Traffic congestion, noise and tailpipe emissions arc negative externalities from transportation that need to he reduced to make cities more livable. Electric buses can help significantly reducing noise and tailpipe emissions. However, they provide nowadays limited range due to battery capacity, affecting their operating flexibility-. Plug-in electric hybrid buses are a versatile solution that offer certain zero-emission capability, which depends on the battery capacity and how electric drive is distributed over a route. This is managed by an electric drive assignment system that determines the optimal locations to use the electric motor. Today's assignment systems are in their early development stages, and do not exploit the full potentials. This work introduces a novel combinatorial optimization problem to find optimal electric drive assignment strategies for a number of bus lines under the presence of zero- and restricted-emissions zones. The latter is a new concept introduced here where tailpipe emissions are allowed but restricted to a predefined limit. The goal is to maximize the electric range of the buses and minimize the total pollution emitted, while at the same time complying with the mandatory zero-emission zones and the restricted-emission zones. CCMOCeII, a parallel Cooperative Co-evolutionary version of the well-known Multi-objective Cellular genetic algorithm, MOCell, is proposed to solve the problem, and solutions are compared against those found by MOCeII itself, and validated using a heuristic from the literature, GreenK. Six lines from Barcelona's bus network (Spain), are considered, and real topological data obtained from administrations and digital elevation models are used. The two multi-objective algorithms reduced pollutant emissions by up to 20% with respect to GreenK. Also, CCMOCeII outperformed it in terms of electric range by up to 6.26%.