New Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming

Process systems design, operation and synthesis problems under uncertainty can readily be formulated as two-stage stochastic mixed-integer linear and nonlinear (nonconvex) programming (MILP and MINLP) problems. These problems, with a scenario based formulation, lead to large-scale MILPs/MINLPs that are well structured. The first part of the thesis proposes a new finitely convergent cross decomposition method (CD), where Benders decomposition (BD) and Dantzig-Wolfe decomposition (DWD) are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. A variant of CD, which includes multiple columns per iteration of DW restricted master problem and multiple cuts per iteration of BD relaxed master problem, called multicolumn-multicut CD is then developed to improve solution time. Finally, an extended cross decomposition method (ECD) for solving two-stage stochastic programs with risk constraints is proposed. In this approach, a CD approach at the first level and DWD at a second level is used to solve the original problem to optimality. ECD has a computational advantage over a bilevel decomposition strategy or solving the monolith problem using an MILP solver. The second part of the thesis develops a joint decomposition approach combining Lagrangian decomposition (LD) and generalized Benders decomposition (GBD), to efficiently solve stochastic mixed-integer nonlinear nonconvex programming problems to global optimality, without the need for explicit branch and bound search. In this approach, LD subproblems and GBD subproblems are systematically solved in a single framework. The relaxed master problem obtained from the reformulation of the original problem, is solved only when necessary. A convexification of the relaxed master problem and a domain reduction procedure are integrated into the decomposition framework to improve solution efficiency. Using case studies taken from renewable resource and fossil-fuel based application in process systems engineering, it can be seen that these novel decomposition approaches have significant benefit over classical decomposition methods and state-of-the-art MILP/MINLP global optimization solvers.

Character in Context: Informing Character Education Programming

The Positive Youth Development (PYD) perspective is a strength-based conceptualization of youth. It highlights the importance of mutually beneficial relationships between youth and their environment to develop the “Five Cs”, key assets that include character. Character has long been a subject of programming due to its focus on helping children lead moral, empathic, and prosocial lives. There are, however, many limitations in character research, including poorly operationalized definitions of character; a failure to examine the developmental and broader social context in which character exists; and a lack of evaluation of more practical character programming. The goal of this dissertation was to address these gaps in knowledge and inform the character education programming literature. The first study examined the relationships among age, gender, the school social context, and character. Moral character was negatively associated with grade, and being a girl was positively associated with moral character. The relationships between positive peer interactions at school and character (fairness, integrity) were stronger among students who reported low initial moral character when positive peer interactions was high. In the second study, the Build Character: Build Success Program, a character education program, was evaluated over six months to examine its effects on character behaviours, victimization, and school climate. No program effects were found for students in grades 1 to 3, but a slight decrease in victimization in one experimental school was found for students in grades 4 to 8. This lack of general program effects may be due to the short-term nature of the intervention, which may not have been long enough to result in measurable behaviour change. Implementation data indicated that teachers did not teach all program elements, which also may have influenced the results of the program evaluation. The present dissertation contributes to knowledge about character and its programming by: introducing new measures to operationalize character, discovering developmental patterns in character in school-aged children, highlighting gender differences in character, examining character within its broad social context, and evaluating short-term character education programming.

Code pattern analysis of object-oriented programming languages

Code patterns, including programming patterns and design patterns, are good references for programming language feature improvement and software re-engineering. However, to our knowledge, no existing research has attempted to detect code patterns based on code clone detection technology. In this study, we build upon the previous work and propose to detect and analyze code patterns from a collection of open source projects using NiPAT technology. Because design patterns are most closely associated with object-oriented languages, we choose Java and Python projects to conduct our study. The tool we use for detecting patterns is NiPAT, a pattern detecting tool originally developed for the TXL programming language based on the NiCad clone detector. We extend NiPAT for the Java and Python programming languages. Then, we try to identify all the patterns from the pattern report and classify them into several different categories. In the end of the study, we analyze all the patterns and compare the differences between Java and Python patterns.