HITL-MGA: Human-in-the-Loop Alternatives

• HITL-MGA is a framework that integrates human feedback with computational optimization to generate diverse and cost-feasible alternatives for complex challenges.
• It employs multi-fidelity data fusion and iterative human input using both model-free and model-based prediction methods to refine solution spaces.
• Applications span energy system design, pilot behavior modeling, and power grid operations, enhancing stakeholder alignment and operational efficiency.

Human-in-the-Loop Modeling-to-Generate Alternatives (HITL-MGA) encompasses a class of modeling approaches that explicitly incorporate human feedback within computational frameworks for generating, selecting, or refining alternative solutions to complex problems. The paradigms and formalizations of HITL-MGA span multi-fidelity human behavior modeling, energy system design, adaptive decision support, and robust optimization, and are distinguished by the central role of human interaction, statistical learning, and iterative search in constructing alternative solution spaces that are both computationally tractable and aligned with expert or stakeholder objectives.

1. Methodologies for Data Fusion and Alternative Generation

HITL-MGA frameworks integrate heterogeneous data sources, most notably through the combination of high-fidelity and low-fidelity human-in-the-loop (HITL) experiments to create predictive models of interacting agents or system outcomes. In the context of modeling human behaviors, multi-fidelity methods leverage abundant but less accurate data collected in simplified environments (such as those on Mechanical Turk) together with limited, high-cost, high-fidelity data (e.g., from expert-staffed simulators). Both model-free and model-based prediction regimes are supported, with multi-fidelity model-free methods augmenting feature spaces by incorporating predictors trained on low-fidelity data to supplement high-fidelity regression (e.g., locally weighted regression using a composite feature of $S$ and $R_l(S)$), and multi-fidelity model-based methods employing Bayesian estimation of behavioral model parameters jointly from both data sources (Schlicht et al., 2012, Schlicht et al., 2014).

In large-scale optimization settings, such as energy infrastructure planning, the solution space for alternatives is often explored via modeling to generate alternatives (MGA) algorithms. Examples include the SPORES method (Lombardi et al., 2022), which explicitly accounts for spatial and technological diversity by assigning weights to each capacity decision variable at each location, and advanced vector selection schemes—Hop-Skip-Jump, Random Vector, Variable Min/Max, Hybrid approaches—deployed to efficiently sample the near-optimal polytope and thus generate diverse design alternatives (Lau et al., 27 May 2024). These methods frequently operate under a cost-slack constraint of the form $c^\top x \leq (1+\varepsilon)c^*$, ensuring that alternatives remain economically comparable to the reference solution.

The schematic below summarizes a representative MGA process:

Step	Description	Key Methods/Equations
1. Baseline Opt.	Solve reference (least-cost) optimization	$\min~c^\top x$
2. Impose Slack	Allow $\varepsilon$ deviation in objective	$c^\top x \leq (1+\varepsilon)c^*$
3. Vector Gen.	Define new objectives to explore alternative space	$d^\top x$ (with $d$ randomized or selected by rules)
4. Generate Alts	Find alternative optima via MGA	Parallel/iterative search across objectives
5. Evaluate	Compare alternatives on multi-criteria metrics	Diversity, feasibility, stakeholder preference matching

2. Incorporation and Decoding of Human Preferences

Direct integration of human judgment into the alternative generation process is a defining attribute of HITL-MGA. In energy system design, a typical workflow begins by generating a preliminary set of alternatives via MGA algorithms (e.g., SPORES). Stakeholders then interact with these options—often via web interfaces—selecting those closest to their preferences, without needing to formalize their rationale (Lombardi et al., 19 Jul 2024). An automated statistical analysis decodes the distinguishing technical features (e.g., low hydrogen capacity, distributed onshore wind) of the most-preferred designs by comparing their values to the design space mean (e.g., flagging features deviating by more than a specified threshold, such as 15%). These features are translated into intensified search objectives by modifying the MGA’s weight structure, guiding subsequent searches toward regions of the solution space that are both cost-feasible and aligned with stakeholder priorities.

The relevant mathematical adjustment to the MGA objective can be formalized as:

$$Y_\text{HITL} = a \cdot \sum_{i,j} w_{ij} x_{ij}^{\mathrm{cap}} + b \cdot \sum_{j} x_{\bar{\imath}j}^{\mathrm{cap}} - c \cdot \sum_{j} x_{\bar{\imath}j}^{\mathrm{cap}}$$

where $w_{ij}$ encodes the original or stakeholder-informed weighting on each decision variable, and $b$, $c$ are coefficients to intensify or penalize specific features as determined by human-guided decoding (Lombardi et al., 19 Jul 2024).

3. Managing Trade-Offs: Diversity, Feasibility, and Computational Overheads

A key challenge in HITL-MGA is the efficient exploration of a high-dimensional alternative space given computational constraints. The SPORES approach demonstrates, empirically and via formal volume analysis, that focusing all resources on maximizing diversity in one dimension (e.g., technology mix) potentially leaves the system blind to diversity in others (e.g., spatial deployment). Conversely, strict spatial exploration may omit extreme technology configurations relevant to stakeholders (Lombardi et al., 2022). Methods that combine both spatial and technological search objectives—tunable via coefficients—strike a balance and can be refined iteratively based on stakeholder “pull” toward particular features or solution classes.

In HITL-MGA applied to power grids, the risk of redundancy and omission of critical alternatives is addressed by combining automated, parallel sampling of the alternative space (with random or guided search directions) and ad-hoc sensitivity analyses (“what-if” experiments), targeted at claims or stakeholder concerns. This approach is shown to reduce computational redundancies while ensuring that the design space is neither artificially restricted nor populated with irrelevant alternatives (Lombardi et al., 2022, Lau et al., 27 May 2024).

4. Predictive Performance and Evaluation Metrics

Performance in HITL-MGA is measured via metrics adapted to model class and application. In human-behavior modeling, predictive efficiency is defined as the ratio of an empirical lower bound error $D^{(lb)}$ (derived from the ground-truth model) to the realized prediction error $D$ across test samples:

$\text{Predictive Efficiency} = D^{(lb)} / D$

Values close to or greater than 1 indicate strong predictive power, though the exact interpretation depends on the estimation of lower bounds (Schlicht et al., 2012, Schlicht et al., 2014). In energy system design, diversity is quantified with shadow-volume metrics (e.g., VESA—Volume Estimation by Shadow Addition), which assess how much of the near-optimal region is covered by sampled alternatives (Lau et al., 27 May 2024). Feasibility is typically enforced via cost, physical, and operational constraints.

Consensus and stakeholder alignment are analyzed via multi-criteria decision analysis (weighted-sum models), counting “near-highest-consensus” designs that perform no worse than a given threshold relative to the best compromise solution. Studies show that MCDA-based consensus options increase substantially when guided HITL-MGA is used: from 1% in the original, “blind” design space to 18% in the human-trained design space with recalibrated search parameters (Lombardi et al., 19 Jul 2024).

5. Applications and Domain Impacts

HITL-MGA frameworks have been applied to:

• Aviation/interaction modeling: Predicting pilot maneuvers in near-collision encounters by fusing online, low-fidelity and simulator, high-fidelity data, leading to improved models for collision avoidance and air traffic management (Schlicht et al., 2012, Schlicht et al., 2014).
• Energy transition planning: Generating robust, diverse portfolios of energy system transition designs, adaptively refined to reflect societal acceptability and spatial equity—accelerating consensus and technical feasibility (Lombardi et al., 2022, Lau et al., 27 May 2024, Lombardi et al., 19 Jul 2024).
• Power grid operation: Suggesting diversified remedial actions (e.g., alternative topologies for transmission network reconfiguration) to operators, incorporating both operator feedback and system simulation for enhanced flexibility under uncertainty (Bannmüller et al., 22 Sep 2025).
• Design process optimization: In user-facing systems, HITL-MGA supports agile design cycles and adaptive optimization by systematically incorporating quantitative user feedback into retrained models, as in HILL Design Cycles (So, 2020).

6. Challenges, Limitations, and Future Directions

Several technical barriers are highlighted in the literature:

• Assumptions on similarity: Multi-fidelity methods often presuppose that low- and high-fidelity agents share utility functions or decision structures; violations reduce model efficacy (Schlicht et al., 2012, Schlicht et al., 2014).
• Scalability and dimensionality: The curse of dimensionality in alternative generation necessitates careful selection of variables (favoring capacity variables over operational ones to preserve operational realism) and the development of hybrid, parallelizable vector selection methods (Lau et al., 27 May 2024).
• Stakeholder representation: The process of decoding stakeholder preferences relies on proxy measures (frequency selection, statistical thresholds) and may require tuning to ensure social robustness (Lombardi et al., 19 Jul 2024).
• Redundancy and coverage: No single approach covers all feasible human-relevant alternatives; iterative human-computer feedback and ad-hoc sensitivity analyses are essential to incrementally expand the solution space (Lombardi et al., 2022).

Continued research targets further integration of feedback mechanisms, more sophisticated fusion of simulation and expert evaluation (e.g., combining model-based uncertainty with stakeholder importance sampling), and improved methodologies for visualizing and navigating large, multi-dimensional design spaces.

7. Table: Representative HITL-MGA Methodological Elements

Domain	Data Fusion/Alternative Gen.	Stakeholder/Human Role
Human behavior/pilots	Multi-fidelity regression/model-based	Selecting design/decision models
Energy system planning	SPORES, MGA, hybrid vector sampling	Feature decoding, guided search
Power grid operation	MGA with expert feedback incorporation	Evaluation, re-ranking alternatives
Design process	Agile sprints/integrated retraining	Quantitative survey/feedback

HITL-MGA thus defines a suite of frameworks and algorithms that couple statistical, optimization, and learning processes with explicit human interaction to generate, evaluate, and select alternatives in engineering, behavioral, and sociotechnical systems, providing both greater robustness to modeling uncertainty and enhanced alignment with decision-maker values.