On Hybrid Heuristics for Steiner Trees on the Plane with Obstacles

Minimal-length Steiner trees in the two-dimensional Euclidean domain are of special interest to enable the efficient coordination of multi-agent and interconnected systems. We propose an approach to compute obstacle-avoiding Steiner trees by using the hybrid between hierarchical optimization of shortest routes through sequential quadratic programming over constrained two-dimensional convex domains, and the gradient-free stochastic optimization algorithms with a convex search space. Our computational experiments involving 3,000 minimal tree planning scenarios in maps with convex and non-convex obstacles show the feasibility and the efficiency of our approach. Also, our comparative study involving relevant classes of gradient-free and nature inspired heuristics has shed light on the robustness of the selective pressure and exploitation abilities of the Dividing Rectangles (DIRECT), the Rank-based Differential Evolution (RBDE) and the Differential Evolution with Successful Parent Selection (DESPS). Our approach offers the cornerstone mechanisms to further advance towards developing efficient network optimization algorithms with flexible and scalable representations.