Modifiable Boltzmann selective pressure is investigated as a tool to control variability in optimizations using genetic algorithms. An implementation of variable selective pressure, modeled after the use of temperature as a parameter in simulated annealing approaches, is described. The convergence behavior of optimization runs is illustrated as a function of selective pressure; the method is compared to a genetic algorithm lacking this control feature and is shown to exhibit superior convergence properties on a small set of test problems. An analysis is presented that compares the selective pressure of this algorithm to a standard selection procedure.

Most classical unconstrained optimization methods require derivative information. Different methods have been proposed for problems where derivative information cannot be used. One class of these methods is heuristics including Evolutionary Algorithms (EAs). In this study, we propose EAs for unconstrained optimization under both deterministic and stochastic environments. We design a crossover operator that tries to lead the algorithm towards the global optimum even when the starting solutions are far from the optimal solution. We also adapt this algorithm to a stochastic environment where there exist only estimates for the function values. We design new parent selection schemes based on statistical grouping methods and a replacement scheme considering existing statistical information. We test the performance of our algorithms using functions from the literature and newly introduced functions and obtain promising results.

Evolutionary algorithms are optimization techniques inspired by the actual evolution of biological species. They use conceptually simple process of two repeating phases of reproduction and fitness-based selection, that iteratively evolves each time better solutions. Evolutionary algorithms receive a lot of attention for being able to solve very hard optimization problems, where other optimization techniques might fail due to existence of many local optima. Wide range of different variants of evolutionary algorithms have been proposed. In this thesis, we will focus on the area of Estimation of Distribution Algorithms (EDA). When creating the next generation, EDAs transform the selected high-fitness population into a probability distribution. New generation is obtained by sampling the estimated distribution. We will design and and implement combinations of existing EDAs that will operate in business-specific environment, that can be characterized as tree-like structure of both discrete and continuous variables. Also, additional linear inequality constraints are specified to applicable solutions. Implemented application communicates with provided interfaces, retrieving the problem model specification and storing populations into database. Database is used to assign externally computed fitness values from...

The field of Learning Automata (LA) has been studied and analyzed extensively for more than four decades; however, almost all the papers have concentrated on the LA working in Environments that have a finite number of actions. This is a well-established model of computation, and expedient, epsilon-optimal and absolutely expedient machines have been designed for stationary and non-stationary Environments. There are only a few papers which deal with Environments possessing an infinite number of actions. These papers assume a well-defined and rather simple uni-modal functional form, like the Gaussian function, for the Environment's infinite reward probabilities. This thesis pioneers the concept and presents a series of continuous action LA (CALA) algorithms that do not require the function of the Environment's infinite reward probabilities to obey a well-established uni-modal functional form. Instead, this function can be, but not limited to, a multi-modal function as long as it satisfies some weak constraints. Moreover, as our discussion evolves, the constraints are further relaxed. In all these cases, we demonstrate that the underlying machines converge in an epsilon-optimal manner to the optimal action of an infinite action set. Based on the CALA algorithms proposed, we report a global maximum search algorithm, which can find the maximum points of a real-valued function by sampling the function's values that could be contaminated by noise. This thesis also investigates the performance limit of the action-taking scheme, sampling actions based on probability density functions, which is used by all currently available CALA algorithms. In more details, given a reward function, we define an index of the function which is the least upper bound of the performance that a CALA algorithm can possibly achieve. Besides, we also report a CALA algorithm that meets this upper bound in an epsilon-optimal manner. By investigating the problem from a different perspective, we argue that the algorithms proposed are closely related to the family of “Stochastic Point Location” problems involving either discretized steps or d-ary parallel machines. The thesis includes the detailed proofs of the assertions and highlights the niche contributions within the broader theory of learning. To the best of our knowledge, there are no comparable results reported in the literature.

Function optimization---finding the minimum or maximum of a given function---is an extremely challenging problem with applications in physics, economics, machine learning, engineering, and many other fields. While optimization is an active area of research, only a portion of this work acknowledges parallel computation, which is now widely available. Today, anyone with a modest budget can buy a cluster with hundreds of cores, pay for access to a supercomputer with thousands of processors, or at least purchase a laptop with 8 cores. Thus, an algorithm that works well in serial but cannot be parallelized is needlessly inefficient in real-life computationalenvironments.We address these issues in three connected threads of development: a high-level programming framework that makes it possible to create flexible and efficient implementations of optimization algorithms; improvements to an existing algorithm, Particle Swarm Optimization, to make it take better advantage of parallel resources; and a statistical model designed to efficiently use available information in parallel optimization by inferring search directions. Each of these is an essential step toward effective parallel optimization. First, without a suitable high-level programming model, expediency leads to purely serial development with parallel issues only an afterthought. Second, PSO has proven effective for optimization and is an excellent candidate to consider for efficient parallel implementations. Third, a model for inference of search directions is useful for understanding communication in the context of parallel optimization and provides a flexible base for continuing optimization research.

Remote sensing techniques are vital for early detection of several problems such as natural disasters, ecological problems and collecting information necessary for finding optimum solutions to those problems. Remotely sensed information has also important uses in predicting the future risks, urban planning, communication.Recent developments in remote sensing instrumentation offered a challenge to the mathematical and statistical methods to process the acquired information. Classification of satellite images in the context of land cover classification is the main concern of this study. Land cover classification can be performed by statistical learning methods like additive models, decision trees, neural networks, k-means methods which are already popular in unsupervised classification and clustering of image scene inverse problems. Due to the degradation and corruption of satellite images, the classification performance is limited both by the accuracy of clustering and by the extent of the classification. In this study, we are concerned with understanding the performance of the available unsupervised methods with k-means, supervised methods with Gaussian maximum likelihood which are very popular methods in land cover classification. A broader approach to the classification problem based on finding the optimal discriminants from a larger range of functions is considered also in this work. A novel method based on threshold decomposition and Boolean discriminant functions is developed as an implementable application of this approach. All methods are applied to BILSAT and Landsat satellite images using MATLAB software.

Energy functions are found to be a key of protein structure prediction. In this work, we propose a novel 3-dimensional energy function based on hydrophobic-hydrophilic properties of amino acid where we consider at least three different possible interaction of amino acid in a 3-dimensional sphere categorized as hydrophilic versus hydrophilic, hydrophobic versus hydrophobic and hydrophobic versus hydrophilic. Each of these interactions are governed by a 3-dimensional parameter alpha used to model the interaction and 3-dimensional parameter beta used to model weight of contribution. We use Genetic Algorithm (GA) to optimize the value of alpha, beta and Z-score. We obtain three energy scores libraries from a database of 4332 protein structures obtained from Protein Data Bank (PDB) server. Proposed energy function is found to outperform nearest competitor by 40.9% for the most challenging Rosetta decoy as well as better in terms of the Z-score based on Moulder and Rosetta decoy sets.

Multimodal function optimization generally focuses on algorithms to find either a local optimum or the global optimum while avoiding local optima. However, there is another class of optimization problems which have the objective of finding multiple optima with either equal or unequal function values. The knowledge of multiple local and global optima has several advantages such as obtaining an insight into the function landscape and selecting an alternative solution when dynamic nature of constraints in the search space makes a previous optimum solution infeasible to implement. Applications include identification of multiple signal sources like sound, heat, light and leaks in pressurized systems, hazardous plumes/aerosols resulting from nuclear/ chemical spills, fire-origins in forest fires and hazardous chemical discharge in water bodies, oil spills, deep-sea hydrothermal vent plumes, etc. Signals such as sound, light, and other electromagnetic radiations propagate in the form of a wave. Therefore, the nominal source profile that spreads in the environment can be represented as a multimodal function and hence, the problem of localizing their respective origins can be modeled as optimization of multimodal functions. Multimodality in a search and optimization problem gives rise to several attractors and thereby presents a challenge to any optimization algorithm in terms of finding global optimum solutions. However, the problem is compounded when multiple (global and local) optima are sought. This thesis develops a novel glowworm swarm optimization (GSO) algorithm for simultaneous capture of multiple optima of multimodal functions. The algorithm shares some features with the ant-colony optimization (ACO) and particle swarm optimization (PSO) algorithms, but with several significant differences. The agents in the GSO algorithm are thought of as glowworms that carry a luminescence quantity called luciferin along with them. The glowworms encode the function-profile values at their current locations into a luciferin value and broadcast the same to other agents in their neighborhood. The glowworm depends on a variable local decision domain, which is bounded above by a circular sensor range, to identify its neighbors and compute its movements. Each glowworm selects a neighbor that has a luciferin value more than its own, using a probabilistic mechanism, and moves toward it. That is, they are attracted to neighbors that glow brighter. These movements that are based only on local information enable the swarm of glowworms to partition into disjoint subgroups, exhibit simultaneous taxis-behavior towards, and rendezvous at multiple optima (not necessarily equal) of a given multimodal function. Natural glowworms primarily use the bioluminescent light to signal other individuals of the same species for reproduction and to attract prey. The general idea in the GSO algorithm is similar in these aspects in the sense that glowworm agents are assumed to be attracted to move toward other glowworm agents that have brighter luminescence (higher luciferin value). We present the development of the GSO algorithm in terms of its working principle, various algorithmic phases, and evolution of the algorithm from the first version of the algorithm to its present form. Two major phases ¡ splitting of the agent swarm into disjoint subgroups and local convergence of agents in each subgroup to peak locations ¡ are identified at the group level of the algorithm and theoretical performance results related to the latter phase are obtained for a simplified GSO model. Performance of the GSO algorithm against a large class of benchmark multimodal functions is demonstrated through simulation experiments. We categorize the various constants of the algorithm into algorithmic constants and parameters. We show in simulations that fixed values of the algorithmic constants work well for a large class of problems and only two parameters have some influence on algorithmic performance. We also study the performance of the algorithm in the presence of noise. Simulations show that the algorithm exhibits good performance in the presence of fairly high noise levels. We observe graceful degradation only with significant increase in levels of measurement noise. A comparison with the gradient based algorithm reveals the superiority of the GSO algorithm in coping with uncertainty. We conduct embodied robot simulations, by using a multi-robot-simulator called Player/Stage that provides realistic sensor and actuator models, in order to assess the GSO algorithm's suitability for multiple source localization tasks. Next, we extend this work to collective robotics experiments. For this purpose, we use a set of four wheeled robots that are endowed with the capabilities required to implement the various behavioral primitives of the GSO algorithm. We present an experiment where two robots use the GSO algorithm to localize a light source. We discuss an application of GSO to ubiquitous computing based environments. In particular, we propose a hazard-sensing environment using a heterogeneous swarm that consists of stationary agents and mobile agents. The agents deployed in the environment implement a modification of the GSO algorithm. In a graph of mini mum number of mobile agents required for 100% source-capture as a function of the number of stationary agents, we show that deployment of the stationary agents in a grid configuration leads to multiple phase-transitions in the heterogeneous swarm behavior. Finally, we use the GSO algorithm to address the problem of pursuit of multiple mobile signal sources. For the case where the positions of the pursuers and the moving source are collinear, we present a theoretical result that provides an upper bound on the relative speed of the mobile source below which the agents succeed in pursuing the source. We use several simulation scenarios to demonstrate the ecacy of the algorithm in pursuing mobile signal sources. In the case where the positions of the pursuers and the moving source are non-collinear, we use numerical experiments to determine an upper bound on the relative speed of the mobile source below which the pursuers succeed in pursuing the source.

In introduction of work, I presented the state of the art of measuring insertion loss of the EMI filter and the description of individual methods of measuring is also included. After that I dealt with global optimization methods and some of them I theoretically described. Mainly PSO method was studied carefully, and the principle of optimization in details are presented in the thesis, because this method was used for optimization of the filters parameters in the thesis. Next part of work deals with theoretical and mathematical expression of insertion loss of the EMI filters. Due to the mathematical expression of the insertion loss, the values of parasitic elements of given filter have been optimized in different measuring systems. This optimization was applied on synthetic data. By this step the functionality of optimization was proved and also the fitness function has been tuned and optimised. The last part of thesis works with optimization on measured data of given filters. I found out inaccuracy in mathematical expression of given model of EMI filter, therefore it was necessary to come up with the new filter model. The accuracy increases by using the new filter model. In next step the new model was enlarged by new spurious components.

The diploma thesis deals with the analyses of demand using standard tools of engineering mathematics. Mathematical models of demand, both single and multi- factor are investigated. Elasticity of demand is applied for decision making in price policy. Problems of optimization of demand reflecting utility and budget constraints are under consideration. Constructions of demand curve and compensated demand curve are presented. The text is accompanied by illustrative examples aiming at methodical aspects of the work