Resilience investment portfolios
Combinations of hardening, redundancy and backup projects are selected to reduce expected service loss across scenarios within a budget.
GCRI · Critical Infrastructure
Optimisation for infrastructure
Optimisation and operations research choose the best use of limited budgets, crews and capacity. In this field they prioritise investments in resilience, schedule restoration and plan network expansion under uncertainty.
01Contents
Optimisation for infrastructure in five parts.
02Application
What optimisation and operations research does here.
Optimisation and operations research develop mathematical methods for allocating resources and making decisions under constraints. They support planning and logistics in complex, interconnected systems. In critical infrastructure and cities and built environment, optimisation supports prepositioning of supplies, network investment and recovery sequencing. Robust formulations help choose options that perform acceptably across many scenarios. The canonical description is on the STEM Commons.
Restoration scheduling
Repair crews and sequences are optimised to restore critical services fastest given dependencies and access.
Network design under uncertainty
Stochastic and robust optimisation choose network expansions that perform acceptably across many demand and hazard scenarios, not only the expected one.
03Geography
Infrastructure exposure in Western Europe.
Night lights, population density and flood water over Western Europe, from NASA GIBS. Each layer carries its own date.
The interactive map needs JavaScript; the layer list and sources are below.
Layers 3
Infrastructure exposure, for this page
About this layer
- Evidence
- Observed
- Source
- VIIRS Black Marble (VNP46A2) (NASA LAADS DAAC)
- Provider
- NASA LAADS DAAC
- Licence
- NASA open data
- Vintage
- daily; Satellite radiance, corrected for moonlight and atmosphere
- Newest at build
- 2026-10-12
- Resolution
- about 500 m grid
- Uncertainty
- Satellite night-time radiance for the date shown; lights are a proxy for electricity use and outages, not a measurement of supply or access.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
About this layer
- Evidence
- Estimated
- Source
- Gridded Population of the World v4.11 (NASA SEDAC (CIESIN, Columbia University))
- Provider
- NASA SEDAC (CIESIN, Columbia University)
- Licence
- CC BY 4.0
- Vintage
- null; Census-based estimate, static (2020)
- Resolution
- about 1 km grid
- Uncertainty
- Census-based estimate of people per square kilometre in 2020, shown as exposure context; not a count of people affected by any hazard.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
About this layer
- Evidence
- Observed (clouds leave gaps)
- Source
- VIIRS Global Flood Product (NASA LANCE)
- Provider
- NASA LANCE
- Licence
- NASA open data
- Vintage
- daily; Satellite detection; clouds leave gaps
- Newest at build
- 2026-10-14
- Resolution
- about 250 m grid
- Uncertainty
- Satellite detection; clouds leave gaps. Satellite or model raster as the provider publishes it. Clouds, swath gaps and retrieval error leave gaps and noise; values are indicators, not measurements at a place.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
About this layer
- Evidence
- Observed
- Source
- VIIRS NOAA-20 corrected reflectance (NASA LANCE)
- Provider
- NASA LANCE
- Licence
- NASA open data
- Vintage
- daily; Satellite image
- Newest at build
- 2026-10-14
- Resolution
- about 250 m grid
- Uncertainty
- Satellite image. Satellite or model raster as the provider publishes it. Clouds, swath gaps and retrieval error leave gaps and noise; values are indicators, not measurements at a place.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
About this layer
- Evidence
- Modelled (latest year GIBS publishes)
- Source
- MODIS Terra and Aqua land cover (MCD12Q1) (NASA LP DAAC)
- Provider
- NASA LP DAAC
- Licence
- NASA open data
- Vintage
- yearly; Satellite classification; latest year GIBS publishes
- Newest at build
- 2024-01-01
- Resolution
- about 500 m grid
- Uncertainty
- Satellite land cover classes for the year shown, including croplands; a classification with known errors, not a farm register.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
About this layer
- Evidence
- Observed (clouds leave gaps)
- Source
- MODIS Terra EVI (NASA LANCE)
- Provider
- NASA LANCE
- Licence
- NASA open data
- Vintage
- daily; Satellite index; clouds leave gaps
- Newest at build
- 2026-10-13
- Resolution
- about 250 m grid
- Uncertainty
- Satellite vegetation index for the 8 days to the date shown, a habitat condition indicator; not a measure of species or biodiversity.
- Reached through
- gibs.earthdata.nasa.gov, only after you allow the live map
Keyboard, with the map focused
Hold Ctrl or ⌘ and scroll to zoom
Latest available
NASA GIBS / EOSDIS · ASTER GDEM (METI, NASA) · Blue Marble (NASA) · © OpenStreetMap contributors (ODbL) · Natural Earth
Loading the latest NASA imagery.
Drag to move. Ctrl or ⌘ and scroll, pinch or the buttons to zoom; hover for the values under the pointer; reset returns to the region.
Infrastructure exposure, framed on Western Europe.Satellite and model products as NASA publishes them, each with its own date. They are indicators, not assessments of any place.
Data: NASA GIBS · ASTER GDEM · Blue Marble · © OpenStreetMap contributors · Natural Earth · NASA EONET · U.S. Geological Survey · NASA JPL OPERA DIST-ALERTSources and licences
- We acknowledge the use of imagery provided by services from NASA’s Global Imagery Browse Services (GIBS), part of NASA’s Earth Science Data and Information System (ESDIS). Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- We acknowledge the use of imagery provided by services from NASA’s Global Imagery Browse Services (GIBS), part of NASA’s Earth Science Data and Information System (ESDIS). Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- VIIRS Black Marble night-time lights, NASA Goddard Space Flight Center; distributed by the NASA Level-1 and Atmosphere Archive and Distribution System (LAADS DAAC); imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- Center for International Earth Science Information Network (CIESIN), Columbia University. 2018. Gridded Population of the World, Version 4 (GPWv4): Population Density, Revision 11. NASA Socioeconomic Data and Applications Center (SEDAC). Licensed under CC BY 4.0. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). doi:10.7927/H49C6VHW. CC BY 4.0
- VIIRS near-real-time products (flood, land surface temperature, snow cover, corrected reflectance), NASA LANCE; imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- MODIS land products (vegetation indices, gross primary production, land cover), NASA LP DAAC and LANCE; imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- ASTER GDEM is a product of METI and NASA (ASTER Global Digital Elevation Model V003, NASA LP DAAC); imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). Cite as: NASA/METI/AIST/Japan Spacesystems and U.S./Japan ASTER Science Team (2019). ASTER Global Digital Elevation Model V003. doi:10.5067/ASTER/ASTGTM.003. NASA open data
- Made with Natural Earth. Free vector and raster map data @ naturalearthdata.com. Public domain
- © OpenStreetMap contributors (ODbL), via NASA GIBS (coastlines, boundaries, roads and place names). Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). ODbL
- Blue Marble, NASA Earth Observatory; imagery via NASA GIBS. Colours redrawn from the published colour map; values averaged into hexagonal cells where shown (modified). NASA open data
- Context on the globe and flat map: coastlines, boundaries, roads and place names from NASA GIBS reference layers (OpenStreetMap data, ODbL, © OpenStreetMap contributors); Blue Marble imagery as an optional base; 3D terrain and the elevation read-out from the ASTER GDEM elevation colour index (5 m to 200 m classes, exaggerated for legibility). Boundaries are drawn as published and imply no position on any territory.
- Live events: NASA Earth Observatory Natural Event Tracker (EONET); events are indicative and keep their original source links.
- Live: NASA EONET Events are indicative, not authority warnings.
- Live: U.S. Geological Survey Events are indicative, not authority warnings.
- Observed (EO): NASA JPL OPERA DIST-ALERT (contains modified Copernicus Sentinel data 2026). We acknowledge the use of imagery provided by services from NASA’s Global Imagery Browse Services (GIBS), part of NASA’s Earth Science Data and Information System (ESDIS).
- NASA GIBS: We acknowledge the use of imagery provided by services from NASA’s Global Imagery Browse Services (GIBS), part of NASA’s Earth Science Data and Information System (ESDIS).
- River discharge forecast, 30 days with range (GloFAS via Open-Meteo): Contains modified Copernicus Emergency Management Service information 2026; not a flood warning.
- Weather data by Open-Meteo.com (https://open-meteo.com/), licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/).
- Optional layers (12 sources in the layer list: live, forecast, observed and context) print their provider credit on the map and here when switched on; forecasts are model output and derived indices are estimates.
Layers and dates
- Night-time lights, daily: VIIRS Black Marble (VNP46A2), NASA LAADS DAAC · 12 Oct 2026
- Population density, 2020: Population: CIESIN, Columbia University, Gridded Population of the World v4.11 (2018), NASA SEDAC, CC BY 4.0 · static
- Flood water, 3-day composite: VIIRS Global Flood Product, NASA LANCE · 14 Oct 2026
- True colour: VIIRS NOAA-20 corrected reflectance, NASA LANCE · 13 Oct 2026
- Land cover type (IGBP), yearly: MODIS Terra and Aqua land cover (MCD12Q1), NASA LP DAAC · 2024
- Enhanced vegetation index, rolling 8 days: MODIS Terra EVI, NASA LANCE · 13 Oct 2026
04Data
What the method consumes.
Datasets and records used by optimisation and operations research on this platform, with the role each plays and the label its values carry. Sources are listed in the source register.
| Data | Role | Label |
|---|---|---|
| Project costs | Options | ESTIMATED |
| Hazard and failure scenarios | Uncertainty | MODELLED |
| Network models | Constraints | Published statistics |
| Crew and spares inventories | Resources | DECLARED |
05Monitor
Optimisation run.
The screen a team would use to follow this method: its measures, states and decisions. Names are examples and values are illustrative.
Optimisation run
Critical infrastructure · Optimisation for infrastructure · Run R-3239
Feasible, gap closingGCRI · Critical Infrastructure
Convergence
Method card
- Method
- Optimisation and operations research
- Variables
- 36,366
- Optimality gap
- 0.9 pct
- Label
- MODELLED
Binding constraints
| Capacity | 0 | 21 | Binding |
| Budget | 0 | 2.8 | Binding |
| Service level | 1 | 0 | Slack |
06Validation
How results are checked.
Solutions are checked for feasibility, tested through simulation and compared with historical decisions. Sensitivity analysis examines how results change with parameters.
| Check | How it is done |
|---|---|
| Scenario coverage | Solutions are tested on scenarios not used for optimisation |
| Constraint validation | Constraints are confirmed with operators |
| Solution stability | Small changes in inputs are tested for large changes in the chosen portfolio |
Optimal solutions can be fragile when assumptions are wrong. Objectives may omit values that are hard to quantify.
07Simulator
A cascade through interdependent networks.
A hazard footprint takes out co-located assets in every layer; fragmentation, dependency between layers and overload of the survivors then spread the failure. The 3D view separates the layers by depth. Teaching model with stated illustrative values, not a prediction. The map on this page shows Western Europe; the model itself is not tied to a place.
Controls
- Assets per layer
- 18
- Hazard footprint
- 8% of area
- Assets that depend on another layer
- 60%
- Spare capacity (tolerance)
- 30%
Readouts
- Assets hit by the hazard
- 11%
- Assets still working
- 44%
- Amplification of the initial damage
- 5.0 times
- Steps to settle
- 6
Numbers, methods and sources
| Step | Transport working (%) | Power working (%) | Telecoms working (%) |
|---|---|---|---|
| 0 | 100 | 83 | 83 |
| 1 | 94 | 83 | 83 |
| 2 | 78 | 83 | 83 |
| 3 | 56 | 83 | 78 |
| 4 | 39 | 78 | 67 |
| 5 | 39 | 56 | 61 |
| 6 | 39 | 33 | 61 |
Methods
- Interdependent networks Buldyrev and others (2010), Catastrophic cascade of failures in interdependent networks, Nature 464
- Overload cascades Motter and Lai (2002), Physical Review E 66
- Betweenness load Brandes (2001), Journal of Mathematical Sociology 25
- Multilayer networks Kivela and others (2014), Journal of Complex Networks 2
- Infrastructure interdependencies Rinaldi, Peerenboom and Kelly (2001), IEEE Control Systems 21(6)
- Uncertainty fan (parameter Monte Carlo) Spiegelhalter, Pearson and Short (2011), Visualising uncertainty about the future, Science 333
- One-at-a-time sensitivity (tornado) Saltelli and others (2008), Global Sensitivity Analysis: The Primer, Wiley
Data
The model runs on the teaching values set by the controls. To calibrate it for a place, read it against these admitted layers and series, which this page’s map can draw:
- Major roads Natural Earth
- Railways Natural Earth
- Seaports Natural Earth
- Airports Natural Earth
- Urban extents Natural Earth
- Night lights tonight, outages (VIIRS Day/Night Band) NASA/NOAA VIIRS (Suomi NPP) · register nasa.gibs.context-live-layers
- Natural events (NASA EONET) NASA EONET · register nasa.eonet.events
Across the six pillars, led by Nexus Consortium
- Experiments Labs
- Built in Critical Infrastructure in Foundry
- Tested at Critical Infrastructure in Universe
- Codified in Energy and Critical Infrastructure in Standards
- Published in Critical Infrastructure in Reports
- Taught in Faculty of Infrastructure, Energy and Industry in Academy
08Connections
Topics that rely on this method.
09Twin and cascade simulator
Model optimisation for infrastructure as a system. Run the cascade.
Assembled from the Nexus Standards area profile Critical infrastructure and critical entities: the hazards it names, the systems and sectors that carry the loss, the controls that dampen it and the data that observe it. Choose the components, pick an initiating hazard and step through the cascade. The Map view places the run on an example geography with open data. Every coupling weight is a stated assumption you can change. A teaching model, not a forecast, an assessment or a certification. To model a place of your own choosing, open the full System Builder.
Hazards
- Dam failure
- River flood (set off downstream)
- Flash flood (set off downstream)
- Mass displacement (set off downstream)
- Widespread power outage (set off downstream)
- Water supply shortfall (set off downstream)
Systems and couplings
- Critical infrastructure and critical entities
- Energy risk standards Dependency
- Space weather, spectrum and timing risk standards Common-mode dependency
- Compound and cascading hazard standards Cascade
- Cyber resilience and digital operational resilience Common driver
Controls
NS-0Constitution and principlesNS-3Risk record UNIs (grammar, legacy crosswalk, allocation authority)NS-9Contextual UNIs (deployments, instances, programme instances)NS-10Policies and clauses (machine-readable obligations: definition, binding, evaluation and enforcement)NS-11Verification and monitoring (evidence, attestations, zero-trust conformance observation)NRS-H61Hazard family: Cascading failure (NHS-1 sys.cascade)NRS-H94Hazard family: Systemic cyber events (NHS-1 cyber.systemic-cyber)NRS-H107Hazard family: Digital infrastructure concentration and monoculture (NHS-1 tech.digital-concentration)NRS-K31Domain pack profile: Cyber national resilience (DOMAIN-031)NRS-K36Domain pack profile: Critical infrastructure (DOMAIN-036)NRS-K48Domain pack profile: Financial system resilience (DOMAIN-048)
Observation
- OpenStreetMap planet and replication (listed for reference)
- Global Power Plant Database (listed for reference)
- NASA Black Marble night-time lights (VNP46) (listed for reference)
- Global Human Settlement Layer (listed for reference)
- Damage to critical infrastructure attributed to disasters
- Number of disruptions to basic services attributed to disasters
- Proportion of the rural population who live within 2 km of an all-season road
Example geography
- Europe: 113 hexagonal cells
- Night lights tonight, outages (VIIRS Day/Night Band), NASA GIBS
- Surface water through cloud, 30 m (OPERA DSWx-S1 radar), NASA GIBS
- Rain rate, last half hour (IMERG), NASA GIBS
- Surface soil moisture (SMAP), NASA GIBS
10Stewardship
Who maintains the method.
Systems Science and Modelling stewards optimisation and operations research for the Consortium and reviews how it is applied across platforms.
11Methods and evidence
How optimisation for infrastructure is modelled, measured and tested.
The model, its assumptions, its data and its uncertainty, in the form a scientist or engineer would check. Structures follow published methods. The values drawn are illustrative, not findings.
System model
The couplings between the systems in optimisation for infrastructure: signs of influence, a reinforcing and a balancing loop, and cross-links where stress jumps.
FAIR guiding principles · GO FAIR and FORCE11W3C PROV · World Wide Web ConsortiumGuidance on consistent treatment of uncertainties · IPCCCEOS Analysis Ready Data · Committee on Earth Observation Satellites
12Connected
Where this page leads across the Consortium.
13Questions
Questions and answers.
What are the limits of optimisation and operations research in this field?
Optimal solutions can be fragile when assumptions are wrong. Objectives may omit values that are hard to quantify.
How are results checked?
Solutions are checked for feasibility, tested through simulation and compared with historical decisions. Sensitivity analysis examines how results change with parameters.
Are the values on this page real?
The data names, roles and checks are real descriptions of practice. The canvas shows a design of the method’s use, not a run; no result is reported here.
Where else is this method applied?
The canonical method page lists every platform that applies it.
ReportsContribute
Contribute evidence from this page.
Reports is the Consortium’s quarterly publication. What you know about this subject can become evidence, a case or a correction in the next edition, credited to you and published under CC BY 4.0 where it is your own work.
GCRICritical InfrastructureStrategic SystemsScenario and Stress-Test
- EmailGateway GW-GCRISend it from this pageEvidence, a correction, a case, a method, a review, a translation or profile input. It arrives tagged with this page, so the editor who owns it receives it.
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Critical Infrastructure
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