Bi-objective Grouping and Tabu Search

When dealing with small sizes in zone design, the problem can have a polynomial cost solution by exact methods. Otherwise, the combinatorial nature of this problem is unavoidable and entails an increasing computational complexity that makes necessary the use of metaheuristics. Specifically, when using partitioned grouping as a tool to solve a territorial design problem, geometric compactness is indirectly satisfied, which is one of the compulsory restrictions in territorial design when optimizing for a single objective. However, the inclusion of additional cost functions such as homogeneity imply a greater difficulty since the objective function becomes multi-objective. In this case, partitioning is used to build compact groups over a territory and the partitions are adjusted to satisfy both, compactness and homogeneity, or balance the number of objects for each group. The work presented here gives answers to territorial design problems where the problem is presented as bi-objective and aims at striking a compromise between geometric compactness and homogeneity and the cardinality of the groups. The approximation method is Tabu Search.