A Chaotic Approach of Differential Evolution Optimization Applied to Loudspeaker Design Problem

Over the past few years, the field of global optimization has been very active, producing different kinds of deterministic and stochastic algorithms for optimization in the continuous domain. These days, the use of evolutionary algorithms (EAs) to solve optimization problems is a common practice due to their competitive performance on complex search spaces. EAs are well known for their ability to deal with nonlinear and complex optimization problems. Differential evolution (DE) algorithms are a family of evolutionary optimization techniques that use a rather greedy and less stochastic approach to problem solving, when compared to classical evolutionary algorithms. The main idea is to construct, at each generation, for each element of the population a mutant vector, which is constructed through a specific mutation operation based on adding differences between randomly selected elements of the population to another element. Due to its simple implementation, minimum mathematical processing and good optimization capability, DE has attracted attention. This paper proposes a new approach to solve electromagnetic design problems that combines the DE algorithm with a generator of chaos sequences. This approach is tested on the design of a loudspeaker model with 17 degrees of freedom, for showing its applicability to electromagnetic problems. The results show that the DE algorithm with chaotic sequences presents better, or at least similar, results when compared to the standard DE algorithm and other evolutionary algorithms available in the literature.

Multiobjective Biogeography-Based Optimization Based on Predator-Prey Approach

Biogeography is the science that studies the geographical distribution and the migration of species in an ecosystem. Biogeography-based optimization (BBO) is a recently developed global optimization algorithm as a generalization of biogeography to evolutionary algorithm and has shown its ability to solve complex optimization problems. BBO employs a migration operator to share information between the problem solutions. The problem solutions are identified as habitat, and the sharing of features is called migration. In this paper, a multiobjective BBO, combined with a predator-prey (PPBBO) approach, is proposed and validated in the constrained design of a brushless dc wheel motor. The results demonstrated that the proposed PPBBO approach converged to promising solutions in terms of quality and dominance when compared with the classical BBO in a multiobjective version.

Space trajectories optimization using variable-chromosome-length genetic algorithms

The problem of optimal design of a multi-gravity-assist space trajectories, with free number of deep space maneuvers (MGADSM) poses multi-modal cost functions. In the general form of the problem, the number of design variables is solution dependent. To handle global optimization problems where the number of design variables varies from one solution to another, two novel genetic-based techniques are introduced: hidden genes genetic algorithm (HGGA) and dynamic-size multiple population genetic algorithm (DSMPGA). In HGGA, a fixed length for the design variables is assigned for all solutions. Independent variables of each solution are divided into effective and ineffective (hidden) genes. Hidden genes are excluded in cost function evaluations. Full-length solutions undergo standard genetic operations. In DSMPGA, sub-populations of fixed size design spaces are randomly initialized. Standard genetic operations are carried out for a stage of generations. A new population is then created by reproduction from all members based on their relative fitness. The resulting sub-populations have different sizes from their initial sizes. The process repeats, leading to increasing the size of sub-populations of more fit solutions. Both techniques are applied to several MGADSM problems. They have the capability to determine the number of swing-bys, the planets to swing by, launch and arrival dates, and the number of deep space maneuvers as well as their locations, magnitudes, and directions in an optimal sense. The results show that solutions obtained using the developed tools match known solutions for complex case studies. The HGGA is also used to obtain the asteroids sequence and the mission structure in the global trajectory optimization competition (GTOC) problem. As an application of GA optimization to Earth orbits, the problem of visiting a set of ground sites within a constrained time frame is solved. The J2 perturbation and zonal coverage are considered to design repeated Sun-synchronous orbits. Finally, a new set of orbits, the repeated shadow track orbits (RSTO), is introduced. The orbit parameters are optimized such that the shadow of a spacecraft on the Earth visits the same locations periodically every desired number of days.

An optimization method for conceptual design in engineering systems based on high order singular value decomposition

Se presenta un nuevo método de diseño conceptual en Ingeniería Aeronáutica basado el uso de modelos reducidos, también llamados modelos sustitutos (‘surrogates’). Los ingredientes de la función objetivo se calculan para cada indiviudo mediante la utilización de modelos sustitutos asociados a las distintas disciplinas técnicas que se construyen mediante definiciones de descomposición en valores singulares de alto orden (HOSVD) e interpolaciones unidimensionales. Estos modelos sustitutos se obtienen a partir de un número limitado de cálculos CFD. Los modelos sustitutos pueden combinarse, bien con un método de optimización global de tipo algoritmo genético, o con un método local de tipo gradiente. El método resultate es flexible a la par que mucho más eficiente, computacionalmente hablando, que los modelos convencionales basados en el cálculo directo de la función objetivo, especialmente si aparecen un gran número de parámetros de diseño y/o de modelado. El método se ilustra considerando una versión simplificada del diseño conceptual de un avión. Abstract An optimization method for conceptual design in Aeronautics is presented that is based on the use of surrogate models. The various ingredients in the target function are calculated for each individual using surrogates of the associated technical disciplines that are constructed via high order singular value decomposition and one dimensional interpolation. These surrogates result from a limited number of CFD calculated snapshots. The surrogates are combined with an optimization method, which can be either a global optimization method such as a genetic algorithm or a local optimization method, such as a gradient-like method. The resulting method is both flexible and much more computationally efficient than the conventional method based on direct calculation of the target function, especially if a large number of free design parameters and/or tunablemodeling parameters are present. The method is illustrated considering a simplified version of the conceptual design of an aircraft empennage.

Dynamic weighting in Monte Carlo and optimization

Dynamic importance weighting is proposed as a Monte Carlo method that has the capability to sample relevant parts of the configuration space even in the presence of many steep energy minima. The method relies on an additional dynamic variable (the importance weight) to help the system overcome steep barriers. A non-Metropolis theory is developed for the construction of such weighted samplers. Algorithms based on this method are designed for simulation and global optimization tasks arising from multimodal sampling, neural network training, and the traveling salesman problem. Numerical tests on these problems confirm the effectiveness of the method.

Particle Swarm Optimization Based Reactive Power Dispatch for Power Networks with Distributed Generation

Reactive power is critical to the operation of the power networks on both safety aspects and economic aspects. Unreasonable distribution of the reactive power would severely affect the power quality of the power networks and increases the transmission loss. Currently, the most economical and practical approach to minimizing the real power loss remains using reactive power dispatch method. Reactive power dispatch problem is nonlinear and has both equality constraints and inequality constraints. In this thesis, PSO algorithm and MATPOWER 5.1 toolbox are applied to solve the reactive power dispatch problem. PSO is a global optimization technique that is equipped with excellent searching capability. The biggest advantage of PSO is that the efficiency of PSO is less sensitive to the complexity of the objective function. MATPOWER 5.1 is an open source MATLAB toolbox focusing on solving the power flow problems. The benefit of MATPOWER is that its code can be easily used and modified. The proposed method in this thesis minimizes the real power loss in a practical power system and determines the optimal placement of a new installed DG. IEEE 14 bus system is used to evaluate the performance. Test results show the effectiveness of the proposed method.

On stable uniqueness in linear semi-infinite optimization

This paper is intended to provide conditions for the stability of the strong uniqueness of the optimal solution of a given linear semi-infinite optimization (LSIO) problem, in the sense of maintaining the strong uniqueness property under sufficiently small perturbations of all the data. We consider LSIO problems such that the family of gradients of all the constraints is unbounded, extending earlier results of Nürnberger for continuous LSIO problems, and of Helbig and Todorov for LSIO problems with bounded set of gradients. To do this we characterize the absolutely (affinely) stable problems, i.e., those LSIO problems whose feasible set (its affine hull, respectively) remains constant under sufficiently small perturbations.

Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem

In recent times the Douglas–Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.

Optimization of wireless power transfer via magnetic resonance in different media

A wide range of non-destructive testing (NDT) methods for the monitoring the health of concrete structure has been studied for several years. The recent rapid evolution of wireless sensor network (WSN) technologies has resulted in the development of sensing elements that can be embedded in concrete, to monitor the health of infrastructure, collect and report valuable related data. The monitoring system can potentially decrease the high installation time and reduce maintenance cost associated with wired monitoring systems. The monitoring sensors need to operate for a long period of time, but sensors batteries have a finite life span. Hence, novel wireless powering methods must be devised. The optimization of wireless power transfer via Strongly Coupled Magnetic Resonance (SCMR) to sensors embedded in concrete is studied here. First, we analytically derive the optimal geometric parameters for transmission of power in the air. This specifically leads to the identification of the local and global optimization parameters and conditions, it was validated through electromagnetic simulations. Second, the optimum conditions were employed in the model for propagation of energy through plain and reinforced concrete at different humidity conditions, and frequencies with extended Debye's model. This analysis leads to the conclusion that SCMR can be used to efficiently power sensors in plain and reinforced concrete at different humidity levels and depth, also validated through electromagnetic simulations. The optimization of wireless power transmission via SMCR to Wearable and Implantable Medical Device (WIMD) are also explored. The optimum conditions from the analytics were used in the model for propagation of energy through different human tissues. This analysis shows that SCMR can be used to efficiently transfer power to sensors in human tissue without overheating through electromagnetic simulations, as excessive power might result in overheating of the tissue. Standard SCMR is sensitive to misalignment; both 2-loops and 3-loops SCMR with misalignment-insensitive performances are presented. The power transfer efficiencies above 50% was achieved over the complete misalignment range of 0°-90° and dramatically better than typical SCMR with efficiencies less than 10% in extreme misalignment topologies.

Robust solutions of bi-blend recipe optimization with quadratic constraints

Production companies use raw materials to compose end-products. They often make different products with the same raw materials. In this research, the focus lies on the production of two end-products consisting of (partly) the same raw materials as cheap as possible. Each of the products has its own demand and quality requirements consisting of quadratic constraints. The minimization of the costs, given the quadratic constraints is a global optimization problem, which can be difficult because of possible local optima. Therefore, the multi modal character of the (bi-) blend problem is investigated. Standard optimization packages (solvers) in Matlab and GAMS were tested on their ability to solve the problem. In total 20 test cases were generated and taken from literature to test solvers on their effectiveness and efficiency to solve the problem. The research also gives insight in adjusting the quadratic constraints of the problem in order to make a robust problem formulation of the bi-blend problem.

Optimization of Wireless Power Transfer via Magnetic Resonance in Different Media

A wide range of non-destructive testing (NDT) methods for the monitoring the health of concrete structure has been studied for several years. The recent rapid evolution of wireless sensor network (WSN) technologies has resulted in the development of sensing elements that can be embedded in concrete, to monitor the health of infrastructure, collect and report valuable related data. The monitoring system can potentially decrease the high installation time and reduce maintenance cost associated with wired monitoring systems. The monitoring sensors need to operate for a long period of time, but sensors batteries have a finite life span. Hence, novel wireless powering methods must be devised. The optimization of wireless power transfer via Strongly Coupled Magnetic Resonance (SCMR) to sensors embedded in concrete is studied here. First, we analytically derive the optimal geometric parameters for transmission of power in the air. This specifically leads to the identification of the local and global optimization parameters and conditions, it was validated through electromagnetic simulations. Second, the optimum conditions were employed in the model for propagation of energy through plain and reinforced concrete at different humidity conditions, and frequencies with extended Debye's model. This analysis leads to the conclusion that SCMR can be used to efficiently power sensors in plain and reinforced concrete at different humidity levels and depth, also validated through electromagnetic simulations. The optimization of wireless power transmission via SMCR to Wearable and Implantable Medical Device (WIMD) are also explored. The optimum conditions from the analytics were used in the model for propagation of energy through different human tissues. This analysis shows that SCMR can be used to efficiently transfer power to sensors in human tissue without overheating through electromagnetic simulations, as excessive power might result in overheating of the tissue. Standard SCMR is sensitive to misalignment; both 2-loops and 3-loops SCMR with misalignment-insensitive performances are presented. The power transfer efficiencies above 50% was achieved over the complete misalignment range of 0°-90° and dramatically better than typical SCMR with efficiencies less than 10% in extreme misalignment topologies.

Modeling the optical properties of AlSb, GaSb, and InSb

Optical constants of AlSb, GaSb, and InSb are modeled in the 1-6 eV spectral range. We employ an extension of Adachi's model of the optical constants of semiconductors. The model takes into account transitions at E-0, E-0 + Delta(0), E-1, and E-1 + Delta(1) critical points, as well as higher-lying transitions which are modeled with three damped harmonic oscillators. We do not consider indirect transitions contribution, since it represents a second-order perturbation and its strength should be low. Also, we do not take into account excitonic effects at E-1, E-1 + Delta(1) critical points, since we model the room temperature data. In spite of fewer contributions to the dielectric function compared to previous calculations involving Adachi's model, our calculations show significantly improved agreement with the experimental data. This is due to the two main distinguishing features of calculations presented here: use of adjustable line broadening instead of the conventional Lorentzian one, and employment of a global optimization routine for model parameter determination.

Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure

The acceptance-probability-controlled simulated annealing with an adaptive move generation procedure, an optimization technique derived from the simulated annealing algorithm, is presented. The adaptive move generation procedure was compared against the random move generation procedure on seven multiminima test functions, as well as on the synthetic data, resembling the optical constants of a metal. In all cases the algorithm proved to have faster convergence and superior escaping from local minima. This algorithm was then applied to fit the model dielectric function to data for platinum and aluminum.

The application of adaptive partitioned random search in feature selection problem

Feature selection is one of important and frequently used techniques in data preprocessing. It can improve the efficiency and the effectiveness of data mining by reducing the dimensions of feature space and removing the irrelevant and redundant information. Feature selection can be viewed as a global optimization problem of finding a minimum set of M relevant features that describes the dataset as well as the original N attributes. In this paper, we apply the adaptive partitioned random search strategy into our feature selection algorithm. Under this search strategy, the partition structure and evaluation function is proposed for feature selection problem. This algorithm ensures the global optimal solution in theory and avoids complete randomness in search direction. The good property of our algorithm is shown through the theoretical analysis.

Methodologies for calibration and predictive analysis of a watershed model

The use of a fitted parameter watershed model to address water quantity and quality management issues requires that it be calibrated under a wide range of hydrologic conditions. However, rarely does model calibration result in a unique parameter set. Parameter nonuniqueness can lead to predictive nonuniqueness. The extent of model predictive uncertainty should be investigated if management decisions are to be based on model projections. Using models built for four neighboring watersheds in the Neuse River Basin of North Carolina, the application of the automated parameter optimization software PEST in conjunction with the Hydrologic Simulation Program Fortran (HSPF) is demonstrated. Parameter nonuniqueness is illustrated, and a method is presented for calculating many different sets of parameters, all of which acceptably calibrate a watershed model. A regularization methodology is discussed in which models for similar watersheds can be calibrated simultaneously. Using this method, parameter differences between watershed models can be minimized while maintaining fit between model outputs and field observations. In recognition of the fact that parameter nonuniqueness and predictive uncertainty are inherent to the modeling process, PEST's nonlinear predictive analysis functionality is then used to explore the extent of model predictive uncertainty.