Preference-Robust eVTOL Design

Research prototype for exploring early-stage eVTOL design decisions when the future weighting of operating cost, lifecycle GWP, and annual profit is uncertain.

Model concept

The multidisciplinary model maps design and operating decisions to performance, normalized single-criterion utility, and system value:

$$ \mathbf{x};\longrightarrow;\mathbf{y}(\mathbf{x},\boldsymbol{\theta}) ;\longrightarrow;\mathbf{u}(\mathbf{y}) ;\longrightarrow;v(\mathbf{x},\mathbf{w})=\mathbf{w}^{\mathsf T}\mathbf{u}(\mathbf{y}). $$

• $\mathbf{x}$: aircraft and operational design variables
• $\boldsymbol{\theta}$: technical and operational parameters
• $\mathbf{y}$: raw performance outcomes
• $\mathbf{u}\in[0,1]^K$: normalized criterion utilities
• $\mathbf{w}$: uncertain preference weights

The current criteria are:

$$ \mathbf{u}=\left[u_{\mathrm{cost}},;u_{\mathrm{GWP}},;u_{\mathrm{profit}}\right]^{\mathsf T}. $$

Preference uncertainty

No probability distribution is assigned to the weights. Plausible valuation regimes are represented by a simplex lattice:

$$ \mathcal{W}_{\Delta w}=\lbrace\mathbf{w}\geq 0 \mid \sum_{k=1}^{K}w_k=1,; w_k\in\lbrace 0,\Delta w,\ldots,1\rbrace\rbrace. $$

For three criteria, $\Delta w=0.05$ gives 231 lattice scenarios; the centroid is added as a reference design.

The lifecycle interpretation motivates the research question. The present implementation evaluates an unordered set of plausible weights; it does not yet model or predict a time-dependent path $\mathbf{w}(t)$.

Robust decision analysis

For each valuation scenario $\mathbf{w}_j$, the model generates a scenario-optimal design:

$$ \mathbf{x}_j^*=\arg\max_{\mathbf{x}\in\mathcal X};\mathbf{w}_j^{\mathsf T}\mathbf{u}(\mathbf{y}(\mathbf{x},\boldsymbol{\theta})). $$

All candidate designs are then evaluated across all valuation scenarios:

$$ V_{ji}=\mathbf{w}_j^{\mathsf T}\mathbf{u}(\mathbf{y}(\mathbf{x}_i,\boldsymbol{\theta})), \qquad r_{ji}=\max_{\ell}V_{j\ell}-V_{ji}. $$

The current pipeline reports the minimax-regret design,

$$ \mathbf{x}^{\mathrm{MMR}}=\arg\min_i\max_j r_{ji}, $$

and exports the utility and regret matrices for comparison using Wald, Savage, Laplace, and Hurwicz criteria.

Current demonstrator

Implemented:

• deterministic low-fidelity eVTOL MDO model;
• linear utility normalization for cost, GWP, and profit;
• set-based preference uncertainty over the complete three-weight simplex;
• scenario-specific optimization and centroid reference design;
• cross-scenario utility and regret evaluation;
• CSV summaries for design, performance, utility, and regret.

The demonstrator reveals a family of similarly robust designs rather than a single sharply defined optimum. Vulnerability is concentrated near specialized valuation regimes.

Run

python "Robust Decision Making/run_rdm_fixed_baseline.py" --step 0.05

Each run creates a timestamped folder under Robust Decision Making/results/ containing candidate summaries, cross-evaluation matrices, regret matrices, and a run summary.

Scope and next steps

This repository is an exploratory research demonstrator, not a validated aircraft-design or certification tool. Planned extensions include bounded and probabilistic preference information, nonlinear utility functions, probabilistic parameter uncertainty, and adaptive vehicle-operation co-design.

Model provenance and citation

The underlying eVTOL multidisciplinary design model builds on:

Janning, J., Armanini, S. F., & Fasel, U. (2024). Future Pathways for eVTOLs: A Design Optimization Perspective. arXiv:2412.18078 [eess.SY].

If you use this research code, please cite the repository using GitHub's Cite this repository function and the underlying model paper above. A software DOI can be added after archiving a stable release.