The accumulation of high-throughput genomic and proteomic data allows for the reconstruction of the increasingly large and complex metabolic networks. In order to analyze the accumulated data and reconstructed networks, it is critical to identify network patterns and evolutionary relations between metabolic networks. But even finding similar networks becomes computationally challenging. The dissertation addresses these challenges with discrete optimization and the corresponding algorithmic techniques. Based on the property of the gene duplication and function sharing in biological network,we have formulated the network alignment problem which asks the optimal vertex-to-vertex mapping allowing path contraction, vertex deletion, and vertex insertions. We have proposed the first polynomial time algorithm for aligning an acyclic metabolic pattern pathway with an arbitrary metabolic network. We also have proposed a polynomial-time algorithm for patterns with small treewidth and implemented it for series-parallel patterns which are commonly found among metabolic networks. We have developed the metabolic network alignment tool for free public use. We have performed pairwise mapping of all pathways among five organisms and found a set of statistically significant pathway similarities. We also have applied the network alignment to identifying inconsistency, inferring missing enzymes, and finding potential candidates.