A hybrid VNS/tabu search algorithm for apportioning the european parliament

Abstract

In a Proportional Representation (PR) electoral system it is assumed that seats are apportioned to the different electoral districts/states according to the corresponding voters' distribution. In a previous paper we proposed a MILP (Mixed Integer Linear Programming) model to apportion the seats in the European Parliament (EP). Since the exact solution to the problem is not computationally efficient, we have designed a hybrid metaheuristic algorithm based on Variable Neighborhood Search (VNS) and Tabu Search (TS). The proposed approach takes into account the existing situation, guaranteeing a minimum number of seats, independently of the population size of each member. The model is illustrated with actual data and its results are compared with the present apportionment. The results show that the proposed approach can significantly improve the proportionality of the present apportionment. © Springer-Verlag Berlin Heidelberg 2006.