Student Number : 0214677F - PhD thesis - School of Camputational and Applied Mathematics - Faculty of Science / Many real-life problems are formulated as global optimization problems with continuous variables. These problems are in most cases nonsmooth, nonconvex and often simulation based, making gradient based methods impossible to be used to solve them. Therefore, ef#2;cient, reliable and derivative-free global optimization methods for solving such problems are needed. In this thesis, we focus on improving the ef#2;ciency and reliability of some global optimization methods. In particular, we concentrate on improving some population set-based methods for unconstrained global optimization, mainly through hybridization. Hybridization has widely been recognized to be one of the most attractive areas of unconstrained global optimization. Experiments have shown that through hybridization, new methods that inherit the strength of the original elements but not their weakness can be formed. We suggest a number of new hybridized population set-based methods based on differential evolution (de), controlled random search (crs2) and real coded genetic algorithm (ga). We propose #2;ve new versions of de. In the #2;rst version, we introduce a localization, called random localization, in the mutation phase of de. In the second version, we propose a localization in the acceptance phase of de. In the third version, we form a de hybrid algorithm by probabilistically combining the point generation scheme of crs2 with that of de in the de algorithm. The fourth and #2;fth versions are also de hybrids. These versions hybridize the mutation of de with the point generation rule of the electromagnetism-like (em) algorithm. We also propose #2;ve new versions of crs2. The #2;rst version modi#2;es the point generation scheme of crs2 by introducing a local mutation technique. In the second and third modi#2;cations, we probabilistically combine the point generation scheme of crs2 with the linear interpolation scheme of a trust-region based method. The fourth version is a crs hybrid that probabilistically combines the quadratic interpolation scheme with the linear interpolation scheme in crs2. In the #2;fth version, we form a crs2 hybrid algorithm by probabilistically combining the point generation scheme of crs2 with that of de in the crs2 algorithm. Finally, we propose #2;ve new versions of the real coded genetic algorithm (ga) with arithmetic crossover. In the #2;rst version of ga, we introduce a local technique. We propose, in the second version, an integrated crossover rule that generates two children at a time using two different crossover rules. We introduce a local technique in the second version to obtain the third version. The fourth and #2;fth versions are based on the probabilistic adaptation of crossover rules. The ef#2;ciency and reliability of the new methods are evaluated through numerical experiments using a large test suite of both simple and dif#2;cult problems from the literature. Results indicate that the new hybrids are much better than their original counterparts both in reliability and ef#2;ciency. Therefore, the new hybrids proposed in this study offer an alternative to many currently available stochastic algorithms for solving global optimization problems in which the gradient information is not readily available.

Generally in most of the applications of estimation theory using the Method of Maximum Likelihood Estimation (MMLE) to dynamical systems one deals with a situation where only the measurement noise alone is present. However in many present day applications where modeling errors and random state noise input conditions occur it has become necessary for MMLE to handle measurement noise as well as process noise. The numerical algorithms accounting for both measurement and process noise require significantly an order of magnitude higher computer time and memory. Further more, implementation difficulties and convergence problems are often encountered. Here one has to estimate the quantities namely, the initial state error covariance matrix Po, measurement noise covariance matrix R, the process noise covariance matrix Q and the system parameter 0 and the present work deals with the above. Since the above problem is fairly involved we need to have a good reference solution. For this purpose we utilize the approach and results of Gemson who considered the above problem via the extended Kalman filter (EKF) route to compare the present results from the MMLE route. The EKF uses the unknown parameters as additional states unlike in MMLE which uses only the system states. Chapter 1 provides a brief historical perspective followed by parameter identification in the presence of process and measurement noises. The earlier formulations such as natural, innovation, combined, and adaptive approaches are discussed. Chapter 2 deals with the heuristic adaptive tuning of the Kalman filter parameters for the matrices Q and R by Myers and Tapley originally developed for state estimation problems involving satellite orbit estimation. It turns out that for parameter estimation problems apart from the above matrices even the choice of the initial covariance matrix Po is crucial for obtaining proper parameter estimates with a finite amount of data and for this purpose the inverse of the information matrix for Po is used. This is followed by a description of the original Controlled Random Search (CRS) of Price and its variant as implemented and used in the present work to estimate or tune Q, R, and 0 which is the aim of the present work. The above help the reader to appreciate the setting under which the present study has been carried out. Chapter 3 presents the results and the analysis of the estimation procedure adopted with respect to a specific case study of the lateral dynamics of an aircraft involving 15 unknown parameters. The reference results for the present work are the ones based on the approach of Gemson and Ananthasayanam (1998). The present work proceeds in two phases. In the first case (i) the EKF estimates for Po, Q, and R are used to obtain 0 and in the second case (ii) the estimate of Po and Q together with a reasonable choice of R are utilized to obtain 0 from the CRS algorithm. Thus one is able to assess the capability of the CRS to estimate only the unknown parameters. The next Chapter 4 presents the results of utilizing the CRS algorithm with R based on a reasonable choice and for Po from the inverse of the information matrix to estimate both Q and 0. This brings out the efficiency of MMLE with CRS algorithm in the estimation of unknown process noise characteristics and unknown parameters. Thus it demonstratesthofcdifficult Q can be estimated using CRS technique without the attendant difficulties of the earlier MMLE formulations in dealing with process noise. Chapter 5 discusses the - implementation of CRS to estimate the unknown measurement noise covariance matrix R together with the unknown 0 by utilizing the values of Po and Q obtained through EKF route. The effect of variation of R in the parameter estimation procedure is also highlighted in This Chapter. This Chapter explores the importance of Po in the estimation procedure. It establishes the importance of Po though most of the earlier works do not appear to have recognized such a feature. It turned out that the CRS algorithm does not converge when some arbitrary value of Po is chosen. It has to be necessarily obtained from a scouting pass of the EKF. Some sensitivity studies based on variations of Po shows its importance. Further studies shows the sequence of updates, the random nature of process and measurement noise effects, the deterministic nature of the parameter, play a critical role in the convergence of the algorithm. The last Chapter 6 presents the conclusions from the present work and suggestions for further work.