This paper formalises path planning problem for a group of heterogeneous Dubins vehicles performing tasks in a remote fashion and develops a memetic algorithm-based method to effectively produce the paths. In the setting, the vehicles are initially located at multiple depots in a two-dimensional space and the objective of planning is to minimise a weighted sum of the total tour cost of the group and the largest individual tour cost amongst the vehicles. While the presented formulation takes the form of a mixed-integer linear programme (MILP) for which off-the-shelf solvers are available, the MILP solver easily loses the tractability as the number of tasks and agents grow. Therefore, a memetic algorithm tailored to the presented formulation is proposed. The algorithm features a sophisticated encoding scheme to efficiently select the order of performing tasks. In addition, a path refinement technique that optimises detailed tours with the sequence of visits fixed is proposed to finally obtain further optimised trajectories. Comparative numerical experiments show the validity and efficiency of the proposed methods compared with the previous methods in the literature.