A Tabu Move Merge Split (TMMS) algorithm is proposed for the polygonal approximation problem. TMMS incorporates a tabu principle to avoid premature convergence into local minima. TMMS is compared to optimal, near to optimal top down Multi-Resolution (TDMR) and classical split and merge heuristics solutions. Experiments show that potential improvements for crudest approximations can be obtained. The evaluation is carried out on 2D geographic maps according to effectiveness and efficiency measures.