Mathematical optimization is a key element in solving many problems from engineering. Areas such as signal processing, communications and networks, industrial design and production, and data analysis saw application of mathematical optimization. Many problems allow modelling as convex optimization programs or integer linear programs. A great advantage in the formulation of problems as convex programs and integer linear programs is the ability to use reliable and efficient solution methods. New advances in branch-and-bound methods, as well as the always increasing processing power of today's computers, makes it possible to solve integer linear programs of practically usable sizes. Ready-to-use solvers exist for both convex programs as well as integer linear programs. As systems become complexer, modelling these problems becomes a greater challenge. A core research challenge is to model these problems such that they can be solved using available solvers. If it is either not possible to model a problem in such a way that the available solvers can solve it or more flexibility is required than provided by these solvers, customly designed solvers and heuristics can lead to the desired solutions. This dissertation models problems from three different areas of engineering. All problems are of combinatorial nature. Most problems are modeled as integer linear programs. Where such a formulation is not applicable, a custom genetic algorithm is used to solve the problem.
