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A genetic algorithm using conventional heuristics as operators is considered in this study for the traveling salesman problem with backhauls (TSPB). Properties of a crossover operator (Nearest Neighbor Crossover, NNX) based on the nearest neighbor heuristic and the idea of using more than two parents are investigated in a series of experiments. Different parent selection and replacement strategies and generation of multiple children are tried as well. Conventional improvement heuristics are also used as mutation operators. It has been observed that 2-edge exchange and node insertion heuristics work well with NNX using only two parents. The best settings among different alternatives experimented are applied on traveling salesman problem with backhauls (TSPB). TSPB is a problem in which there are two groups of customers. The aim is to minimize the distance traveled visiting all the cities, where the second group can be visited only after all cities in the first group are already visited. The approach we propose shows very good performance on randomly generated TSPB instances.

The Vehicle Routing Problem (VRP) is a classical problem in logistics that has been well studied by the operations research and transportation science communities. VRPs are defined as follows. Given a transportation network with a depot, a set of pickup or delivery locations, and a set of vehicles to service these locations: find a collection of routes starting and ending at the depot, such that (i) the customer's demand at a node is satisfied by exactly one vehicle, (ii) the total demand satisfied by a vehicle does not exceed its capacity, and (iii) the total distance traveled by the vehicles is minimized. This problem is especially hard to solve because of the presence of sub--tours, which can be exponential in number. In this dissertation, a special case of the VRP is considered -- where the underlying network has a tree structure (TVRP). Such tree structures are found in rural areas, river networks, assembly lines of manufacturing systems, and in networks where the customer service locations are all located off a main highway. Solution techniques for TVRPs that explicitly consider their tree structure are discussed in this dissertation. For example, TVRPs do not contain any sub-tours, thereby making it possible to develop faster solution methods. The variants that are studied in this dissertation include TVRPs with Backhauls, TVRPs with Heterogeneous Fleets, TVRPs with Duration Constraints, and TVRPs with Time Windows. Various properties and observations that hold true at optimality for these problems are discussed. Integer programming formulations and solution techniques are proposed. Additionally, heuristic methods and conditions for lower bounds are also detailed. Based on the proposed methodology, extensive computational analysis are conducted on networks of different sizes and demand distributions. / text

This study focuses on two types of routing problems based on standard Traveling Salesman Problem, which are TSP with pickup and delivery (TSPPD) and TSP with backhauls (TSPB). In both of these problems, there are two types of customers, i.e. &ldquo / delivery customers&rdquo / demanding goods from depot and &ldquo / pickup customers&rdquo / sending goods to depot. The objective is to minimize the cost of the tour that visits every customer once without violating the side constraints. In TSPB, delivery customers should precede the pickup customers, whereas the vehicle capacity should not be exceeded in TSPPD. The aim of the study is to propose good Evolutionary Algorithms (EA) for these two problems and also analyze the adaptability of an EA, originally designed for the standard TSP, to the problems with side constraints. This effort includes commenting on the importance of feasibility of the solutions in the population with respect to these side constraints. Having this in mind, different EA strategies involving feasible or infeasible solutions are designed. These strategies are compared by quantitative experiments realized over a set of problem instances and the results are given.