Hybrid Metaheuristics and Matheuristics for Problems in Bioinformatics and Transportation

The general aim of this doctoral thesis was to thoroughly investigate diverse hybrid optimization strategies for certain classes ofNP-hard combinatorial optimization problems. For this basic concepts should be refined and further developed. The ultimate goals were twofold: to come up with highly effective, new state-of-the-art methods for solving the selected benchmark problems, and to gain further experience and knowledge of the specific pros and cons in order to apply the methods more generally in meaningful ways also to other problems. In general, such hybrids try to combine in various ways the strengths of two or more methods from possibly different streams. It was further intended to focus in particular on combining exact and (meta-)heuristic algorithms, especially exploiting the power of mathematical programming techniques, yielding so-called matheuristics (or model-based metaheuristics). Although we did not decide on the problems which would be tackled right from the start— as I was more interested in the methodical aspect—it eventually turned out that we dealt with problems that are not only interesting from an academic perspective but highly relevant in practical application areas, too. The first is the consensus tree problem which primarily arises in phylogenetics and thus belongs to the domain of bioinformatics. Its objective is to build a single solution tree out of several phylogenetic trees given as input, somehow best representing the whole available information. All remaining problems arise in the field of transportation and are extensions of the capacitated vehicle routing problem (CVRP) motivated by important real-world aspects. These variants are in fact generalizations, as the CVRP can be considered a special case of each one. Following ones are considered: the periodic vehicle routing problem and the periodic vehicle routing problem with time windows, where customers usually need to be visited multiple times in a given planning horizon, also respecting (hard) customer time windows in case of the latter; the location-routing problem as well as the periodic location-routing problem, which add to the CVRP the task of simultaneously placing some facilities at given locations (i.e. corresponding to theNP-hard facility location problem); and finally the vehicle routing problem with compartments, considering not a single loading area and product but several compartments and products, possibly involving certain incompatibilities. Several forms of hybridization are investigated in this work: collaboratively exchanging solutions, tight integration of the concepts of a method in another one, multilevel refinement, the guidance of a method by information gathered by another one, heuristic column generation as well as heuristic cut separation, very large neighborhood search based on integer linear programming and a more sophisticated variant of it also realizing an optimal merging by exploiting the information of several solutions, and finally solving subproblems to optimality.