A Local Search Heuristic for Biobjective Intersecting Geometric Graphs

In this work, we consider the problem of constructing spanning trees from two geometric graphs corresponding to two nets, each with multiple terminals, with a goal to minimize the total edge cost and the number of intersections among the edges of the two trees. Such an optimization problem is computationally hard for which no efficient algorithm or good heuristic is known to exist. Additionally, in a biobjective setting, the major challenge to solve a problem is to obtain many representative diverse solutions across the (near-) optimal Pareto-front. We present a local search based heuristic to find near-optimal Pareto-front in the feasible solution space. Each element of this solution set is a tuple of two spanning trees corresponding to the given geometric graphs. The heuristic is shown to give superior results over the existing stochastic technique