The increasing traffic congestion problem can be solved by an adaptive traffic signal control (ATSC) system as it utilises real-time traffic information to control traffic signals. Recently, deep reinforcement learning (DRL) has shown its potential in solving the traffic signal timing. However, one of the main challenges of DRL is to design a proper reward function and special attention needs for a multi-objective reward design. Since the feedback to the agent depends on the reward function, a proper design of reward function is needed for fast and stable learning. In this study, the authors proposed a new reward architecture called composite reward architecture (CRA) for multi-objective ATSC to optimise multiple objectives. It calculates multiple rewards in parallel for each action and applies the majority voting method to choose the desired action. Since the traffic signal of one intersection affects the adjacent intersections, a new coordination approach is proposed to get the overall smooth traffic flow. The proposed reward architecture CRA is compared with several existing reward functions used in the literature for different traffic scenarios. The new coordinated approach is compared with the non-coordinated approach. The authors demonstrated that the proposed approaches outperform the others concerning waiting time, halting the number of vehicles, and so on.