⚡ electrical engineering

Beyond the Pareto Front: Interpretable and Uncertainty-Aware Decision Support for Sustainable Subsurface Energy Strategy Selection

This paper proposes an interpretable, uncertainty-aware decision-support workflow that translates multi-objective Pareto sets into defensible subsurface energy strategies by integrating structured preference weighting, rule-based analysis, and sensitivity testing to distinguish robust recommendations from those highly dependent on specific priorities.

Original authors: Auref Rostamian, Enrico Riccardi, Remus G. Hanea, Reidar B. Bratvold

Published 2026-08-26

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Auref Rostamian, Enrico Riccardi, Remus G. Hanea, Reidar B. Bratvold

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Planning the future of an oil or gas field is a high-stakes balancing act. Engineers must decide how to drill wells and pump fluids to extract energy, but every choice involves a trade-off. A strategy that maximizes profit might leave valuable fuel trapped underground or release too much carbon dioxide. A method that is gentle on the environment might cost too much money to be viable. To navigate these conflicts, experts use a mathematical tool called multi-objective optimization. This process does not produce a single "best" answer. Instead, it generates a list of top-tier options, known as a Pareto set. In this group, no single option is perfect; improving one goal, like profit, inevitably worsens another, like environmental impact. The list reveals the boundaries of what is possible, but it leaves the hardest question unanswered: which of these imperfect options should a company actually build?

This is where a new study by researchers at the University of Stavanger and Equinor steps in. They have developed a decision-making framework designed to move beyond the list of trade-offs and help leaders choose a single, defensible strategy. The researchers call their approach the FST framework, a system that combines three distinct steps to handle not just the data, but the uncertainty in human priorities. First, it uses a method called FUCOM to translate a decision-maker's vague preferences into a structured set of rules. This ensures that if a leader says economic safety is more important than environmental impact, that judgment is applied consistently. Second, the system acknowledges that these priorities are never perfectly fixed. It runs thousands of simulations, slightly shifting the importance of each goal to see how the ranking of options changes. This reveals which strategies are robust—meaning they stay the best choice even if priorities wiggle—and which are fragile, collapsing under the slightest change in focus. Finally, the system uses a decision tree to explain the results in plain language, showing exactly which combination of priorities leads to which specific drilling plan.

The researchers tested this workflow on two different underground reservoir models to see how it performed in the real world. The first test case involved a complex, synthetic field representing the pre-salt carbonate systems found in Brazil. This model was challenging because it had to account for deep geological uncertainty, meaning the engineers did not know the exact shape of the rock formations underground. They optimized for two economic goals: the expected total profit and the worst-case profit to ensure safety. When the decision-support framework was applied, the result was strikingly clear. Out of the four top strategies generated by the initial optimization, one specific plan emerged as the winner in nearly every scenario. Whether the decision-makers cared most about maximizing profit, minimizing risk, or reducing carbon emissions, this single strategy remained the top choice. The system showed that this plan was so strong that it could withstand significant shifts in how the priorities were weighted. The researchers found that the recommended strategy would only change if the decision-makers completely reversed their fundamental goals, a level of uncertainty that rarely happens in practice. This gave the team a high degree of confidence that this specific plan was the right one to implement, regardless of whether the market was booming or the regulations were tightening.

The second test case used a different model, a simpler reservoir known as the Egg model, which focuses on water injection to push oil toward production wells. Here, the situation was more complicated. The initial optimization produced a much larger list of top strategies—168 different options. When the decision-support framework was applied, the results were not as uniform. In scenarios where the priority was strictly economic or focused on technical recovery, the system identified a clear winner that remained stable even when priorities were perturbed. However, in scenarios where environmental concerns, such as carbon emissions or water management, were the top priority, the system found no single dominant strategy. Instead, several different plans competed closely for the top spot. In these cases, a tiny shift in how much weight was given to carbon emissions versus water usage could flip the recommendation from one plan to another. The framework did not force a choice; instead, it highlighted that in these specific environmental scenarios, the decision was genuinely contingent. It told the decision-makers that they could not rely on a single "best" answer and that they needed to be very precise about their values before committing to a specific well layout.

The study also used decision trees to map out exactly why different strategies won in different situations. For the complex Brazilian-style field, the tree showed that the winning strategy was so versatile that it dominated across almost the entire range of possible priorities. For the Egg model, the tree revealed a more nuanced landscape. It showed that if a leader cared most about recovery, one specific plan was best. If they cared most about money, a different plan took the lead. But if they cared most about the environment, the system showed a tight race between three or four different options, with the winner changing based on very small adjustments in the numbers. This level of detail is crucial for reservoir engineers because the decisions they make are irreversible. Once a well is drilled and a facility is built, it is incredibly expensive and difficult to change course. The framework provides a safety net by quantifying how much a recommendation can be trusted. If a strategy remains the top choice even when the priorities are shaken, it is a safe bet. If the top choice flips with a minor change in the numbers, the team knows they must pause and clarify their goals before spending billions of dollars.

Ultimately, this research offers a bridge between the mathematical world of optimization and the practical world of investment. It does not replace the decision-maker or tell them what to value. Instead, it takes the list of trade-offs produced by complex computer simulations and translates them into a transparent, logical recommendation. It separates the choices that are stable and robust from those that are fragile and dependent on a narrow set of assumptions. By doing so, it allows energy companies to move forward with their development plans, knowing that their choice is not just a guess, but a decision supported by a rigorous analysis of uncertainty and preference. Whether the goal is to maximize profit, minimize risk, or protect the environment, the framework ensures that the final choice is defensible, clear, and ready for the real world.

Technical Summary: Beyond the Pareto Front: Interpretable and Uncertainty-Aware Decision Support for Sustainable Subsurface Energy Strategy Selection

Problem Statement
Subsurface energy development planning requires selecting a single field strategy from a set of non-dominated alternatives generated by multi-objective optimization (MOO). While MOO identifies the Pareto front—representing optimal trade-offs between conflicting objectives such as economic performance, operational efficiency, and environmental sustainability—it does not determine which specific strategy to implement. Closing the gap between a set of trade-offs and a single actionable decision necessitates a post-optimization selection step. Existing methods often struggle with two critical issues: (1) the cognitive burden and potential inconsistency of eliciting precise preference weights from decision-makers (DMs), and (2) the inability to account for preference uncertainty, where DM priorities may be imprecise or shift over time. Without addressing these, rankings can be highly sensitive to minor weight adjustments, leading to recommendations that lack robustness and transparency.

Methodology
The study proposes a post-optimization decision-support workflow, termed the FUCOM–SMAA–TOPSIS (FST) framework, designed to translate a Pareto set into a defensible recommendation while preserving preference information and uncertainty. The workflow operates in two stages:

Pareto-Optimal Strategy Generation: An NSGA-II (Non-dominated Sorting Genetic Algorithm II) engine generates the set of non-dominated strategies. In the benchmark cases, this involves optimizing economic objectives (Expected Monetary Value, EMV; and worst-case Net Present Value, NPV $_{eco,min}$ ) alongside technical recovery factors, subject to geological and economic uncertainties.
FST Decision-Support Workflow:
- Preference Weighting (FUCOM): The Full Consistency Method (FUCOM) is used to derive attribute weights. Unlike pairwise comparison methods (e.g., AHP) that require $n(n-1)$ comparisons, FUCOM requires only $n-1$ comparative judgments between consecutively ranked attributes. It enforces consistency through a mathematical optimization model, minimizing deviation from stated ratios. The study utilizes an interval-valued FUCOM approach to represent preference uncertainty, defining admissible ranges for comparative ratios.
- Stochastic Ranking (SMAA-TOPSIS): Stochastic Multi-criteria Acceptability Analysis (SMAA) is integrated with the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Instead of using a single fixed weight vector, the framework employs Monte Carlo sampling to draw thousands of weight vectors from the admissible FUCOM-consistent space defined by the interval constraints. For each sampled vector, TOPSIS ranks the alternatives based on their distance from ideal and anti-ideal solutions.
- Robustness Metrics: The aggregation of rankings yields three key metrics:
  - Rank-1 Acceptability Index: The probability that a strategy is ranked first across the admissible preference space.
  - Central Weight Vector: The typical priority profile that most strongly supports a specific strategy.
  - Confidence Factor: A measure of stability obtained by perturbing the central weight vector (via Gaussian noise on comparative ratios) to determine how far preferences can shift before the preferred strategy changes.
- Interpretability (Decision Trees): To provide transparent logic linking preferences to outcomes, entropy-based decision trees are trained on the sampled weight vectors and their corresponding top-ranked strategies. These trees extract explicit if-then rules identifying which attribute weight thresholds lead to specific strategy selections.

Case Studies
The framework was applied to two benchmark subsurface energy cases:

UNISIM-II-D: A synthetic pre-salt carbonate reservoir model representing complex geological heterogeneity. The Pareto set contained four non-dominated strategies. The evaluation included economic objectives (EMV, NPV $_{eco,min}$ ), environmental attributes (CO $_2$ emissions), and operational metrics (water cut, exergy).
Egg Model: A synthetic channelized reservoir with a single geological realization. The Pareto set contained 168 solutions. The evaluation focused on the trade-off between Recovery Factor (RF) and economic performance (NPV $_{eco}$ ), alongside environmental and thermodynamic attributes.

Key Results

UNISIM-II-D Case: The framework identified a single strategy (S1) as robust across all four constructed preference scenarios (ranging from economic to environmental priorities). S1 achieved a rank-1 acceptability near 1.0 in all scenarios and maintained a confidence factor of 1.0 even under 20% perturbation. Decision trees confirmed that S1 dominates unless the weight on Expected Monetary Value (EMV) is exceptionally high, a condition rarely met in the sampled space. This suggests the choice is stable regardless of whether economic or environmental priorities dominate.
Egg Model Case: The results were highly scenario-dependent.
- In the economic-focused scenario (Sc2), Strategy S3 was dominant (85% acceptability) with a high confidence factor (dropping only to 0.88 under 20% perturbation), indicating a stable recommendation.
- In recovery-focused (Sc1) and environmental scenarios (Sc3, Sc4), no single strategy dominated. Acceptability was split among multiple strategies (e.g., S1 vs. S2 in Sc1; S3, S4, S5 in Sc3/Sc4). Confidence factors for leading strategies in these scenarios dropped significantly (e.g., from ~0.91 to ~0.44 under 20% perturbation), indicating that recommendations in these contexts are contingent on precise priority settings.
- Decision trees revealed that in environmental scenarios, small shifts in the weights of CO $_2$ emissions or water cut could switch the preferred strategy, highlighting a lack of robustness compared to the economic scenario.

Significance and Claims
The paper claims that the FST workflow addresses a critical gap in subsurface decision-making by moving beyond the Pareto front to provide a transparent, preference-aware, and uncertainty-aware selection process. Its primary contributions are methodological:

Integration of Consistency and Uncertainty: By combining FUCOM (for consistent, low-burden weighting) with SMAA (for stochastic propagation of preference uncertainty), the framework avoids the pitfalls of fixed-weight assumptions and inconsistent pairwise comparisons.
Quantification of Robustness: The use of confidence factors and perturbation analysis allows decision-makers to distinguish between "stable" recommendations (which hold across a wide range of priorities) and "contingent" ones (which depend on narrow preference bands).
Interpretability: The integration of decision trees transforms the probabilistic output of SMAA into explicit, rule-based logic, explaining why a strategy is preferred under specific priority structures without introducing additional optimization steps.
Sustainability Integration: The framework successfully incorporates sustainability metrics (CO $_2$ emissions, exergy efficiency) alongside traditional economic and technical metrics, enabling a holistic evaluation of sustainable development strategies.

The authors emphasize that the workflow does not replace the decision-maker but provides a defensible, inspectable basis for selection. It highlights that while some decisions (like the UNISIM-II-D case) may be robust to preference uncertainty, others (like the Egg model environmental scenarios) require careful scrutiny of priorities before irreversible capital commitments are made. The study concludes that this structured approach strengthens the transparency and defensibility of strategic decisions in reservoir management under uncertainty.

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