A novel algorithm to detect an optimal set of semantic lines is proposed in this work. We develop two networks: selection network (S-Net) and harmonization network (H-Net). First, S-Net computes the probabilities and offsets of line candidates. Second, we filter out irrelevant lines through a selection-and-removal process. Third, we construct a complete graph, whose edge weights are computed by H-Net. Finally, we determine a maximal weight clique representing an optimal set of semantic lines. Moreover, to assess the overall harmony of detected lines, we propose a novel metric, called HIoU. Experimental results demonstrate that the proposed algorithm can detect harmonious semantic lines effectively and efficiently. Our codes are available at https://github.com/dongkwonjin/Semantic-Line-MWCS.