### Studies on local search-based approaches for vehicle routing and scheduling problems

Hideki Hashimoto
Preface Vehicle routing and scheduling are problems concerning the distribution of goods between depots and final users. The standard objective is minimizing the total travel distance of a number of vehicles, under various constraints, where every customer must be visited exactly once by a vehicle. They have been intensively studied since a paper by Dantzig and Ramser appeared in 1959, and there have been hundreds of successful applications in many industries. These application successes have
more » ... en aided by the growing computer power, the geographic information system (GIS) technology, and so on. Including vehicle routing and scheduling problems, a variety of combinatorial optimization problems appear in many application fields. It is known to be difficult to obtain exact optimal solutions to them, and the difficulties were proved in the sense of NP-hardness. It is strongly believed that an NP-hard problem cannot be solved in polynomial time of the input size. In other words, solving an NP-hard problem exactly may necessitate enumerating an essential portion of the set of all solutions, whose number increases exponentially as problem size grows. However, in most practical applications, we do not need exact optimal solutions and are satisfied with sufficiently good solutions. In this sense, heuristic algorithms, which provide reasonably good solutions in practical time, have a significant benefit. There are several representative heuristic algorithms, such as greedy methods and local search. A greedy method directly constructs a solution by successively determining the values of variables on the basis of some local information. This method can find good solutions in very short time in many cases. Local search is the method that improves the current solution iteratively. Although, in general, it is not a polynomial time algorithm, it was reported that near-optimal solutions could typically be obtained in reasonable time. More sophisticated algorithms that utilize the local search in more flexible frameworks such as iterated local search, tabu search, simulated annealing, genetic algorithm and their variants have been studied well, and applied to many NP-hard problems. Such algorithms are generically called metaheuristics. In this thesis, we describe general models for vehicle routing and scheduling problems iv Preface and propose efficient local search-based algorithms for them incorporating mathematical programming techniques. We also propose a high-performance metaheuristic algorithm for a standard vehicle routing and scheduling problem. The aim of the thesis is to propose general models that can include various types of specific variants, and to develop highperformance algorithms. Vehicle routing and scheduling problems are fundamental issues in human society. As information tools related to vehicle routing and scheduling (e.g., GIS, demand forecasting) have recently been enhanced, an efficient algorithm may immediately make an improvement on these issues.