Combinatorial Optimization

Combinatorial Optimization is an active research area that developed from the rich interaction among many mathematical areas, including combinatorics, graph theory, geometry, optimization, probability, theoretical computer science, and many others. It combines algorithmic and complexity analysis with a mature mathematical foundation and it yields both basic research and applications in manifold areas such as, for example, communications, economics, traffic, network design, VLSI, scheduling, production, computational biology, to name just a few. Through strong inner ties to other mathematical fields it has been contributing to and benefiting from areas such as, for example, discrete and convex geometry, convex and nonlinear optimization, algebraic and topological methods, geometry of numbers, matroids and combinatorics, and mathematical programming. Moreover, with respect to applications and algorithmic complexity, Combinatorial Optimization is an essential link between mathematics, computer science and modern applications in data science, economics, and industry

Multi-objective combinatorial optimization problems in transportation and defense systems

Multi-objective Optimization problems arise in many applications; hence, solving them efficiently is important for decision makers. A common procedure to solve such problems is to generate the exact set of Pareto efficient solutions. However, if the problem is combinatorial, generating the exact set of Pareto efficient solutions can be challenging. This dissertation is dedicated to Multi-objective Combinatorial Optimization problems and their applications in system of systems architecting and railroad track inspection scheduling. In particular, multi-objective system of systems architecting problems with system flexibility and performance improvement funds have been investigated. Efficient solution methods are proposed and evaluated for not only the system of systems architecting problems, but also a generic multi-objective set covering problem. Additionally, a bi-objective track inspection scheduling problem is introduced for an automated ultrasonic inspection vehicle. Exact and approximation methods are discussed for this bi-objective track inspection scheduling problem --Abstract, page iii

Pattern-driven neighborhood search for biclustering of microarray data

Biclustering aims at finding subgroups of genes that show highly correlated behaviors across a subgroup of conditions. Biclustering is a very useful tool for mining microarray data and has various practical applications. From a computational point of view, biclustering is a highly combinatorial search problem and can be solved with optimization methods