Advances in computational methods that allow for exploration of the combinatorial mutation space are needed to realize the potential of synthetic biology based strain engineering efforts. Here, we present Constrictor, a computational framework that uses flux balance analysis (FBA) to analyze inhibitory effects of genetic mutations on the performance of biochemical networks. Constrictor identifies engineering interventions by classifying the reactions in the metabolic model depending on the extent to which their flux must be decreased to achieve the overproduction target. The optimal inhibition of various reaction pathways is determined by restricting the flux through targeted reactions below the steady state levels of a baseline strain. Constrictor generates unique in silico strains, each representing an "expression state", or a combination of gene expression levels required to achieve the overproduction target. The Constrictor framework is demonstrated by studying overproduction of ethylene in Escherichia coli network models iAF1260 and iJO1366 through the addition of the heterologous ethylene-forming enzyme from Pseudomonas syringae. Targeting individual reactions as well as combinations of reactions reveals in silico mutants that are predicted to have as high as 25% greater theoretical ethylene yields than the baseline strain during simulated exponential growth. Altering the degree of restriction reveals a large distribution of ethylene yields, while analysis of the expression states that return lower yields provides insight into system bottlenecks. Finally, we demonstrate the ability of Constrictor to scan networks and provide targets for a range of possible products. Constrictor is an adaptable technique that can be used to generate and analyze disparate populations of in silico mutants, select gene expression levels and provide non-intuitive strategies for metabolic engineering.