An (n, k, p, t) lotto design is a collection of k-subsets of a set X of n numbers wherein every p-subset of X must intersect at least one k-subset in t or more elements. L(n,k,p,t) is the minimum number of k-subsets which guarantees an intersection of at least t numbers between any p-subset of X and at least one of the k-subsets. To determine L(n,k,p,t) is the main goal of lotto design research. In previous work on lotto designs, other researchers used sequential algorithms to find bounds for L(n,k,p,t). We will determine the number of non-isomorphic optimal lotto designs on 5 or 6 blocks for n,k,p,t <= 20 and also improve lower bounds for L(n,k,p,t) >= 6 if possible by a more efficient implementation of a backtracking algorithm. / May 2005

An (n, k, p, t) lotto design is a collection of k-subsets of a set X of n numbers wherein every p-subset of X must intersect at least one k-subset in t or more elements. L(n,k,p,t) is the minimum number of k-subsets which guarantees an intersection of at least t numbers between any p-subset of X and at least one of the k-subsets. To determine L(n,k,p,t) is the main goal of lotto design research. In previous work on lotto designs, other researchers used sequential algorithms to find bounds for L(n,k,p,t). We will determine the number of non-isomorphic optimal lotto designs on 5 or 6 blocks for n,k,p,t <= 20 and also improve lower bounds for L(n,k,p,t) >= 6 if possible by a more efficient implementation of a backtracking algorithm.

An (n, k, p, t) lotto design is a collection of k-subsets of a set X of n numbers wherein every p-subset of X must intersect at least one k-subset in t or more elements. L(n,k,p,t) is the minimum number of k-subsets which guarantees an intersection of at least t numbers between any p-subset of X and at least one of the k-subsets. To determine L(n,k,p,t) is the main goal of lotto design research. In previous work on lotto designs, other researchers used sequential algorithms to find bounds for L(n,k,p,t). We will determine the number of non-isomorphic optimal lotto designs on 5 or 6 blocks for n,k,p,t <= 20 and also improve lower bounds for L(n,k,p,t) >= 6 if possible by a more efficient implementation of a backtracking algorithm.

The optimization of photovoltaic (PV) power generation system requires an accurate system performance model capable of validating the PV system optimization design. Currently, many commercial PV system modeling programs are available, but those programs are not able to model PV systems on a distorted ground level. Furthermore, they were not designed to optimize PV systems that are already installed. To solve these types of problems, this thesis proposes an optimization method using model simulations and a MATLAB-based PV system performance model. The optimization method is particularly designed to address partial shading issues often encountered in PV system installed on distorted ground. The MATLAB-based model was validated using the data collected from the Cal Poly Gold Tree Solar Field. It was able to predict the system performance with 96.4 to 99.6 percent accuracy. The optimization method utilizes the backtracking algorithm already installed in the system and the pitch distance to control the angle of the tracker and reduces solar panels partial shading on the adjacent row to improve system output. With pitch distances reduced in the backtracking algorithm between 2.5 meters and 3 meters, the inverter with inter-row shading can expect a 10.4 percent to 28.9 percent increase in power production. The implementation and calibration of this optimization method in the field this spring was delayed due to COVID-19. The field implementation is now expected to start this summer.

This thesis studies two problems centered around non-backtracking walks on graphs. First, we analyze the spectrum of the non-backtracking matrix of a graph. We show how to obtain the eigenvectors of the non-backtracking matrix using a smaller matrix and in doing so, create a block diagonal decomposition which more clearly expresses the non-backtracking matrix eigenvalues. Additionally, we develop upper and lower bounds on the matrix spectrum and use the spectrum to investigate properties of the graph. Second, we investigate the difference between PageRank and non-backtracking PageRank. We show some instances where there is no difference and develop an algorithm to compare PageRank and non-backtracking PageRank under certain conditions using $\mu$-PageRank.

Boolean Satisfiability (SAT) is a fundamental NP-complete problem of determining whether there exists an assignment of variables which makes a Boolean formula evaluate to True. SAT is a convenient representation for many naturally occurring optimization and decisions problems such as planning and circuit verification. SAT is most commonly solved by a form of backtracking search which systematically explores the space of possible variable assignments. We show that the order in which variable polarities are assigned can have a significant impact on the performance of backtracking algorithms. We present several ways of transforming SAT instances into non-linear objective functions and describe three value-ordering methods based on iterative optimization techniques. We implement and test these heuristics in the widely-recognized MiniSAT framework. The first approach determines polarities by applying Newton's Method to a sparse system of non-linear objective functions whose roots correspond to the satisfying assignments of the propositional formula. The second approach determines polarities by minimizing an objective function corresponding to the number of clauses conflicting with each assignment. The third approach determines preferred polarities by performing stochastic gradient descent on objective functions sampled from a family of continuous potentials. The heuristics are evaluated on a set of standard benchmarks including random, crafted and industrial problems. We compare our results to five existing heuristics, and show that MiniSAT equipped with our heuristics often outperforms state-of-the-art SAT solvers.

Boolean Satisfiability (SAT) is a fundamental NP-complete problem of determining whether there exists an assignment of variables which makes a Boolean formula evaluate to True. SAT is a convenient representation for many naturally occurring optimization and decisions problems such as planning and circuit verification. SAT is most commonly solved by a form of backtracking search which systematically explores the space of possible variable assignments. We show that the order in which variable polarities are assigned can have a significant impact on the performance of backtracking algorithms. We present several ways of transforming SAT instances into non-linear objective functions and describe three value-ordering methods based on iterative optimization techniques. We implement and test these heuristics in the widely-recognized MiniSAT framework. The first approach determines polarities by applying Newton's Method to a sparse system of non-linear objective functions whose roots correspond to the satisfying assignments of the propositional formula. The second approach determines polarities by minimizing an objective function corresponding to the number of clauses conflicting with each assignment. The third approach determines preferred polarities by performing stochastic gradient descent on objective functions sampled from a family of continuous potentials. The heuristics are evaluated on a set of standard benchmarks including random, crafted and industrial problems. We compare our results to five existing heuristics, and show that MiniSAT equipped with our heuristics often outperforms state-of-the-art SAT solvers.

Stuttgart, Univ., Diplomarb., 2004.

This thesis describes the social table game Scrabble, and its realization in the form of computer games. Gradually examines all important aspects that affect the performance of the implementation. Especially after the election of the appropriate data structures retained for the vocabulary, affecting the efficiency of generating moves, and the selection of appropriate algorithms with regard to the maximum speed. There is particular emphasis on artificial intelligence opponent and its ability to compete not only amateurs, but professional SCRABBLE players.

Many utility-scale solar farms use horizontal single axis tracking to follow the sun throughout the day and produce more energy. Solar farms on skewed topography produce complex shading patterns that require precise modeling techniques to determine the energy output. To accomplish this, MATLAB was used in conjunction with NREL weather predictions to predict shading shapes and energy outputs. The MATLAB models effectively predicted the sun’s position in the sky, panel tilt angle throughout the day, irradiance, cell temperature, and shading size. The Cal Poly Gold Tree Solar Farm was used to validate these models for various lengths of time. First, the models predicted the shading and power output for a single point in time. Four points of time measurements were taken; resulting in 6 to 32 percent difference in shade height, 5 to 60 percent difference for shade length, and 29 to 59 percent difference for power output. This shows the difficulty of predicting a point in time and suggests the sensitivity of numerous variables like solar position, torque tube position, panel tilt, and time itself. When predicting the power over an entire day, the power output curves for a single inverter matched almost exactly except for in the middle of the day due to possible inaccurate cell temperature modeling or the lack of considering degradation and soiling. Since the backtracking region of the power curve is modeled accurately, the optimization routine could be used to reduce interrow shading and maximize the energy output for a single zone of the solar field. By assuming every day is sunny, the optimization routine adjusted the onset of backtracking to improve the energy output by 117,695 kilowatt hours for the year or 8.14 percent compared to the nominal settings. The actual solar farm will likely never see this increase in energy due to cloudy days but should improve by a similar percentage. Further optimization of other zones can be analyzed to optimize the entire solar field.