The core problem pyMOODS addresses is one that optimization researchers have long acknowledged but rarely solved. Multi-objective optimization does not yield one optimal design; it yields an ensemble of Pareto-optimal candidates, each representing a different compromise among objectives such as cost, generation capacity, and environmental impact. Choosing among them is a human judgment call, informed by policy goals and stakeholder priorities. Yet the tools available for this post-optimization stage are fragmented. Algorithmic toolkits like pymoo, PlatEMO, and Borg generate Pareto fronts but offer little for the decision-maker. Multi-criteria decision analysis libraries such as pymcdm and pyDecision rank alternatives once objectives are fixed, but expose no exploratory interface. Visualization tools like PAVED and Parasol support interactive exploration but stop short of preference-weighted ranking. What has been missing, the PNNL team argues, is a single interactive platform that connects the visualization layer to a complete decision-support workflow on fronts that have already been computed.

pyMOODS fills that gap with a decoupled software architecture that separates heavy computation from interactive exploration. The frontend is a React and MUI application rendering linked interactive plots built with React Plotly, while a Python backend handles the analytics. User actions issue asynchronous requests to a Flask REST API, which mediates all communication between the two. Because interaction state lives in the frontend while analysis runs in the backend, computation never blocks the interface. A data access module loads, validates, and caches datasets held as CSV and JSON files, and a data processing module performs transformations and filtering before invoking the analytical routines. Notably, the dashboard evolved from early Plotly Dash prototypes into the current React-based implementation, gaining dynamic rendering of parameters, plots, and objective functions, along with better responsiveness under high-dimensional workloads.

One of the framework’s most elegant design decisions is its declarative input schema. A problem formulation is supplied as a single JSON configuration file that links to the data files and assigns each column to one of five categories: input parameters, hyperparameters, decision variables, objective functions, and control inputs. This means a single deployment can serve formulations whose objectives, decision variables, and hyperparameters differ in number and meaning, without any code changes. That flexibility matters because the framework targets real infrastructure applications, such as offshore wind co-design, MTDC-ESS system design, and load-shedding-constrained network expansion, where problem structures vary dramatically across use cases. It is a practical requirement that benchmark-oriented tools, typically evaluated on synthetic test problems like ZDT and DTLZ, simply do not address.

The analytical heart of pyMOODS combines two very different classes of methods. For structuring the solution space, the framework turns to unsupervised machine learning: a Uniform Manifold Approximation and Projection (UMAP) embedding projects the high-dimensional objective and decision space into two dimensions, and density-based HDBSCAN clustering groups similar solutions within that latent space. This gives users a navigable map of the entire front, where clusters of comparable candidates are visible at a glance and outliers stand out immediately. Users can also plot any pair of objectives or decision variables directly, or restrict the working set to solutions sharing a chosen hyperparameter configuration, such as a particular technology option.

For trade-off interpretation, pyMOODS takes a deliberately different path: a deterministic, parameter-free rank analysis. Every solution is ranked on each objective, and a solution’s generalizability is defined as its worst rank across all objectives. A solution is said to specialize in an objective when its rank there is strictly better than that of every more generalizable solution. Because this characterization derives entirely from the rank matrix, it introduces no trained model, no tuned threshold, and no random seed; identical inputs always produce identical generalizer and specializer assignments. This answers a question that ranking alone cannot: not merely which solutions score well under a given weighting, but which specific compromise each one represents. Solutions can additionally be ordered by an aggregate score reflecting user-specified objective weights, giving stakeholders a familiar mechanism for expressing their priorities, and the ranking is computed from the stored front rather than by re-solving, so stakeholders with different priorities can interrogate the same results interactively.

The framework’s workflow comes alive in its demonstration on the MoCoDo dataset for offshore wind farm planning with battery energy storage. The problem involves six objectives, including battery cost, cable material cost, day-ahead revenue, real-time revenue, and two reserve revenue streams, along with two decision variables: cable capacity and battery rated power. A conventional approach would aggregate all revenue streams into one total and all costs into another, reducing the problem to a simple two-way trade-off, but that aggregation obscures how individual solutions perform across specific revenue mechanisms. pyMOODS instead guides the user through four linked views: a scatter plot offering a first overview of the solution space, a ranking table for selecting a candidate, a parallel coordinates plot distinguishing generalizers from specializers across all six objectives, and beeswarm plots showing the distribution of all candidates per objective and decision variable. Selection propagates across views, so a candidate can be examined from several perspectives without losing context.

Performance testing suggests the architecture delivers on its responsiveness promise. On a local deployment running on an Apple M2 Pro with 16 GB of RAM, the team profiled three representative user tasks across two built-in formulations, Cameo_datacenter and MoCoDo_v2, repeating each measurement three times. Formulation initialization took roughly five milliseconds in both cases, while full dashboard load sequences averaged 3.838 seconds for the larger formulation and 0.475 seconds for the smaller one, with filter and selection interactions showing nearly identical latencies. The release also includes automated frontend tests using Playwright, which verify that dashboard components load correctly, the solution table sorts properly, and the generalizer-specializer controls update results, using simulated backend responses to validate the interface without requiring the full backend to run.

A capability comparison against representative open-source tools underscores what makes pyMOODS distinctive. Front-generation frameworks and metaheuristic platforms are not designed to be driven by a decision-maker; multi-criteria decision analysis libraries rank alternatives but expose no exploratory interface; and interactive visualization tools support exploration but stop short of preference-weighted ranking. In the published comparison, pyMOODS is the only tool that simultaneously offers an interactive user interface, operates on precomputed fronts from any solver, supports user-weighted ranking, provides automatic trade-off characterization, and accepts schema-agnostic problem formulations. The authors are candid about the release’s limitations, however: performance has been characterized on only two formulations on a single machine, rank-and-weight aggregation cannot recover non-convex regions of a Pareto front, and no usability evaluation has yet been conducted. Planned features include additional MCDM methods for comparison and an AI chatbot assistant.

The implications reach well beyond software engineering. As power systems worldwide absorb rising penetrations of onsite energy sources and face intensifying extreme weather, the co-optimization of generation, transmission, and storage investments is becoming one of the defining computational challenges of the energy transition. Tools like pyMOODS aim to ensure that the enormous computational effort poured into optimizing these systems does not end in an unreadable list of trade-offs. Released under the BSD 3-Clause License and archived on GitHub and Zenodo, version v0.0.3 puts a complete post-optimization decision-support pipeline into the hands of the planners, engineers, and researchers who must ultimately decide which compromises our future infrastructure will embody. Whether it changes real-world decisions, the authors acknowledge, is a question that future work, and future users, will have to answer.

Subject of Research: An open-source visual analytics framework for multi-objective decision support in large-scale infrastructure planning

Article Title: pyMOODS: An open-source framework for multi-objective decision support in large-scale infrastructure planning

Article References: Mattoo, P., Pham, J. N., Jain, M., Arendt, D., Avila, P., Ramachandran, T., Adetola, V., Yun, J. Y., & Wenskovitch, J. (2026). pyMOODS: An open-source framework for multi-objective decision support in large-scale infrastructure planning. SoftwareX, 36, Article 103095. https://doi.org/10.1016/j.softx.2026.103095

Image Credits: AI Generated

DOI: 10.1016/j.softx.2026.103095

Keywords: pyMOODS, multi-objective optimization, Pareto front, visual analytics, infrastructure planning, offshore wind, UMAP, HDBSCAN, decision support systems, open-source software, energy systems, Pacific Northwest National Laboratory

The core innovation is called vertically augmented three-dimensional Empirical Bayesian Kriging, or EBK3D. Classical kriging, a statistical interpolation technique borrowed from geostatistics, estimates values at unsampled locations by weighting nearby observations according to their spatial correlation. The Bayesian variant automates the difficult process of fitting the underlying semi-variogram, the mathematical function describing how similarity decays with distance, by simulating many plausible models and averaging the results. What the research team recognized, however, is that simply feeding three-dimensional coordinates into a standard kriging engine fails spectacularly for geotechnical data, because the statistics of soil change far more rapidly with depth than they do laterally.

To correct this anisotropy, the researchers introduced two empirically calibrated vertical adjustments. The first, an Elevation Inflation Factor, or EIF, rescales vertical separation distances relative to horizontal distances, so that a one-meter change in depth can be made statistically equivalent to tens or hundreds of meters of lateral separation. The second, a Vertical Trend Order, or VTO, captures systematic depth-related drift in soil properties, such as the steady increase in stiffness as overburden pressure compacts sediments. These two parameters are not chosen arbitrarily; the team calibrated them against a quality-controlled regional database compiled from field and laboratory investigation records, ensuring that the vertical geometry of the model reflects the actual behavior of the deposit rather than a convenient mathematical assumption.

Conventional two-dimensional and pseudo-three-dimensional approaches, the authors note, suffer from a cluster of related failures. They commonly assume planar stationarity, meaning they treat the statistical character of the soil as uniform across the mapped area, which is rarely true in layered alluvial environments. They discretize the subsurface into fixed layers, discarding information from observations that straddle layer boundaries. And they underrepresent directional covariance, ignoring the fact that correlations in soil properties often stretch further along a valley axis than across it. The consequences are over-smoothed predictions that wash out sharp geological contacts, dilution of lateral edges where data are sparse, and distorted volumetric estimates that can mislead foundation designers and zoning authorities alike.

The EBK3D framework attacks each of these weaknesses directly. Beyond the vertical adjustments, it couples directionally dependent semi-variogram parameterization, allowing the correlation structure to stretch and compress according to compass direction, with depth-aware spatial weighting that gives nearby observations in the vertical profile proportionally greater influence. It also employs covariance-optimized sector-based neighborhoods, dividing the space around each prediction point into sectors so that sample support is distributed evenly across directions rather than clustering where boreholes happen to be dense. Together, these components enable adaptive three-dimensional prediction and what the team calls digital stratigraphic reconstruction, essentially a probabilistic portrait of the stacked soil architecture at any point in the volume.

To demonstrate the power of the approach, the researchers generated computer-aided geotechnical soil maps, or cGSMs, for five critical engineering parameters: the Standard Penetration Test blow count, known as SPT-N, which indexes soil density and stiffness; lithology, the identity of the soil or rock type; shear strength, which governs bearing capacity and slope stability; the plasticity index, or PI, which characterizes how a fine-grained soil behaves when wet; and linear shrinkage, or LS, which reflects a clay’s tendency to crack and swell as moisture changes. These maps were then benchmarked against a suite of baseline two-dimensional and pseudo-three-dimensional models using identical data, providing a rigorous head-to-head comparison.

The results were dramatic. For the investigated dataset, a K-Bessel semi-variogram integrated with EBK3D proved the best performer, cutting predictive error by as much as 76 percent and raising the correlation between predicted and observed values by up to 40 percent. Focal standard deviation analysis, which measures how well a method preserves genuine localized variability rather than smearing it into regional averages, showed that EBK3D retained far more of the true spatial texture of the subsurface. Independent validation against field observations yielded correlation coefficients ranging from 0.87 to 0.98, an exceptionally tight band for spatial interpolation of geotechnical properties. Taken as a whole, the framework achieved improvements of up to 36 percent over the evaluated 2D and pseudo-3D competitors.

Just as important as accuracy is honesty about uncertainty, and here the study introduces a three-tier validation scheme spanning diagnostic, deterministic, and probabilistic metrics. Diagnostic checks confirm that the model’s internal error estimates are statistically well calibrated, comparing average standard errors against actual residuals. Deterministic metrics, including root mean square error, mean absolute error, Nash-Sutcliffe efficiency, Pearson correlation, and Kling-Gupta efficiency, quantify point-prediction skill. Probabilistic measures, such as the continuous ranked probability score, evaluate whether the full predictive distributions are trustworthy, which matters enormously when engineers must decide how much margin to build into a foundation design. This layered verification supports the practical applicability of the resulting three-dimensional cGSMs for preliminary geotechnical zoning and for targeting site investigations where they will yield the most information.

The implications reach well beyond one study region. Reliable regional subsurface characterization is a bottleneck for infrastructure planning worldwide, particularly in rapidly urbanizing areas where funding for dense drilling campaigns is scarce. By extracting maximal value from existing borehole archives and field investigation records, and by explicitly quantifying where predictions are confident and where they are not, uncertainty-aware 3D mapping can direct scarce investigation budgets to the locations of greatest risk and ignorance. It can also sharpen seismic site-response zonation, excavation design, and pile foundation assessment, all of which are acutely sensitive to vertical soil variability. The study’s authors, drawn from Tongji University, Quanzhou University of Information Engineering, Northern Border University, the University of Derby, and Khwaja Fareed University of Engineering and Information Technology, acknowledge support from the National Natural Science Foundation of China, the Shanghai Post-doctoral Excellence Program, the Natural Science Foundation of Fujian Province, and the Deanship of Scientific Research at Northern Border University. As cities dig deeper and climate change stresses the ground beneath our infrastructure, tools that reveal the third dimension of the subsurface, together with the confidence attached to every prediction, may become as indispensable to civil engineers as the maps they already hang on their walls. What began as a statistical refinement of kriging may end up changing how the ground itself is charted.

Subject of Research: Uncertainty-aware three-dimensional digital stratigraphic reconstruction of geotechnical soil variability using vertically augmented empirical Bayesian Kriging

Article Title: Uncertainty-aware digital stratigraphic reconstruction of geotechnical variability using vertically augmented empirical Bayesian Kriging

Article References: Ijaz, Z., Zhao, C., Ijaz, N., Hussain, W., Akbar, M., Rehman, Z. U., & Khalid, U. (2026). Uncertainty-aware digital stratigraphic reconstruction of geotechnical variability using vertically augmented empirical Bayesian Kriging. Earth Science Informatics, 19(11), Article 192. https://doi.org/10.1007/s12145-026-02243-2

Image Credits: AI Generated

DOI: 10.1007/s12145-026-02243-2

Keywords: geotechnical engineering, Empirical Bayesian Kriging, 3D subsurface mapping, spatial interpolation, semi-variogram, soil variability, digital stratigraphy, uncertainty quantification, infrastructure planning, geospatial modeling, SPT-N, shear strength