Heuristics for the traveling repairman problem with profits

In the traveling repairman problem with profits, a repairman (also known as the server) visits a subset of nodes in order to collect time-dependent profits. The objective consists of maximizing the total collected revenue. We restrict our study to the case of a single server with nodes located in the Euclidean plane. We investigate properties of this problem, and we derive a mathematical model assuming that the number of visited nodes is known in advance. We describe a tabu search algorithm with multiple neighborhoods, and we test its performance by running it on instances based on TSPLIB. We conclude that the tabu search algorithm finds good-quality solutions fast, even for large instances

Solving Rich Vehicle Routing Problem Using Three Steps Heuristic

Vehicle Routing Problem (VRP) relates to the problem of providing optimum service with a fleet of vehicles to customers. It is a combinatorial optimization problem. The objective is usually to maximize the profit of the operation. However, for public transportation owned and operated by government, accessibility takes priority over profitability. Accessibility usually reduces profit, while increasing profit tends to reduce accessibility. In this research, we look at how accessibility can be increased without penalizing the profitability. This requires the determination of routes with minimum fuel consumption, maximum number of ports of call and maximum load factor satisfying a number of pre-determined constraints: hard and soft constraints. To solve this problem, we propose a heuristic algorithm. The results from this experiment show that the algorithm proposed has better performance compared to the partitioning set

Minimum Makespan Multi-vehicle Dial-a-Ride

Dial a ride problems consist of a metric space (denoting travel time between vertices) and a set of m objects represented as source-destination pairs, where each object requires to be moved from its source to destination vertex. We consider the multi-vehicle Dial a ride problem, with each vehicle having capacity k and its own depot-vertex, where the objective is to minimize the maximum completion time (makespan) of the vehicles. We study the "preemptive" version of the problem, where an object may be left at intermediate vertices and transported by more than one vehicle, while being moved from source to destination. Our main results are an O(log^3 n)-approximation algorithm for preemptive multi-vehicle Dial a ride, and an improved O(log t)-approximation for its special case when there is no capacity constraint. We also show that the approximation ratios improve by a log-factor when the underlying metric is induced by a fixed-minor-free graph.Comment: 22 pages, 1 figure. Preliminary version appeared in ESA 200