Mathematical optimization is a common tool for numerous real-world optimization problems.
However, in some application domains there is a scope for improvement of currently used optimization techniques.
For example, this is typically the case for applications that contain features which are difficult to model, and applications of interdisciplinary nature where no strong optimization knowledge is available.
The goal of this thesis is to demonstrate how to overcome these challenges by considering five problems from two application domains.
The first domain that we address is scheduling in Cloud computing systems, in which we investigate three selected problems.
First, we study scheduling problems where jobs are required to start immediately when they are submitted to the system.
This requirement is ubiquitous in Cloud computing but has not yet been addressed in mathematical scheduling.
Our main contributions are (a) providing the formal model, (b) the development of exact and efficient solution algorithms, and (c) proofs of correctness of the algorithms.
Second, we investigate the problem of energy-aware scheduling in Cloud data centers.
The objective is to assign computing tasks to machines such that the energy required to operate the data center, i.e., the energy required to operate computing devices plus the energy required to cool computing devices, is minimized.
Our main contributions are (a) the mathematical model, and (b) the development of efficient heuristics.
Third, we address the problem of evaluating scheduling algorithms in a realistic environment.
To this end we develop an approach that supports mathematicians to evaluate scheduling algorithms through simulation with realistic instances.
Our main contributions are the development of (a) a formal model, and (b) efficient heuristics.
The second application domain considered is powerline routing.
We are given two points on a geographic area and respective terrain characteristics.
The objective is to find a ``good'' route (which depends on the terrain), connecting both points along which a powerline should be built.
Within this application domain, we study two selected problems.
First, we study a geometric shortest path problem, an abstract and simplified version of the powerline routing problem.
We introduce the concept of the k-neighborhood and contribute various analytical results.
Second, we investigate the actual powerline routing problem.
To this end, we develop algorithms that are built upon the theoretical insights obtained in the previous study.
Our main contributions are (a) the development of exact algorithms and efficient heuristics, and (b) a comprehensive evaluation through two real-world case studies.
Some parts of the research presented in this thesis have been published in refereed publications [119], [110], [109].
