Near Optimal Solutions
Geometry
Objective
Determine the optimal capacity and operational schedule of these facilities at the minimum cost.
Question?
What are the other options if we allow the solution to be ε-suboptimal?
Network schematic based on PyPSA's single-node capacity expansion example.
Near Optimal Solutions
Motivation
Use cases
- Preferable alternatives in political, social, or environmental terms.[1]
- Robust solutions to weather variability[2] and cost uncertainty[3].
- Participatory modeling that lets stakeholders explore trade-offs near the optimum.[4]
[1] Neumann, Fabian, and Tom Brown. "The near-optimal feasible space of a renewable power system model." Electric Power Systems Research 190 (2021): 106690.
[2] Grochowicz, Aleksander, et al. "Intersecting near-optimal spaces: European power systems with more resilience to weather variability." Energy Economics 118 (2023): 106496.
[3] Neumann, Fabian, and Tom Brown. "Broad ranges of investment configurations for renewable power systems, robust to cost uncertainty and near-optimality." iScience 26.5 (2023).
[4] Vågerö, Oskar, et al. "Exploring near-optimal energy systems with stakeholders: a novel approach for participatory modelling." arXiv preprint arXiv:2501.05280 (2025).
Exploration
Trivial Approach
Key Question
Is there any near-optimal solution with more than X PV Capacity and Y Wind Turbine Capacity?
Trivial Approach
Add the constraints to the main problem and solve it
Disadvantage
- A new problem for each question
- May take several hours for large models (~106 vars.)
Exploration
Real-Time Approach
Real-Time Approach
Preparation Phase
- Define properties of interest (m ~ 101).
- Find the corner points (n ~ 103).[1]
Exploration Phase
- Define the question.
- Solve the Navigation problem (n vars. and m constrs.).
- Traverse between the start and end point.
Pros and Cons
- Size of the Navigate problem is independent of the main model.
- For realistic m and n it takes seconds.
- Finding the corner points is computationally expensive but ...potentially parallelizable.
[1] Lau, Michael, Neha Patankar, and Jesse D. Jenkins. "Measuring exploration: evaluation of modelling to generate alternatives methods in capacity expansion models." Environmental Research: Energy 1.4 (2024): 045004.
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