Genome-Scale Metabolic Reconstructions (GSMRs), along with optimization-based methods, predominantly Flux Balance Analysis (FBA) and its derivatives, are widely applied for assessing and predicting the behavior of metabolic networks upon perturbation, thereby enabling identification of potential novel drug targets and biotechnologically relevant pathways. The abundance of alternate flux profiles has led to the evolution of methods to explore the complete solution space aiming to increase the accuracy of predictions. Herein we present a novel, generic algorithm to characterize the entire flux space of GSMR upon application of FBA, leading to the optimal value of the objective (the optimal flux space). Our method employs Modified Latin-Hypercube Sampling (LHS) to effectively border the optimal space, followed by Principal Component Analysis (PCA) to identify and explain the major sources of variability within it. The approach was validated with the elementary mode analysis of a smaller network of Saccharomyces cerevisiae and applied to the GSMR of Pseudomonas aeruginosa PAO1 (iMO1086). It is shown to surpass the commonly used Monte Carlo Sampling (MCS) in providing a more uniform coverage for a much larger network in less number of samples. Results show that although many fluxes are identified as variable upon fixing the objective value, majority of the variability can be reduced to several main patterns arising from a few alternative pathways. In iMO1086, initial variability of 211 reactions could almost entirely be explained by 7 alternative pathway groups. These findings imply that the possibilities to reroute greater portions of flux may be limited within metabolic networks of bacteria. Furthermore, the optimal flux space is subject to change with environmental conditions. Our method may be a useful device to validate the predictions made by FBA-based tools, by describing the optimal flux space associated with these predictions, thus to improve them.