Diversity optimization and parameterized analysis of heuristic search methods for combinatorial optimization problems

Abstract

Heuristic search algorithms belong to the most successful approaches for many combinatorial optimization problems which have wide real world applications in various areas. The heuristic algorithms usually provide solutions with acceptable quality in reasonable timeframe which is different from exact algorithms. Fixed-parameter approach provides a way for understanding how and why heuristic methods perform well for prominent combinatorial optimization problems. In this thesis, there are two main topics discussed. Firstly, we integrate the well-known branching approach for the classical combinatorial optimization problem, namely minimum vertex cover problem, to a local search algorithm and compare its performance with the core component of the state-of-the-art algorithm. After that, we investigate how well-performing local search algorithms for small or medium size instances can be scaled up to solve massive input instances. A parallel kernelization technique is proposed which is motivated by the assumption that huge graphs are composed of several easy to solve components while the overall problem is hard to solve. Using evolutionary algorithms to generate a diverse set of solutions where all of them meet certain quality criteria has gained increasing interests in recent years. As the second section, we put forward an evolutionary algorithm which allows us to maximize the diversity over a set of solutions with good quality and then focus on the theoretical analysis of the algorithm to provide understanding of how evolutionary algorithms maximize the diversity of a population and guarantee the quality of all solutions at the same time. Then the idea is extended to evolving hard/easy optimization problem instances with diverse feature values. The feature-based analysis of heuristic search algorithms plays an important role in understanding the behaviour of the algorithm and our results show good classification of the problem instances in terms of hardness based on different combinations of feature values.