Parallel nonconvex generalized Benders decomposition for natural gas production network planning under uncertainty

A scenario-based two-stage stochastic programming model for gas production network planning under uncertainty is usually a large-scale nonconvex mixed-integer nonlinear programme (MINLP), which can be efficiently solved to global optimality with nonconvex generalized Benders decomposition (NGBD). This paper is concerned with the parallelization of NGBD to exploit multiple available computing resources. Three parallelization strategies are proposed, namely, naive scenario parallelization, adaptive scenario parallelization, and adaptive scenario and bounding parallelization. Case study of two industrial natural gas production network planning problems shows that, while the NGBD without parallelization is already faster than a state-of-the-art global optimization solver by an order of magnitude, the parallelization can improve the efficiency by several times on computers with multicore processors. The adaptive scenario and bounding parallelization achieves the best overall performance among the three proposed parallelization strategies.

Linear Hyperspectral Unmixing Using L0-norm Approximations and Nonnegative Matrix Factorization

Spectral unmixing (SU) is a technique to characterize mixed pixels of the hyperspectral images measured by remote sensors. Most of the existing spectral unmixing algorithms are developed using the linear mixing models. Since the number of endmembers/materials present at each mixed pixel is normally scanty compared with the number of total endmembers (the dimension of spectral library), the problem becomes sparse. This thesis introduces sparse hyperspectral unmixing methods for the linear mixing model through two different scenarios. In the first scenario, the library of spectral signatures is assumed to be known and the main problem is to find the minimum number of endmembers under a reasonable small approximation error. Mathematically, the corresponding problem is called the $\ell_0$-norm problem which is NP-hard problem. Our main study for the first part of thesis is to find more accurate and reliable approximations of $\ell_0$-norm term and propose sparse unmixing methods via such approximations. The resulting methods are shown considerable improvements to reconstruct the fractional abundances of endmembers in comparison with state-of-the-art methods such as having lower reconstruction errors. In the second part of the thesis, the first scenario (i.e., dictionary-aided semiblind unmixing scheme) will be generalized as the blind unmixing scenario that the library of spectral signatures is also estimated. We apply the nonnegative matrix factorization (NMF) method for proposing new unmixing methods due to its noticeable supports such as considering the nonnegativity constraints of two decomposed matrices. Furthermore, we introduce new cost functions through some statistical and physical features of spectral signatures of materials (SSoM) and hyperspectral pixels such as the collaborative property of hyperspectral pixels and the mathematical representation of the concentrated energy of SSoM for the first few subbands. Finally, we introduce sparse unmixing methods for the blind scenario and evaluate the efficiency of the proposed methods via simulations over synthetic and real hyperspectral data sets. The results illustrate considerable enhancements to estimate the spectral library of materials and their fractional abundances such as smaller values of spectral angle distance (SAD) and abundance angle distance (AAD) as well.

EXAMINING HOW SAME-GENDER AND MIXED-GENDER COUPLES NAVIGATE SEXUAL ISSUES IN THEIR RELATIONSHIPS

Sexual scripts—the definitions and expectations that individuals hold for sexual interactions—are thought to play an important role in the maintenance of sexual well-being. Sexual scripts can be rigid or flexible, and they can be concordant or discordant between members of a couple. Sex therapists support sexual script flexibility for maintaining sexual and relationship satisfaction when couples are navigating sexual issues. However, empirical research examining the role of sexual script flexibility and the degree of script concordance/discordance in couples’ sexual well-being has been limited, due in part to the limited measures available. Furthermore, within the existing research, there has been an unfortunate tendency to exclude individuals in same-gender relationships – perpetuating the long-standing knowledge gap in the literature on positive sexuality in diverse relationships. To address these gaps in the literature, we conducted a series of online studies that recruited individuals in diverse relationships. A measure of individual sexual script flexibility in response to sexual issues was developed (Chapter 2); in addition, the structure of an existing measure assessing couple sexual scripts in response to a sexual issue was evaluated (Chapter 3). Chapter 4 examined how individuals in diverse relationships compared on measures of individual sexual script flexibility and on couple sexual scripts. Findings suggest that there are more similarities than differences across diverse couples. Chapter 5 explored how flexibility in an individual’s approach to sexual issues relates to sexual well-being, specifically by assessing sexual communication and partner responses as mediators. Results suggest that individual sexual script flexibility relates to sexual well-being through reciprocal partner processes. Collectively, this research program suggests that more similarities than differences exist between individuals in same- and mixed-gender relationships, and that partners are important to consider in the relationship between individual sexual script flexibility and sexual well-being. These findings have implications for sex and couple therapy; these results emphasize the importance of interventions that target both members of the couple, and further our understanding of sexuality in same- and mixed-gender relationships.