We study call routing policies commonly used in call centers with multiple call types and multiple agent groups. We propose a new weight-based routing policy where each pair (call type, agent group) is given a matching priority defined as an affine combination of the longest waiting time for that call type and the longest idle time in that agent group. The coefficients in this combination are parameters to be optimized. This type of policy is more flexible than traditional ones found in practice, and it performs better in many situations. We consider objective functions that account for the service levels, the abandonment ratios, and the fairness of occupancy across agent groups. We select the parameters of all considered policies via simulation-based optimization heuristics. This only requires the availablity of a simulation model of the call center, which can be much more detailed and realistic than the models used elsewhere in the literature to study the optimality of certain types of routing rules. We offer a first numerical study of realistic routing rules that takes into account the complexity of real-life call centers. Key words: multi-skill call centers; contact centers; call routing policies; simulation; stochastic optimization History: 1.