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An evolutionary approach for the dubins' traveling salesman problem with neighborhoods

In this work we propose an efficient and simple three-stage evolutionary algorithm to tackle the difficult problem of planning shorter paths through regions of an environment which are feasible for a nonholonomic vehicle with curvature constraints (e.g. Dubins' vehicle). Our method is able to efficiently solve both the combinatorial and the continuous steps of the problem in a combined manner. In the first phase, the method varies the position of the waypoints within the boundaries of each region, it then optimizes the path orientation at each waypoint, and finally it chooses the best actual sequence of visit. Numerous trials, under different scenarios in a simulated environment, were executed providing a thorough evaluation and validation of the methodology. The results show that a substantial improvement was obtained on the search for optimal paths in the DTSPN over current works in the literature. Numerical simulations also exhibit a significant performance improvement when compared with classical solutions that use the Alternating Algorithm, and they also show that our method outperforms a random sampling based technique. Our results present a reduction on the final path length of about 25% on average when compared to paths generated by the aforementioned methods.