The problem of multimodal functional optimization has been addressed by much research producing many different search techniques. Niche Genetic Algorithms is one area that has attempted to solve this problem. Many Niche Genetic Algorithms use some type of radius. When multiple optima occur within the radius, these algorithms have a difficult time locating them. Problems that have arbitrarily close optima create a greater problem. This paper presents a new Niche Genetic Algorithm framework called Dynamic-radius Species-conserving Genetic Algorithm. This new framework extends existing Genetic Algorithm research. This new framework enhances an existing Niche Genetic Algorithm in two ways. As the name implies the radius of the algorithm varies during execution. A uniform radius can cause issues if it is not set correctly during initialization. A dynamic radius compensates for these issues. The framework does not attempt to locate all of the optima in a single pass. It attempts to find some optima and then uses a tabu list to exclude those areas of the domain for future iterations. To exclude these previously located optima, the framework uses a fitness sharing approach and a seed exclusion approach. This new framework addresses many areas of difficulty in current multimodal functional optimization research. This research used the experimental research methodology. A series of classic benchmark functional optimization problems were used to compare this framework to other algorithms. These other algorithms represented classic and current Niche Genetic Algorithms. Results from this research show that this new framework does very well in locating optima in a variety of benchmark functions. In functions that have arbitrarily close optima, the framework outperforms other algorithms. Compared to other Niche Genetic Algorithms the framework does equally well in locating optima that are not arbitrarily close. Results indicate that varying the radius during execution and the use of a tabu list assists in solving functional optimization problems for continuous functions that have arbitrarily close optima.

The simulation of diffractive optical structures allows for the efficient testing of a large number of structures without having to actually fabricate these devices. Various forms of analysis of these structures have been done through computer programs in the past. However, programs that can actually design a structure to perform a given task are very limited in scope. Optimization of a structure can be a task that is very processor time intensive, particularly if the optimization space has many dimensions. This thesis describes the creation of a computer program that is able to find an optimal structure while maintaining a low-dimensional search space, thus greatly reducing the processor time required to find the solution. The program can design the optimal structure for a wide variety of planar optical devices that conform to the weakly-guiding approximation with an efficient code that incorporates the low-dimensional search space concept. This work is the first use of an electromagnetic field solver inside of an optimization loop for the design of an optimized diffractive-optic structure.

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

published_or_final_version / Business Administration / Master / Master of Business Administration

published_or_final_version / abstract / Civil Engineering / Master / Master of Philosophy

With aggressive technology scaling, within-die random variations are becoming the most dominant source of process variations. Gate-level statistical static timing is becoming a widely accepted approach as an alternative to static timing analysis. However, statistical timing approaches lack good models for handling timing variations due to within-die random variations. Before performing statistical timing analysis on a design or System On Chip (SoC), the cells in the library are pre-characterized for delay as well as constraints due to these random variations. This is referred to as statistical characterization of the cells. The major contribution of this dissertation is the development of novel techniques for statistical characterization and optimization of cells. The methods couple the knowledge of circuits along with the significant factor analysis methods to compute the sensitivities, to perform statistical timing and to perform sensitivity-aware cell optimizations. The first contribution of this dissertation is a statistical delay characterization method developed for computing delay sensitivities of standard cells considering both global and mismatch process variations. In addition to the cells being characterized for delay, the sequential cells are characterized for timing constraints like setup and hold time constraints. The second contribution of this dissertation addresses the problem of constraint sensitivity characterization in sequential cells. Block-based statistical timing approaches lack accurate consideration of the impact of slew variations on both delay and arrival time variations. Specifically, the delay variations due to within-die random variables (mismatch variables) result in a slew-based correlation during timing propagation. Handling within-die random variations more accurately during statistical timing propagation is the topic of the third contribution of this dissertation. Clock networks are more prone to these within-die random variations and can result in significant clock-skew variations. In the fourth contribution, a timing margining methodology is presented that accurately accounts for the clock skew variations in a timing sign-off flow. Typically, the standard cells are designed very early in the design cycle and long before the process reaches production maturity. Any subtle improvements to reduce variability in standard cells can improve parametric yield significantly. Statistical characterization of cells for timing provides a key baseline for understanding the circuit behavior due to different sources of variation. The sensitivity information can also help increase yield by reducing the variability during the circuit design itself. The final contribution in the dissertation addresses this by defining key cell and device criticality metrics. A sensitivity-aware standard cell layout optimization is demonstrated using the proposed criticality metrics. / text

This dissertation focuses on three cases of the following two stage problem in the context of multi-product inventories of vertically differentiated products. In Stage 1 of the problem, the manager determines the optimal production quantities of different products when the demands are uncertain. In Stage 2 of the problem, the demands for different products are observed. Now, the manager meets the demand of each product using the inventory of the product or by carrying out a downward substitution from the inventories of higher performance products. The manager’s objective is to maximize the expected revenue from the decisions made at the two stages collectively. The first problem addressed in this dissertation focuses on the case when different products are produced simultaneously on the same set of machines due to random variations in the manufacturing process. These systems, referred to as co-production systems, are very common in the semi- conductor industry, the textile industry and the agriculture industry. For this problem, we provide an analytical solution to the two stage problem, and discuss managerial insights that are specific to co-production systems and are not extendible to multi-item inventories of products that can be ordered or manufactured independently. The second problem addressed in this dissertation focuses on the case when different products can be ordered or manufactured independently, and no constraints to meet minimum fill rate requirements or to restrict the total inventory below a certain level are present. We present an analytical solution to this problem. The third problem addressed in this dissertation focuses on the case when different products can be ordered or manufactured independently and fill rate constraints and total inventory constraints are present. When the demands are multivariate normal, we show that this two stage problem can be reduced to a non-linear program using some new results for the determination of partial expectations. We also extend these results to higher order moments of the multivariate distribution and discuss their applications in solving some common operations management problems. / text

Compiler optimizations in the context of traditional program execution is a well-studied research area, and modern compilers typically offer a suite of optimization options. This thesis reports the first study (to our knowledge) on how standard compiler optimizations influence symbolic execution. We study 33 optimization flags of the LLVM compiler infrastructure, which are used by the KLEE symbolic execution engine. Specifically, we study (1) how different optimizations influence the performance of KLEE for Unix Coreutils, (2) how the influence varies across two different program classes, and (3) how the influence varies across three different back-end constraint solvers. Some of our findings surprised us. For example, KLEE's setting for applying the 33 optimizations in a pre-defined order provides sub-optimal performance for a majority of the Coreutils when using the basic depth-first search; moreover, in our experimental setup, applying no optimization performs better for many of the Coreutils. / text

As the semiconductor technology scales into deeper sub-micron domain, billions of transistors can be used on a single system-on-chip (SOC) makes interconnection optimization more important roughly for two reasons. First, congestion, power, timing in routing and buffering requirements make inter- connection optimization more and more challenging. Second, gate delay get- ting shorter while the RC delay gets longer due to scaling. Study of interconnection construction and optimization algorithms in real industry flows and designs ends up with interesting findings. One used to be overlooked but very important and practical problem is how to utilize over- the-block routing resources intelligently. Routing over large IP blocks needs special attention as there is almost no way to insert buffers inside hard IP blocks, which can lead to unsolvable slew/timing violations. In current design flows we have seen, the routing resources over the IP blocks were either dealt as routing blockages leading to a significant waste, or simply treated in the same way as outside-the-block routing resources, which would violate the slew constraints and thus fail buffering. To handle that, this work proposes a novel buffering-aware over-the- block rectilinear Steiner minimum tree (BOB-RSMT) algorithm which helps reclaim the “wasted” over-the-block routing resources while meeting user-specified slew constraints. Proposed algorithm incrementally and efficiently migrates initial tree structures with buffering-awareness to meet slew constraints while minimizing wire-length. Moreover, due to the fact that timing optimization is important for the VLSI design, in this work, timing-driven over-the-block rectilinear Steiner tree (TOB-RST) is also studied to optimize critical paths. This proposed TOB-RST algorithm can be used in routing or post-routing stage to provide high-quality topologies to help close timing. Then a follow-up problem emerges: how to accomplish the whole routing with over-the-block routing resources used properly. Utilizing over-the- block routing resources could dramatically improve the routing solution, yet require special attention, since the slew, affected by different RC on different metal layers, must be constrained by buffering and is easily violated. Moreover, even of all nets are slew-legalized, the routing solution could still suffer from heavy congestion problem. A new global router, BOB-Router, is to solve the over-the-block global routing problem through minimizing overflows, wire-length and via count simultaneously without violating slew constraints. Based on my completed works, BOB-RSMT and BOB-Router tremendously improve the overall routing and buffering quality. Experimental results show that proposed over-the-block rectilinear Steiner tree construction and routing completely satisfies the slew constraints and significantly outperforms the obstacle-avoiding rectilinear Steiner tree construction and routing in terms of wire-length, via count and overflows. / text

This report discusses a multi-stage stochastic programming model that maximizes expected ending time profit assuming investors can forecast a bull or bear market trend. If an investor can always predict the market trend correctly and pick the optimal stochastic strategy that matches the real market trend, intuitively his return will beat the market performance. For investors with different levels of prediction accuracy, our analytical results support their decision of selecting the highest return strategy. Real stock prices of 154 stocks on 73 trading days are collected. The computational results verify that accurate prediction helps to exceed market return while portfolio profit drops if investors partially predict or forecast incorrectly part of the time. A sensitivity analysis shows how risk control requirements affect the investor's decision on selecting stochastic strategies under the same prediction accuracy. / text