This study aims at improving the solution efficiency of Mixed Integer Nonlinear Programming (MINLP) through parallelism. Unlike most conventional parallel implementations of MINLP solvers, which utilize multi-threads to share the burden in the serial mode, the proposed method combines hybrid algorithms running on different threads. Two types of algorithms are designed in a parallel structure. One is the Quesada and Grossman's LP/NLP based branch and bound algorithm (QG); the other is Tabu Search (TS). The proposed method attempts to minimize the search space through continuous communication and exchange of intermediate results from each thread. Three kinds of information are exchanged between the two threads. First, the best solution in TS, if feasible, serves as a valid upper bound for QG. Second, new approximations which can further tighten the lower bound of QG can be generated at nodes provided by the TS. Third, strong branching in QG may fix some integer variables, which can help reduce the search space of TS. Both threads can thus benefit from the exchanged information in the hybrid method. Numerical results show that solution time can be greatly reduced for the tested MINLP. In addition, complexity analysis of the parallel approach suggests that the proposed method has the potential for superlinear speedup.

Keywords: Marketing Competition, Numerical Solution, Boundary Value Problem, Differential Game, Pricing Option, Leader-Follower Differential Game, Cooperative Differential Game, Evolutionary Computation, Stochastic Differential Game.

Model checking is a formal technique widely used to verify security and communication protocols in epistemic multi-agent systems against given properties. Qualitative properties such as safety and liveliness have been widely analysed in the literature. However, systems also have quantitative and uncertain (i.e., probabilistic) properties such as degree of reliability and reachability, which still need further attention from the model checking perspective. In this dissertation, we analyse such properties and present a new method for probabilistic model checking of epistemic multi-agent systems specified by a new probabilistic-epistemic logic PCTLK. We model multiagent systems distributed knowledge bases using probabilistic interpreted systems. We also define transformations from those interpreted systems into discrete-time Markov chains and from PCTLK formulae to PCTL formulae, an existing extension of CTL with probabilities. By so doing, we are able to convert the PCTLK model checking problem into the PCTL one. We address the problem of verifying probabilistic properties and epistemic properties in concurrent probabilistic systems as well. We then prove that model checking a formula of PCTLK in concurrent probabilistic systems is PSPACE-complete. Furthermore, we represent models associated with PCTLK logic symbolically with Multi-Terminal Binary Decision Diagrams (MTBDDs). Finally, we make use of PRISM, the model checker of PCTL without adding new computation cost. Dining cryptographers protocol is implemented to show the applicability of the proposed technique along with performance analysis and comparison in terms of execution time and state space scalability with MCK, an existing epistemic-probabilistic model checker, and MCMAS, a model checker for multi-agent systems. Another example, NetBill protocol, is also implemented with PRISM to verify probabilistic epistemic properties and to evaluate the complexity of this verification.