| Abstract [eng] |
The dissertation investigates several constrained planar multi-location problems. Problem variables here are the coordinates of a given number of points in the plane, and the goal is to put these points in such a way that the cost of the placement is minimal. The unifying feature of the problems considered is that optimization variables (the points) are required to belong to a constrained set, which is not assumed to be convex (e.g., can contain ``holes’’). This makes the problems challenging and interesting. In the thesis, three main constrained planar multi-location models are considered. - Net-constrained equal area Voronoi tessellation. The goal is to place a number of points, called sites, in such a way that the resulting Voronoi cells have equal areas. Sites are restricted to belong to a net (i.e., a union of segments). - Net-constrained minimum sum of squares clustering. The goal is to group the given point set (called clients) into clusters and to determine the optimal cluster centers (called facilities) such that the sum of squared distances from the clients to the facilities is minimal. Optimization variables are the facility locations, these points are required to satisfy the net constraint. - Multi-Weber problem with polyhedral barriers. Here, barriers in the plane are introduced where traveling is prohibited. The goal is to determine the optimal facility locations such that the sum of barrier-induced distances between the clients and the facilities is minimal. |
