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A solution to the multiple depot heterogeneous traveling salesman problem with a min-max objective is in great demand with many potential applications of unmanned vehicles, as it is highly related to a reduction in the job completion time. As an initial idea for solving the min-max multiple depot heterogeneous traveling salesman problem, new heuristics for path planning problem of two heterogeneous unmanned vehicles are proposed in this article. Specifically, a task allocation and routing problem of two (structurally) heterogeneous unmanned vehicles that are located in distinctive depots and a set of targets to visit is considered. The unmanned vehicles, being heterogeneous, have different travel costs that are determined by their motion constraints. The objective is to find a tour for each vehicle such that each target location is visited at least once by one of the vehicles while the maximum travel cost is minimized. Two heuristics based on a primal-dual technique are proposed to solve the cases where the travel costs are symmetric and asymmetric. The computational results of the implementation have shown that the proposed algorithms produce feasible solutions of good quality within relatively short computation times.

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In this article, we present the first approximation algorithm for a routing problem that is frequently encountered in the motion planning of Unmanned Vehicles (UVs). The considered problem is a variant of a Multiple Depot-Terminal Hamiltonian Path Problem and is stated as follows: There is a collection of m UVs equipped with different sensors on-board and there are n targets to be visited by them collectively. There are restrictions on the targets of the following type: (1) A target may be visited by any UV, (2) a target must be visited only by a subset of UVs (with appropriate on-board sensor) and (3) a target may not be visited by a subset of UVs (as the set of onboard sensors on the UV may not be suitable for viewing the targets). The UVs are otherwise identical from the viewpoint of dynamic constraints on their motion and hence, the cost of traveling from a target A to a target B is the same for all vehicles. We will assume that triangle inequality is satisfied by the cost associated with travel, i.e., it is cheaper to travel from a target A to a target B directly than to go via an intermediate target C. The UVs may possibly start from different locations (referred to as depots) and are not required to return to the depot. While there are different objectives that can be considered for this problem, we consider the total cost of travel of all the UVs as an objective to be minimized. The problem considered in this article is a generalized version of single depot-terminal Hamiltonian Path Problem and is NP-hard.