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.

Bullying Victimization and Perpetration Among Adolescent Sport Teammates

Purpose: Bullying is a specific pattern of repeated victimization explored with great frequency in school-based literature, but receiving little attention within sport. The current study explored the prevalence of bullying in sport, and examined whether bullying experiences were associated with perceptions about relationships with peers and coaches. Method: Adolescent sport team members (n = 359, 64% female) with an average age of 14.47 years (SD = 1.34) completed a pen-and-paper or online questionnaire assessing how frequently they perpetrated or were victimized by bullying during school and sport generally, as well as recent experiences with 16 bullying behaviors on their sport team. Participants also reported on relationships with their coach and teammates. Results: Bullying was less prevalent in sport compared with school, and occurred at a relatively low frequency overall. However, by identifying participants who reported experiencing one or more act of bullying on their team recently, results revealed that those victimized through bullying reported weaker connections with peers, whereas those perpetrating bullying only reported weaker coach relationships. Conclusion: With the underlying message that bullying may occur in adolescent sport through negative teammate interactions, sport researchers should build upon these findings to develop approaches to mitigate peer victimization in sport.