In this paper, we formulate a resource allocation optimization problem for a cooperative relay-assisted cognitive radio system, comprising a single source node, multiple relays and multiple destinations. Our formulation takes into account the effects of the resource allocation on CO₂ emission, and we refer to it as a green resource allocation problem. The green resource allocation problem is formulated as a non-linear multi-objective optimization problem. We modify the objective function by applying the weighted sum method, which results in a non-convex mixed integer non-linear programming problem. We propose a hybrid evolutionary scheme that utilizes an enhanced version of Estimation of Distributions Algorithm to solve this optimization problem. Simulation results demonstrate the efficiency of our evolutionary algorithm approach in comparison to other schemes such as GA and EDA.