Global optimization: techniques and applications

Optimization problems arise in a wide variety of scientific disciplines. In many practical problems, a global optimum is desired, yet the objective function has multiple local optima. A number of techniques aimed at solving the global optimization problem have emerged in the last 30 years of research. This thesis first reviews techniques for local optimization and then discusses many of the stochastic and deterministic methods for global optimization that are in use today. Finally, this thesis shows how to apply global optimization techniques to two practical problems: the image segmentation problem (from imaging science) and the 3-D registration problem (from computer vision)

Why are probabilistic laws governing quantum mechanics and neurobiology?

We address the question: Why are dynamical laws governing in quantum mechanics and in neuroscience of probabilistic nature instead of being deterministic? We discuss some ideas showing that the probabilistic option offers advantages over the deterministic one.Comment: 40 pages, 8 fig

Stochastics global optimization methods and their applications in Chemical Engineering

Ph.DDOCTOR OF PHILOSOPH

Optimization in Quasi-Monte Carlo Methods for Derivative Valuation

Computational complexity in financial theory and practice has seen an immense rise recently. Monte Carlo simulation has proved to be a robust and adaptable approach, well suited for supplying numerical solutions to a large class of complex problems. Although Monte Carlo simulation has been widely applied in the pricing of financial derivatives, it has been argued that the need to sample the relevant region as uniformly as possible is very important. This led to the development of quasi-Monte Carlo methods that use deterministic points to minimize the integration error. A major disadvantage of low-discrepancy number generators is that they tend to lose their ability of homogeneous coverage as the dimensionality increases. This thesis develops a novel approach to quasi-Monte Carlo methods to evaluate complex financial derivatives more accurately by optimizing the sample coordinates in such a way so as to minimize the discrepancies that appear when using lowdiscrepancy sequences. The main focus is to develop new methods to, optimize the sample coordinate vector, and to test their performance against existing quasi-Monte Carlo methods in pricing complicated multidimensional derivatives. Three new methods are developed, the Gear, the Simulated Annealing and the Stochastic Tunneling methods. These methods are used to evaluate complex multi-asset financial derivatives (geometric average and rainbow options) for dimensions up to 2000. It is shown that the two stochastic methods, Simulated Annealing and Stochastic Tunneling, perform better than existing quasi-Monte Carlo methods, Faure' and Sobol'. This difference in performance is more evident in higher dimensions, particularly when a low number of points is used in the Monte Carlo simulations. Overall, the Stochastic Tunneling method yields the smallest percentage root mean square relative error and requires less computational time to converge to a global solution, proving to be the most promising method in pricing complex derivativesImperial Users onl

Selecting a global optimization method to estimate the oceanic particle cycling rate constants

The objective is to select an inverse method to estimate the parameters of a dynamical model of the oceanic particle cycling from in situ data. Estimating the parameters of a dynamical model is a nonlinear inverse problem, even in the case of linear dynamics. Generally, biogeochemical models are characterized by complex nonlinear dynamics and by a high sensitivity to their parameters. This makes the parameter estimation problem strongly nonlinear. We show that an approach based on a linearization around an a priori solution and on a gradient descent method is not appropriate given the complexity of the related cost functions and our poor a priori knowledge of the parameters. Global Optimization Algorithms (GOAs) appear as better candidates. We present a comparison of a deterministic (TRUST), and two stochastic (simulated annealing and genetic algorithm) GOAs. From an exact model integration, a synthetic data set is generated which mimics the space-time sampling of a reference campaign. Simulated optimizations of two to the eight model parameters are performed. The parameter realistic ranges of values are the only available a priori information. The results and the behavior of the GOAs are analyzed in details. The three GOAs can recover at least two parameters. However, the gradient requirement of deterministic methods proves a serious drawback. Moreover, the complexity of the TRUST makes the estimation of more than two parameters hardly conceivable. The genetic algorithm quickly converges toward the eight parameter solution, whereas the simulated annealing is trapped by a local minimum. Generally, the genetic algorithm is less computationally expensive, swifter to converge, and has more robust procedural parameters than the simulated annealing