joint objective and constraint in fitness functions, and the third one use Holland's Schema Theorem for finding an interrelation between selection pressure and the probabilities of crossover and mutation that, if obeyed, is expected to result in better performance of the GA in terms of the solution quality found within a given number of generations and/or the number of generations to find a solution of a given quality than if the interrelation is not obeyed

Coupling Matrix Representation of Nonreciprocal Filters Based on Time Modulated Resonators

This paper addresses the analysis and design of non-reciprocal filters based on time modulated resonators. We analytically show that time modulating a resonator leads to a set of harmonic resonators composed of the unmodulated lumped elements plus a frequency invariant element that accounts for differences in the resonant frequencies. We then demonstrate that harmonic resonators of different order are coupled through non-reciprocal admittance inverters whereas harmonic resonators of the same order couple with the admittance inverter coming from the unmodulated filter network. This coupling topology provides useful insights to understand and quickly design non-reciprocal filters and permits their characterization using an asynchronously tuned coupled resonators network together with the coupling matrix formalism. Two designed filters, of orders three and four, are experimentally demonstrated using quarter wavelength resonators implemented in microstrip technology and terminated by a varactor on one side. The varactors are biased using coplanar waveguides integrated in the ground plane of the device. Measured results are found to be in good agreement with numerical results, validating the proposed theory

Nonreciprocal Wavefront Engineering with Time-Modulated Gradient Metasurfaces

We propose a paradigm to realize nonreciprocal wavefront engineering using time-modulated gradient metasurfaces. The essential building block of these surfaces is a subwavelength unit cell whose reflection coefficient oscillates at low frequency. We demonstrate theoretically and experimentally that such modulation permits tailoring the phase and amplitude of any desired nonlinear harmonic and determines the behavior of all other emerging fields. By appropriately adjusting the phase delay applied to the modulation of each unit cell, we realize time-modulated gradient metasurfaces that provide efficient conversion between two desired frequencies and enable nonreciprocity by (i) imposing drastically different phase gradients during the up/down conversion processes and (ii) exploiting the interplay between the generation of certain nonlinear surface and propagative waves. To demonstrate the performance and broad reach of the proposed platform, we design and analyze metasurfaces able to implement various functionalities, including beam steering and focusing, while exhibiting strong and angle-insensitive nonreciprocal responses. Our findings open an alternative direction in the field of gradient metasurfaces, in which wavefront control and magnetic-free nonreciprocity are locally merged to manipulate the scattered fields