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.

Classifying And Predicting Software Security Vulnerabilities based on Reproducibility

Security defects are common in large software systems because of their size and complexity. Although efficient development processes, testing, and maintenance policies are applied to software systems, there are still a large number of vulnerabilities that can remain, despite these measures. Some vulnerabilities stay in a system from one release to the next one because they cannot be easily reproduced through testing. These vulnerabilities endanger the security of the systems. We propose vulnerability classification and prediction frameworks based on vulnerability reproducibility. The frameworks are effective to identify the types and locations of vulnerabilities in the earlier stage, and improve the security of software in the next versions (referred to as releases). We expand an existing concept of software bug classification to vulnerability classification (easily reproducible and hard to reproduce) to develop a classification framework for differentiating between these vulnerabilities based on code fixes and textual reports. We then investigate the potential correlations between the vulnerability categories and the classical software metrics and some other runtime environmental factors of reproducibility to develop a vulnerability prediction framework. The classification and prediction frameworks help developers adopt corresponding mitigation or elimination actions and develop appropriate test cases. Also, the vulnerability prediction framework is of great help for security experts focus their effort on the top-ranked vulnerability-prone files. As a result, the frameworks decrease the number of attacks that exploit security vulnerabilities in the next versions of the software. To build the classification and prediction frameworks, different machine learning techniques (C4.5 Decision Tree, Random Forest, Logistic Regression, and Naive Bayes) are employed. The effectiveness of the proposed frameworks is assessed based on collected software security defects of Mozilla Firefox.