Sparse representations provide a flexible and parsimonious description of high‐dimensional model parameters for reconstructing subsurface flow property distributions from limited data. To further constrain ill‐posed inverse problems, group‐sparsity regularization can take advantage of possible relations among the entries of unknown sparse parameters when: (i) groups of sparse elements are either collectively active or inactive and (ii) only a small subset of the groups is needed to approximate the parameters of interest. Since subsurface properties exhibit strong spatial connectivity patterns they may lead to sparse descriptions that satisfy the above conditions. When these conditions are established, a group‐sparsity regularization can be invoked to facilitate the solution of the resulting inverse problem by promoting sparsity across the groups. The proposed regularization penalizes the number of groups that are active without promoting sparsity within each group. Two implementations are presented in this paper: one based on the multiresolution tree structure of Wavelet decomposition, without a need for explicit prior models, and another learned from explicit prior model realizations using sparse principal component analysis (SPCA). In each case, the approach first classifies the parameters of the inverse problem into groups with specific connectivity features, and then takes advantage of the grouped structure to recover the relevant patterns in the solution from the flow data. Several numerical experiments are presented to demonstrate the advantages of additional constraining power of group‐sparsity in solving ill‐posed subsurface model calibration problems.
Nowadays, most manufacturing units try to locate their requirements and the depot vehicle routing in order to transport the goods at optimum cost. Needless to mention that the locations of the required warehouses influence on the performance of vehicle routing. In this paper, a mathematical programming model to optimize the storage location and vehicle routing are presented. The first objective function of the model minimizes the total cost associated with the transportation and storage, and the second objective function minimizes the difference distance traveled by vehicles. The study uses Imperialist Competitive Algorithm (ICA) to solve the resulted problems in different sizes. The preliminary results have indicated that the proposed study has performed better than NSGA-II and PAES methods in terms of Quality metric and Spacing metric.
Adopting representative geologic connectivity scenarios is critical for reliable modeling and prediction of subsurface flow and transport processes in subsurface environments. Geologic scenarios are often developed by integrating several sources of information, including knowledge of the depositional environment, qualitative and quantitative data such as outcrop and well logs, and process-based geologic modeling. In general, flow and transport response data are usually not included in constructing geologic scenarios for a basin. Instead, these data are typically matched using a given prior geologic scenario as constraint. Since data limitations, modeling assumptions and subjective interpretations can lead to significant uncertainty in adopted geologic scenarios, flow and transport data may also be useful for constraining the uncertainty in proposed geologic scenarios. Constraining geologic scenarios with flow-related data opens an interesting and challenging research area, which goes beyond the traditional model calibration formulations
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.