Feasibility Expansion: Concepts & Applications

• Feasibility expansion is a framework that systematically identifies and enlarges the viable parameter set of technical, economic, or physical systems.
• It employs simulation, parameter range selection, and iterative constraint mapping to refine and extend feasibility boundaries.
• Its practical applications span renewable energy, infrastructure planning, robotics, and quantum cryptography, emphasizing robust optimization under uncertainty.

Feasibility Expansion refers to the analytical, algorithmic, and methodological frameworks designed to systematically identify, characterize, and expand the set of parameters, states, or decisions for which a technical, economic, or physical system can be considered viable, operable, or optimal. This concept is employed in diverse domains including renewable energy conversion, large-scale infrastructure planning, robust optimization, robotics, data center siting, and quantum cryptography, each of which operationalizes feasibility and its expansion according to the structural constraints and objectives of the problem space.

1. Formal Definitions and Foundational Frameworks

The core construct in feasibility expansion is the feasibility space: a subset, typically denoted $F \subseteq X$, of an n-dimensional parameter space $X$ defined by ranges of technical, economic, and operational parameters. For renewable energy systems, the feasibility space is defined as

$F = \{x \in X : \forall i,\, g_i(x) \leq 0 \}$

where $X$ is a Cartesian product of admissible parameter intervals and $g_i(x) \leq 0$ represent the set of technical and economic constraints (e.g., Levelized Cost of Energy (LCOE) not exceeding local grid tariff, minimum technological efficiency, or Net Present Value non-negativity). The precise formulation of $g_i$ is context-dependent: in energy systems, it may encode LCOE, NPV, efficiency and capacity requirements, whereas in other domains such as stochastic programming or robotics, it encodes constraint violation, risk, or terrain traversability (Silva et al., 2020, Luo et al., 8 Feb 2026, Freitas et al., 3 Dec 2025).

2. Methodologies for Feasibility-Space Construction and Expansion

Renewable Energy Technologies

The process for constructing and expanding the feasibility space involves the following stages (Silva et al., 2020):

1. Problem specification: Definition of the technology and system under consideration, along with all relevant financial and resource parameters.
2. Parameter range selection: Setting lower and upper bounds for all design and economic parameters.
3. Simulation and constraint mapping: Use of simulation tools (e.g., HOMER, RETScreen) or optimization solvers to assess system operation over the full parameter grid; objective metrics such as COE, NPV, and IRR are evaluated.
4. Boundary determination and refinement: Identification of the parameter sets where constraints are exactly met (defining the feasibility boundary), and iterative refinement of bounds to encompass relevant solution regions.
5. Feasibility-space assembly: Construction of the interior (viable) and boundary (marginal) regions in parameter space; subsequent expansions correspond to improved technology or market conditions (e.g., reduced capital costs, increased conversion efficiency) pushing the feasible set outward.

Power System and Infrastructure Planning

In large-scale network optimization—for example, continental-scale capacity expansion—feasibility expansion is realized via auxiliary constraint sets. The relative ε-optimal feasible space is defined as

$$X^\epsilon = \{x \in X : f(x) \leq (1+\epsilon)f(x^*) \}$$

where $f(x)$ is the objective (e.g., system cost), and $x^*$ the optimal solution. The envelope $X^\epsilon$ expands from the unique optimum ($\epsilon = 0$) to the entire feasible region as $\epsilon$ increases, enabling systematic relaxation and identification of necessary conditions (e.g., minimal required transmission or storage capacity) for near-optimal operation (Dubois et al., 2021).

Inverse feasibility expansion addresses the problem of mapping low-resolution model outputs upward to high-resolution feasible solutions. Strategies include regional re-optimization (computationally expensive but best for feasibility), minimization of excess electricity (convex, efficient), and simple proportional allocation (poor performance). Operational feasibility is assessed by dispatching the disaggregated capacities under granular network constraints (Frysztacki et al., 2022).

3. Advanced Representations: Feasible Planning Regions and Robust Feasibility Recursions

The Feasible Planning Region (FPR) extends the concept of feasibility by introducing a cost dimension—yielding a convex hull over all feasible operation points at various stages of distribution grid expansion. The FPR is constructed by stacking all Feasible Operation Regions (FORs) corresponding to incremental investment levels: $$\mathrm{FPR} = \bigcup_{g\in\mathcal G}\{ (P_{pcc}, Q_{pcc}, c_g): (P_{pcc}, Q_{pcc}) \in \mathrm{FOR}^g \}$$ This multi-stage representation enables system-level planning models to incorporate realistic cost-constraint trade-offs at the TSO-DSO interface and to partition expansion into operationally meaningful increments across voltage hierarchies (Böttcher et al., 2023).

In multi-stage stochastic optimization (e.g., SDDP for hydrothermal energy systems), the Penalty-Free SDDP framework introduces a Future Feasibility Function (FFF), decoupling constraint violation recourse from economic objectives. Feasibility is propagated through dedicated Benders-type cuts, ensuring robust constraint satisfaction across all realizations without artificial penalties or slack calibration (Freitas et al., 3 Dec 2025).

4. Feasibility-Guided Planning in Robotics and Control

The feasibility expansion paradigm generalizes beyond energy systems into multi-expert planning under physical constraints, as in the case of legged robots traversing unstructured terrain. Each local policy is paired with a learned Feasibility-Net, predicting a tensor of feasibility scores over state-action pairs given environmental observations. Node expansion in planning (Dijkstra-style graph search) is feasibility-guided: only transitions above a threshold feasibility are explored, and transition costs are penalized inversely by predicted feasibility, yielding optimized trajectories that dynamically switch between specialized locomotion policies in accordance with terrain-traversability boundaries (Luo et al., 8 Feb 2026).

5. Quantification, Sensitivity, and Decision Support

Feasibility expansion frameworks are inherently sensitive to input data (e.g., cost forecasts, technical performance curves, resource availability, or climate constraints), and systematic quantification is essential for robust decision support. Sensitivity analysis is performed by exploring parameter space along key axes (e.g., capital costs, efficiency, grid price) and observing the movement of the feasibility boundary. Benchmarking enables technologies deep inside the feasibility set to be prioritized for investment, while marginal or boundary cases may require targeted design improvement or policy support (e.g., feed-in tariffs, regulatory relaxation).

For spatial allocation (e.g., U.S. hyperscale data centers), feasibility envelopes are constructed by empirically deriving constraint distributions from existing deployment patterns and strictly gating candidate areas against power, environmental, and land-use requirements, producing a nested hierarchy of feasible, marginal, and excluded zones (Janosov, 27 Jan 2026). Relaxation of certain constraints (raising ε, relaxing percentile thresholds) expands the feasibility envelope but must be justified against system-wide risk tolerance and the cost of violations.

6. Case Studies and Applications Across Domains

Renewable Energy Conversion

In Brazilian wave energy, explicit mapping of the feasibility boundary reveals that only combinations achieving conversion efficiency ≥30%, capital cost ≤233 M USD, and grid tariff ≥0.118 USD/kWh are viable investments under contemporary market conditions (Silva et al., 2020).

Decarbonization Pathways

In Korea's power sector, feasibility analysis reveals that certain pathways (high-renewables/CCS versus nuclear expansion) differ fundamentally in their expansion feasibility: the former requires unprecedented build rates and early CCS deployment, the latter is technically feasible but currently not politically admissible (Hyun et al., 2021).

Extreme Environments

For AI datacenters in arid regions, feasibility expansion involves explicit mapping of resource, climate, and grid-intensity constraints, and establishes that advanced cooling and co-siting with renewables can overcome—but not eliminate—fundamental environmental limits (Hassan et al., 21 Nov 2025).

Astroengineering

Expansion of feasibility for interplanetary material transfer by solar-powered spacecraft demonstrates quantitative feasibility bounds (≈50 AU) for planetesimal redirection, with technical improvements (beam pointing, thruster efficiency) increasing the system-scale envelope (Morozov et al., 5 Sep 2025).

7. Implications, Extensions, and Future Directions

Feasibility expansion methodologies underpin rigorous assessment of new technology introduction, infrastructure planning under uncertainty, and optimization for robustness. As system boundaries, resource conditions, or component technologies improve, the feasibility space expands, creating opportunities for further capacity, lower operational risk, or larger envelopes for near-optimal operation. Ongoing research focuses on automating boundary-surface mapping under multidimensional constraints, incorporating uncertainty explicitly (robust or adaptive optimization), expanding to multi-stage and multi-agent settings, and integrating data-driven approaches for dynamic, rolling-horizon feasibility monitoring. Advances in algorithmic scalability and interpretability, as well as domain-specific extensions (e.g., transactive energy systems, planetary engineering), continue to broaden both the theoretical and applied impact of the feasibility expansion paradigm (Silva et al., 2020, Dubois et al., 2021, Böttcher et al., 2023, Freitas et al., 3 Dec 2025, Luo et al., 8 Feb 2026, Morozov et al., 5 Sep 2025).