This paper presents an application of parallel genetic algorithm to optimal long-range generation expansion planning. The problem is formulated as a combinatorial optimization problem that determines the number of newly introduced generation units of each technology during different time intervals. A new string representation method for the problem is presented. Binary and decimal coding for the string representation method are compared. The method is implemented on transputers, one of the practical multi-processors. The effectiveness of the proposed method is demonstrated on a typical generation expansion problem with four technologies, five intervals, and a various number of generation units. It is compared favorably with dynamic programming and conventional genetic algorithm. The results reveal the speed and effectiveness of the proposed method for solving this problem.

The task of finding saddle points on potential energy surfaces plays a crucial role in understanding the dynamics of a micromolecule as well as in studying the folding pathways of macromolecules like proteins. The problem of finding the saddle points on a high dimensional potential energy surface is transformed into the problem of finding decomposition points of its corresponding nonlinear dynamical system. This paper introduces a new method based on TRUST-TECH (TRansformation Under STability reTained Equilibria CHaracterization) to compute saddle points on potential energy surfaces using stability boundaries. Our method explores the dynamic and geometric characteristics of stability boundaries of a nonlinear dynamical system. A novel trajectory adjustment procedure is used to trace the stability boundary. Our method was successful in finding the saddle points on different potential energy surfaces of various dimensions. A simplified version of the algorithm has also been used to find the saddle points of symmetric systems with the help of some analytical knowledge. The main advantages and effectiveness of the method are clearly illustrated with some examples. Promising results of our method are shown on various problems with varied degrees of freedom.

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The main goal of the motif finding problem is to detect novel, over-represented unknown signals in a set of sequences (e.g. transcription factor binding sites in a genome). The most widely used algorithms for finding motifs obtain a generative probabilistic representation of these overrepresented signals and try to discover profiles that maximize the information content score. Although these profiles form a very powerful representation of the signals, the major difficulty arises from the fact that the best motif corresponds to the global maximum of a non-convex continuous function. Popular algorithms like Expectation Maximization (EM) and Gibbs sampling tend to be very sensitive to the initial guesses and are known to converge to the nearest local maximum very quickly. In order to improve the quality of the results, EM is used with multiple random starts or any other powerful stochastic global methods that might yield promising initial guesses (like projection algorithms). Global methods do not necessarily give initial guesses in the convergence region of the best local maximum but rather suggest that a promising solution is in the neighborhood region. In this paper, we introduce a novel optimization framework that searches the neighborhood regions of the initial alignment in a systematic manner to explore the multiple local optimal solutions. This effective search is achieved by transforming the original optimization problem into its corresponding dynamical system and estimating the practical stability boundary of the local maximum. Our results show that the popularly used EM algorithm often converges to suboptimal solutions which can be significantly improved by the proposed neighborhood profile search. Based on experiments using both synthetic and real datasets, our method demonstrates significant improvements in the information content scores of the probabilistic models. The proposed method also gives the flexibility in using different local solvers and global methods depending on their suitability for some specific datasets.