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.

THE DESIGN OF A POWER SYSTEM FOR A WIRELESS SENSOR NETWORK FOR LONG-TERM OPERATION

Wireless sensor networks (WSNs) have shown wide applicability to many fields including monitoring of environmental, civil, and industrial settings. WSNs however are resource constrained by many competing factors that span their hardware, software, and networking. One of the central resource constrains is the charge consumption of WSN nodes. With finite energy supplies, low charge consumption is needed to ensure long lifetimes and success of WSNs. This thesis details the design of a power system to support long-term operation of WSNs. The power system’s development occurs in parallel with a custom WSN from the Queen’s MEMS Lab (QML-WSN), with the goal of supporting a 1+ year lifetime without sacrificing functionality. The final power system design utilizes a TPS62740 DC-DC converter with AA alkaline batteries to efficiently supply the nodes while providing battery monitoring functionality and an expansion slot for future development. Testing tools for measuring current draw and charge consumption were created along with analysis and processing software. Through their use charge consumption of the power system was drastically lowered and issues in QML-WSN were identified and resolved including the proper shutdown of accelerometers, and incorrect microcontroller unit (MCU) power pin connection. Controlled current profiling revealed unexpected behaviour of nodes and detailed current-voltage relationships. These relationships were utilized with a lifetime projection model to estimate a lifetime between 521-551 days, depending on the mode of operation. The power system and QML-WSN were tested over a long term trial lasting 272+ days in an industrial testbed to monitor an air compressor pump. Environmental factors were found to influence the behaviour of nodes leading to increased charge consumption, while a node in an office setting was still operating at the conclusion of the trail. This agrees with the lifetime projection and gives a strong indication that a 1+ year lifetime is achievable. Additionally, a light-weight charge consumption model was developed which allows charge consumption information of nodes in a distributed WSN to be monitored. This model was tested in a laboratory setting demonstrating +95% accuracy for high packet reception rate WSNs across varying data rates, battery supply capacities, and runtimes up to full battery depletion.