Conventional neural generative models tend to generate safe and generic responses which have little connection with previous utterances semantically and would disengage users in a dialog system. To generate relevant responses, we propose a method that employs two types of constraints - topical constraint and semantic constraint. Under the hypothesis that a response and its context have higher relevance when they share the same topics, the topical constraint encourages the topics of a response to match its context by conditioning response decoding on topic words’ embeddings. The semantic constraint, which encourages a response to be semantically related to its context by regularizing the decoding objective function with semantic distance, is proposed. Optimal transport is applied to compute a weighted semantic distance between the representation of a response and the context. Generated responses are evaluated by automatic metrics, as well as human judgment, showing that the proposed method can generate more topic-relevant and content-rich responses than conventional models.