The green communications paradigm has been receiving much attention in wireless networks in recent years. More specifically, in the context of cellular communications, the concept of Cell Switch Off (CSO) has been recognized as a promising approach to reduce the energy consumption. The need is expected to be pressing especially in the next decade with the increasing small cell deployment. However, the cell switch on/off decisions compounded by the resource allocation task in CSO constitute a highly challenging optimization problem due to the fact that this problem can be viewed as a generalized version of the resource allocation (scheduling) problem in the conventional cellular networks without CSO, which itself is already difficult. This paper introduces a novel framework to CSO based on multiobjective evolutionary optimization. The main contribution of this paper is that the proposed multiobjective framework takes the traffic behaviour in both space and time (known by operators) into account in the optimal cell switch on/off decision making which is entangled with the corresponding resource allocation task. The exploitation of this statistical information is done in a number of ways, including through the introduction of a weighted network capacity metric. This indicator prioritizes cells which are expected to have traffic concentration resulting in on/off decisions that achieve substantial energy savings in scenarios where traffic is highly unbalanced, without compromising the QoS. The proposed framework distinguishes itself from the CSO papers in the literature in two ways: 1) The number of cell switch on/off transitions as well as handoffs are minimized. 2) The computationally-heavy part of the algorithm is executed offline, which makes the real-time implementation feasible.