An exact algorithm for a heterogeneous, multiple depot, multiple traveling salesman problem

Abstract

Unmanned aerial vehicles are being used in several monitoring applications to collect data from a set of targets. These vehicles are heterogeneous in the sense that they can differ either in their motion constraints or sensing capabilities. Furthermore, not all vehicles may be able to visit a given target because vehicles may occasionally be equipped with disparate sensors due to the respective payload restrictions. This article addresses a problem where a group of heterogeneous vehicles located at distinct depots visit a set of targets. The targets are partitioned into disjoint subsets: targets to be visited by specific vehicles and targets that any of the vehicles can visit. The objective is to find an optimal tour for each vehicle starting at its respective depot such that each target is visited at least once by some vehicle, the vehicle-target constraints are satisfied and the sum of the costs of the tours for all the vehicles is minimized. We formulate the problem as a mixed-integer linear program and develop a branch-and-cut algorithm to compute an optimal solution to the problem. Computational results show that optimal solutions for problems involving 100 targets and 5 vehicles can be obtained within 300 seconds on average, further corroborating the effectiveness of the proposed approach.

Memetic algorithm-based path generation for multiple Dubins vehicles performing remote tasks

“…Whenever the solver gets a feasible solution of the relaxed problem, the callback procedure is called which checks whether the solution violates any of the constraints in Eq. (6). If the tasks assigned to each vehicle are connected and satisfy the subtour elimination constraints, the solution is regarded as a true solution for the given problem and it is accepted.…”

“…Recent decades have observed significant signs of progress in research on automation/autonomy of unmanned vehicles in many different aspects such as mission planning, resource allocation, motion coordination, path planning, lowlevel control, sensing, and communication [1,2]. In particular, multi-agent aspects of a group of unmanned vehicles have been studied to enhance mission performance and resource utilization [3], particularly allowing for heterogeneity in agent capabilities and characteristics [4,5,6]. One crucial decision to fully take advantage of the extended capability of heterogeneous multiple autonomous vehicles is to design paths/tours for the agents in such a way that optimizes a certain mission performance metric.…”

Path planning for cooperative routing of air-ground vehicles

“…This section introduces a class of valid inequalities for the CAGVRP. These inequalities are derived from the 2matching inequalities for the traveling salesman problem [28]- [30] and is also valid for the ring-star problem and its variants [16], [17], [31]. Specifically, we consider the following inequality:…”

“…The proof of validity of the above inequality is given by the following proposition. One can refer to [16], [17], [31] for the proof of this proposition.…”

Min-Max Tours for Task Allocation to Heterogeneous Agents

“…In order to effectively utilize these multi-robot systems in such applications, it is necessary to allocate an appropriate set of tasks to each robot or agent in the system. Such problems have been widely considered in the literature [1][2][3][4][5], most typically for the case where all agents are the same. However, future multi-robot systems are also projected to have a large amount of diversity in terms of the capabilities of the agents, and the applications will consist of tasks that can only be done by agents that possess certain capabilities [6][7][8][9][10].…”