This work focuses on the use of a genetic algorithm for optimization in a search-based problem. The Genetic Algorithm (GA) is a subset of evolutionary algorithms that models biological processes to optimize highly complex functions. A GA allows a population composed of many individuals to evolve under specified selection rules to a state that maximizes the “fitness” (i.e. minimize the objective function). A major advantage of using GA over most stochastic techniques is its parallelism, which speeds up the simulation results leading to faster convergence. With mutation, the GA is also less likely to get stuck in local minima compared to other stochastic techniques. However, some notable drawbacks of the Standard GA (SGA) include slow convergence and a possibility of being stuck in local optimum solution. The SGA uses a random process to generate parameter values for the initial population generation, crossover and mutation processes. Random number generators are designed to result in either uniform distributions or Gaussian distributions. We conjecture that the evolutionary processes in genetics are driven by a random non-linear deterministic dynamic process rather than a random non-deterministic process. Therefore, in the GA evolutionary process, a chaotic map is incorporated into the initial population generation, the crossover and mutation processes of the SGA; this is termed the Chaotic GA (CGA). The properties of a chaotic system that provides additional benefits over randomly generated solutions are sensitivity to initial conditions, topological density and topological transitivity (robust diversity). These properties ensure that the CGA is able to explore the entire solution space. Introducing chaos into the whole process of a standard genetic algorithm may help improve convergence time and accuracy. Simulation was done using Matlab and Java.

In this work, the potential of intelligent algorithms for optimizing the real power loss and enhancing the grid connection power factor in a real hydrocarbon facility electrical system is assessed. Namely, genetic algorithm (GA), improve strength Pareto evolutionary algorithm (SPEA2) and differential evolutionary algorithm (DEA) are developed and implemented. The economic impact associated with these objectives optimization is highlighted. The optimization of the subject objectives is addressed as single and multi-objective constrained nonlinear problems. Different generation modes and system injected reactive power cases are evaluated. The studied electrical system constraints and parameters are all real values. The uniqueness of this thesis is that none of the previous literature studies addressed the technical and economic impacts of optimizing the aforementioned objectives for real hydrocarbon facility electrical system. All the economic analyses in this thesis are performed based on real subsidized cost of energy for the kingdom of Saudi Arabia. The obtained results demonstrate the high potential of optimizing the studied system objectives and enhancing the economics of the utilized generation fuel via the application of intelligent algorithms.

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Quantum computation has attracted a great deal of attention from the scientific community in recent years. By using the quantum mechanical phenomena of superposition and entanglement, a quantum computer can solve certain problems much faster than classical computers. Several quantum algorithms have been developed to demonstrate this quantum speedup. Two important examples are Shor’s algorithm for the factorization problem, and Grover’s algorithm for the search problem. Significant efforts are on to build a large scale quantum computer for implementing these quantum algorithms. This thesis deals with Grover’s search algorithm, and presents its several generalizations that perform better in specific contexts. While writing the thesis, we have assumed the familiarity of readers with the basics of quantum mechanics and computer science. For a general introduction to the subject of quantum computation, see [1]. In Chapter 1, we formally define the search problem as well as present Grover’s search algorithm [2]. This algorithm, or more generally the quantum amplitude amplification algorithm [3, 4], drives a quantum system from a prepared initial state (s) to a desired target state (t). It uses O(α-1 = | (t−|s)| -1) iterations of the operator g = IsIt on |s), where { IsIt} are selective phase inversions selective phase inversions of the corresponding states. That is a quadratic speedup over the simple scheme of O(α−2) preparations of |s) and subsequent projective measurements. Several generalizations of Grover’s algorithm exist. In Chapter 2, we study further generalizations of Grover’s algorithm. We analyse the iteration of the search operator S = DsI t on |s) where Ds is a more general transformation than Is, and I t is a selective phase rotation of |t) by angle . We find sufficient conditions for S to produce a successful quantum search algorithm. In Chapter 3, we demonstrate that our general framework encapsulates several previous generalizations of Grover’s algorithm. For example, the phase-matching condition for the search operator requires the angles and and to be almost equal for a successful quantum search. In Kato’s algorithm, the search operator is where Ks consists of only single-qubit gates, which are easier to implement physically than multi-qubit gates. The spatial search algorithms consider the search operator where is a spatially local operator and provides implementation advantages over Is. The analysis of Chapter 2 provides a simpler understanding of all these special cases. In Chapter 4, we present schemes to improve our general quantum search algorithm, by controlling the operators through an ancilla qubit. For the case of two dimensional spatial search problem, these schemes yield an algorithm with time complexity . Earlier algorithms solved this problem in time steps, and it was an open question to design a faster algorithm. The schemes can also be used to find, for a given unitary operator, an eigenstate corresponding to a specified eigenvalue. In Chapter 5, we extend the analysis of Chapter 2 to general adiabatic quantum search. It starts with the ground state |s) of an initial Hamiltonian Hs and evolves adiabatically to the target state |t) that is the ground state of the final Hamiltonian The evolution uses a time dependent Hamiltonian HT that varies linearly with time . We show that the minimum excitation gap of HT is proportional to α. Also, the ground state of HT changes significantly only within a very narrow interval of width around the transition point, where the excitation gap has its minimum. This feature can be used to reach the target state (t) using adiabatic evolution for time In Chapter 6, we present a robust quantum search algorithm that iterates the operator on |s) to successfully reach |t), whereas Grover’s algorithm fails if as per the phase-matching condition. The robust algorithm also works when is generalized to multiple target states. Moreover, the algorithm provides a new search Hamiltonian that is robust against certain systematic perturbations. In Chapter 7, we look beyond the widely studied scenario of iterative quantum search algorithms, and present a recursive quantum search algorithm that succeeds with transformations {Vs,Vt} sufficiently close to {Is,It.} Grover’s algorithm generally fails if while the recursive algorithm is nearly optimal as long as , improving the error tolerance of the transformations. The algorithms of Chapters 6-7 have applications in quantum error-correction, when systematic errors affect the transformations The algorithms are robust as long as the errors are small, reproducible and reversible. This type of errors arise often from imperfections in apparatus setup, and so the algorithms increase the flexibility in physical implementation of quantum search. In Chapter 8, we present a fixed-point quantum search algorithm. Its state evolution monotonically converges towards |t), unlike Grover’s algorithm where the evolution passes through |t) under iterations of the operator . In q steps, our algorithm monotonically reduces the failure probability, i.e. the probability of not getting |t), from . That is asymptotically optimal for monotonic convergence. Though the fixed-point algorithm is of not much use for , it is useful when and each oracle query is highly expensive. In Chapter 9, we conclude the thesis and present an overall outlook.

用QR與LR迭代法求矩陣特徵值與特徵向量之過程中，前人曾提出位移策略以加速其收斂速度，其中最有效的是Wilkinson 移位值。在此我們希望尋求能使收斂更快速的位移值。 我們首先嘗使用一三階子矩陣之特徵值作為一次QR迭代之移位值。在此子矩陣之特徵值中，我們選擇最接近Wilkinson 移位值的特徵值為移位值，期使特徵值之收斂更快。 另一移位策略是用一較快速省功的算則先計算矩陣之特徵值，再以這些計算值作為QR迭代之位移值，來計算較為費功的特徵向量。希望能較快得到所需要的特徵值與特徵向量。 在計算特徵值之算則中，Cholesky迭代法以其計算簡單，執行速度快為我們所選擇。由程式執行結果可知這兩種算則較EISPACK 的算則分別節省了約10% 與30% 的運算量。我們比較這些策略，並將結果列於文中。 / Abstract The QR and LR algorithms are the general methods for computing eigenvalues and eigenvectors of a dense matrix. In this paper, we propose some shift strategies that can increase the efficiency of the QR algorithm by first computing the eigenvalues of the matrix (or its trailing submatrix) in a fast and economical way, and then using them as shifts to find the eigenvalues and their corresponding eigenvectors. When incorporated with QR algorithm, these kinds of shift strategies can save about 10 to 30percent of work in arithmetic operations.

In this thesis, we investigate the use of adaptive antenna algorithms for OFDM systems to suppress interference in various channel conditions including narrowband and wideband interference, flat and frequency selective fading. We propose a novel frequency-domain beamformer, based on the linearly constrained modified constant modulus hybrid LMS (LCMCM-HLMS) algorithm for OFDM systems to improve the performance of interference suppression in AWGN channel with narrowband interference, Rayleigh fast fading channel with phase distortion, and the multipath environment. To verify the merits of the frequency-domain beamformer, the effect due to narrowband interference and random phase distortion are investigated. Moreover, to improve the performance of adaptive beamforming algorithm, the frequency-domain linearly constrained modified constant modulus hybrid LMS (LCMCM-HLMS) algorithm is proposed. Computer simulation results show that the proposed frequency-domain LCMCM-HLMS beamformer has good capability of interference supression in various environment, and can mitigate the phase distortion of channel. However, in the time-domain beamformer based on LMS [33], RLS ,LC-LMS and LC-FLS algorithm for OFDM systems, the performance may severely degraded under some situations. We will show that in terms of output SINR, beampatern, received signal constellation and mean square error (MSE), for narrowband interference suppression in AWGN channel, phase distortion in Rayleigh fast fading channel and the multipath environment.

Šiame darbe nagrinėjama negiljotininio, dvimačio, stačiakampių pjaustymo uždavinio atliekų minimizavimo problema ir jos sprendimo metodai. Dėl uždavinio kombinatorinio sudėtingumo neįmanoma tiksliai ir visais atvejais pateikti optimalų jo sprendinį, todėl pasirinkti apytiksliai sprendimo metodai. Uždavinys sprendžiamas metaeuristiniais hibridiniais genetiniu ir modeliuojamo atkaitinimo algoritmais apjungtais su euristiniais „Žemiausio kairėn užpildymo“ ir „Žemiausio tarpo“, kuris yra originali „Geriausiai tinkamo“ metodo modifikacija. Taip pat realizuojami minėti euristiniai algoritmai atskirai nuo hibridinių. Atliekama šių metodų lyginamoji analizė bei jų parametrų ir pradinių sąlygų parinkimo įtakos tyrimas sprendinio kokybei. Suformuojama ir pateikiama metodika pjaustymo uždavinių sprendimui. / A non – guillotinable, two – dimensional, rectangular cutting stock problem is being introduced in this paper and its solving methods either. Due to the combinatorial complexity of a problem, it is impossible to solve it optimally for every instance. Consequently an aproximate methods have been chosen. The problem is solved by metaheuristic genetic and simulated annealing methods hybridised with heuristic „Bottom Left Fill“ and „Lowest Gap“, which is an originally modified version of „Best Fit“ algorithm. The same heuristic algorithms are implemented separately from hybridised ones. A comparation analysis of these methods is done and the influence on solution quality depending on the selection of algorithms parameters and its initial conditions is considered. The methodology of solving cutting stock problems is being formulated and presented.

This work is focused on advanced methods of mobile robot's path planning. The theoretical part describes selected graphical methods, which are useful for speeding up the process of finding the shortest paths, for example through reduction of explored nodes of the state space. In the practical part was created simulate environment in the Python language and in this environment, selected algorithms was implemented.

Context: Data compression is the technique that is used for the fast transmission of the data and also to reduce the storage size of the transmitted data. Data compression is the massive and ubiquitous technology where almost every communication company make use of data compression. Data compression is categorized mainly into lossy and lossless data compression. Ericsson is the telecommunication company that deals with millions of user data and, all these data get compressed using the Deflate compression algorithm. Due to the compression ratio and compression speed, the deflate algorithm is not optimal for the present use case(compress twice and decompress once) of Ericsson. This research is all about finding the best alternate algorithm which suits the current use case so that the deflate algorithm can replace it. Objectives: The objective of the research is to replace the Deflate algorithm with the algorithm, which is useful for compressing the Serving GPRS Support Node-Mobility Management Entity(SGSN-MME) user data effectively. The main objectives to achieve this goal are: Investigating the better algorithm which fits the SGSN-MME compression patterns, investigating the few alternate algorithms for Deflate algorithm, the SGSN- MME dataset used to perform experimentation, the experiment should perform by using all selected algorithms on the dataset, the results of the experiment were compared based on the compression factors, based on the performance of algorithm the Deflate algorithm will get replaced with the suitable algorithm. Methods: In this research, a literature review performed to investigate the alternate algorithms for the Deflate algorithm. After selecting the algorithm, an experiment conducted on the data which was provided by Ericsson AB, Gothenburg and based on the compression factors like compression ratio, compression speed the performance of the algorithm evaluated. Results: By analyzing the results of the experiment, Z-standard is the better performance algorithm with the optimal compression sizes, compression ratio, and compression speed. Conclusions: This research concludes by identifying an alternate algorithm that can replace the Deflate algorithm and also which is suitable for the present Use case.