Deep neural networks have achieved promising results in automatic image captioning due to their effective representation learning and context-based content generation capabilities. As a prominent type of deep features used in many of the recent image captioning methods, the well-known bottomup features provide a detailed representation of different objects of the image in comparison with the feature maps directly extracted from the raw image. However, the lack of high-level semantic information about the relationships between these objects is an important drawback of bottom-up features, despite their expensive and resource-demanding extraction procedure. To take advantage of visual relationships in caption generation, this paper proposes a deep neural network architecture for image captioning based on fusing the visual relationships information extracted from an image's scene graph with the spatial feature maps of the image. A multi-modal reward function is then introduced for deep reinforcement learning of the proposed network using a combination of language and vision similarities in a common embedding space. The results of extensive experimentation on the MSCOCO dataset show the effectiveness of using visual relationships in the proposed captioning method. Moreover, the results clearly indicate that the proposed multi-modal reward in deep reinforcement learning leads to better model optimization, outperforming several state-of-the-art image captioning algorithms, while using light and easy to extract image features. A detailed experimental study of the components constituting the proposed method is also presented.