# Multi-Objective Optimisation Based Planning of Power-Line Grid Expansions

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## Abstract

**:**

## 1. Introduction

- development and implementation of a client-server based Pareto-optimisation system for power-line routing,
- design and implementation of an interactive visualisation system for intuitive navigation of Pareto-optimal solutions and support of decision-making.

## 2. Background

#### 2.1. Common Planning Workflow

#### 2.2. State of the Art in Multi-Criteria Spatial Analysis

#### 2.3. State of the Art in Multi-Objective Shortest Path Methods

## 3. Methods

#### 3.1. Overview

#### 3.2. Modelling of Optimisation Criteria

#### 3.3. Building the Grid Graph

#### 3.4. Multi-Objective Optimisation

#### 3.5. Designing an Interactive Visualisation System

## 4. Data

#### 4.1. Study Area

#### 4.2. Criteria

**economic efficiency**(see Figure 5a),

**settlement structures and important land use types**(see Figure 5d) as well as

**nature and environmental protection**, biodiversity and recreation areas (see Figure 5c) and priority areas of

**regional planning regulations**(see Figure 5b).

## 5. Results

#### 5.1. Automated Identification of Power-Line Routes

#### 5.2. Interactive Identification of Power-Line Routes

#### 5.2.1. Scenario 1 “Settlement”

#### 5.2.2. Scenario 2 “Environment”

#### 5.2.3. Scenario 3 “Bundling”

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Federal Ministry for Economic Affairs and Energy. Fifth “Energy Transition” Monitoring Report; Federal Ministry for Economic Affairs and Energy: Berlin, Germany, 2016.
- Federal Ministry for Economic Affairs and Energy; Silber Druck oHG. Germany’s New Energy Policy—Heading Towards 2050 with Secure, Affordable and Environmentally Sound Energy; Federal Ministry for Economic Affairs and Energy: Berlin, Germany, 2012.
- German Energy Agency (Dena). Dena Grid Study II. Integration of Renewable Energy Sources in the German Power Supply System from 2015–2020 with an Outlook to 2025; German Energy Agency: Berlin, Germany, 2011.
- Federal Network Agency. Grid Expansion in Germany. What You Need to Know; Federal Network Agency: Bonn, Germany, 2016.
- 50Hertz Transmission GmbH; Amprion GmbH; TenneT TSO GmbH; TransnetBW GmbH. [Application for Federal Sectoral Planning. Sample Application according to § 6 NABEG. Part 1: Coarse and Route Corridors] Antrag auf Bundesfachplanung. Musterantrag nach § 6 NABEG. Teil 1: Grob- und Trassenkorridore; 50Hertz Transmission GmbH; Amprion GmbH; TenneT TSO GmbH; TransnetBW GmbH: Berlin/Dortmund/Bayreuth/Stuttgart, Germany, 2015. [Google Scholar]
- Monteiro, C.; Ramirez-Rosado, I.J.; Miranda, V.; Zorzano-Santamaria, P.J.; Garcia-Garrido, E.; Fernandez-Jimenez, L.A. GIS Spatial Analysis Applied to Electric Line Routing Optimization. IEEE Trans. Power Deliv.
**2005**, 20, 934–942. [Google Scholar] [CrossRef] - Eroğlu, H.; Aydın, M. Genetic Algorithm in Electrical Transmission Lines Path Finding Problems. In Proceedings of the 2013 8th International Conference on Electrical and Electronics Engineering (ELECO), Bursa, Turkey, 28–30 November 2013; pp. 112–116. [Google Scholar]
- Douglas, D.H. Least-cost Path in GIS Using an Accumulated Cost Surface and Slopelines. Cartogr. Int. J. Geogr. Inf. Geovis.
**1994**, 31, 37–51. [Google Scholar] [CrossRef] - Saaty, T.L. A Scaling Method for Priorities in Hierarchical Structures. J. Math. Psychol.
**1977**, 15, 234–281. [Google Scholar] [CrossRef] - Saaty, T.L. Multicriteria Decision Making: The Analytic Hierarchy Process: Planning, Priority Setting Resource Allocation; RWS: Chalfont St Peter, UK, 1990. [Google Scholar]
- Ho, W.; Ma, X. The State-of-the-Art Integrations and Applications of the Analytic Hierarchy Process. Eur. J. Oper. Res.
**2018**, 267, 399–414. [Google Scholar] [CrossRef] - Jeong, J.S.; García-Moruno, L.; Hernández-Blanco, J. A Site Planning Approach for Rural Buildings into a Landscape using a Spatial Multi-criteria Decision Analysis Methodology. Land Use Policy
**2013**, 32, 108–118. [Google Scholar] [CrossRef] - Abudeif, A.; Moneim, A.A.; Farrag, A. Multicriteria Decision Analysis based on Analytic Hierarchy Process in GIS Environment for Siting Nuclear Power Plant in Egypt. Ann. Nucl. Energy
**2015**, 75, 682–692. [Google Scholar] [CrossRef] - Terh, S.H.; Cao, K. GIS-MCDA Based Cycling Paths Planning: A Case Study in Singapore. Appl. Geogr.
**2018**, 94, 107–118. [Google Scholar] [CrossRef] - Mileu, N.; Queirós, M. Integrating Risk Assessment into Spatial Planning: RiskOTe Decision Support System. ISPRS Int. J. Geo-Inf.
**2018**, 7, 184. [Google Scholar] [CrossRef] - Hu, H.; Lin, T.; Wang, S.; Rodriguez, L.F. A cyberGIS Approach to Uncertainty and Sensitivity Analysis in Biomass Supply Chain Optimization. Appl. Energy
**2017**, 203, 26–40. [Google Scholar] [CrossRef] - Houston, G.; Johnson, C. EPRI-GTC Overhead Electric Transmission Line Siting Methodology; Georgia Transmission Corporation: Georgia, CA, USA, 2006. [Google Scholar]
- Linstone, H.A.; Turoff, M. The Delphi Method: Techniques and Applications; Addison-Wesley: Reading, MA, USA, 1975. [Google Scholar]
- Schmidt, A.J. Implementing a GIS Methodology for Siting High Voltage Electric Transmission Lines. Pap. Resour. Anal.
**2009**, 11, 17. [Google Scholar] - ArcMap Model Builder. Available online: http://desktop.arcgis.com/de/arcmap/latest/analyze/modelbuilder/what-is-modelbuilder.htm (accessed on 4 May 2018).
- Bagli, S.; Geneletti, D.; Orsi, F. Routeing of Power Lines through Least-Cost Path Analysis and Multicriteria Evaluation to Minimise Environmental Impacts. Environ. Impact Assess. Rev.
**2011**, 31, 234–239. [Google Scholar] [CrossRef] - Janssen, R.; Herwijnen, M.V.; Beinat, E. Definite-Case Studies and User Manual; Vrije Universiteit Amsterdam/IVM: Amsterdam, The Netherlands, 2003. [Google Scholar]
- Grassi, S.; Friedli, R.; Grangier, M.; Raubal, M. A GIS-Based Process for Calculating Visibility Impact from Buildings During Transmission Line Routing. In Connecting a Digital Europe Through Location and Place; Huerta, J., Schade, S., Granell, C., Eds.; Springer: Cham, Switzerland, 2014; pp. 383–402. [Google Scholar]
- Beryozkina, S.; Sauhats, A.; Neimane, V. Designing a Transmission Line Using Pareto Approach. In Proceedings of the IEEE Grenoble PowerTech (POWERTECH) Conference, Grenoble, France, 16–20 June 2013. [Google Scholar]
- Aissi, H.; Chakhar, S.; Mousseau, V. GIS-Based Multicriteria Evaluation Approach for Corridor Siting. Environ. Plan. B Plan. Des.
**2012**, 39, 287–307. [Google Scholar] [CrossRef] - Medrano, F.A.; Church, R.L. Corridor Location for Infrastructure Development A Fast Bi-objective Shortest Path Method for Approximating the Pareto Frontier. Int. Reg. Sci. Rev.
**2014**, 37, 129–148. [Google Scholar] [CrossRef] - Hansen, P. Bicriterion Path Problems. In Multiple Criteria Decision Making Theory and Application; Fandel, G., Gal, T., Eds.; Lecture Notes in Economics and Mathematical Systems; Springer: Berlin/ Heidelberg, Germay; New York, NY, USA, 1979; Volume 177, pp. 109–127. [Google Scholar]
- Bökler, F.; Ehrgott, M.; Morris, C.; Mutzel, P. Output-sensitive Complexity of Multiobjective Combinatorial Optimization. J. Multi-Criteria Decis. Anal.
**2017**, 24, 25–36. [Google Scholar] [CrossRef] - Paixao, J.; Santos, J. Labelling Methods for the General Case of the Multiobjective Shortest Path Problem: A Computational Study. In Computational Intelligence and Decision Making; Intelligent Systems, Control and Automation: Science and Engineering; Springer: Dordrecht, The Netherlands, 2009; pp. 489–502. [Google Scholar]
- Guerriero, F.; Musmanno, R. Label Correcting Methods to Solve Multicriteria Shortest Path Problems. J. Optim. Theory Appl.
**2001**, 111, 589–613. [Google Scholar] [CrossRef] - Bökler, F.; Mutzel, P. Tree-Deletion Pruning in Label-Correcting Algorithms for the Multiobjective Shortest Path Problem. In WALCOM: Algorithms and Computation. WALCOM 2017; Poon, S.H., Rahman, M., Yen, H.C., Eds.; Lecture Notes in Computer Science 10167; Springer: Cham, The Netherlands, 2017; pp. 190–203. [Google Scholar]
- Erb, S.; Kobitzsch, M.; Sanders, P. Parallel Bi-objective Shortest Paths Using Weight-Balanced B-trees with Bulk Updates. In Experimental Algorithms. SEA 2014; Lecture Notes in Computer Science 8504; Springer: Cham, Switzerland, 2014. [Google Scholar]
- Warburton, A. Approximation of Pareto Optima in Multiple-Objective Shortest-Path Problems. Oper. Res.
**1987**, 35, 70–79. [Google Scholar] [CrossRef] - Tsaggouris, G.; Zaroliagis, C.D. Multiobjective Optimization: Improved FPTAS for Shortest Paths and Non-Linear Objectives with Applications. Algorithms Comput.
**2006**, 4288, 389–398. [Google Scholar] - ESRI (Environmental Systems Research Institute) ArcGIS Desktop. Available online: http://desktop.arcgis.com/en/arcmap/ (accessed on 20 March 2018).
- Adamczyk, P.; Smith, P.H.; Johnson, R.; Hafiz, M. REST and Web Services: In Theory and in Practice. In REST: From Research to Practice; Springer: New York, NY, USA, 2011. [Google Scholar]
- Bökler, F. Output-Sensitive Complexity of Multiobjective Combinatorial Optimization with an Application to the Multiobjective Shortest Path Problem. Ph.D. Thesis, Department of Computer Science, TU Dortmund University, Dortmund, Germany, 2018. [Google Scholar]
- Chambers, J.; Cleveland, W.; Kleiner, B.; Tukey, P. Graphical Methods for Data Analysis; The Wadsworth Statistics/Probability Series; Duxury: Boston, MA, USA, 1983. [Google Scholar]
- Amprion GmbH. Available online: https://www.amprion.net/index-2.html (accessed on 6 April 2018).
- European Habitats Directive. Available online: http://ec.europa.eu/environment/nature/legislation/habitatsdirective/index_en.htm (accessed on 10 April 2018).
- Federal Agency for Cartography and Geodesy. Digitalc Basic Landscape Model (AAA Modelling); Geodaten der Deutschen Landesvermessung; Federal Agency for Cartography and Geodesy: Frankfurt am Main, Germany, 2016. [Google Scholar]
- GDI-DE: German Data Infrastructure. Available online: http://www.geoportal.de/EN/GDI-DE/INSPIRE/Legal_Implementation/legal_implementation.html?lang=en (accessed on 6 June 2018).
- Flaxman, M. Fundamentals of Geodesign. In Peer Reviewed Proceedings of Digital Landscape Architecture 2010 at Anhalt University of Applied Sciences; Wichmann Herbert: Berlin, Germany, 2010; Volume 2, pp. 28–41. [Google Scholar]
- Steinitz, C. A Framework for Geodesign: Changing Geography by Design; Esri: Redlands, CA, USA, 2012. [Google Scholar]

**Figure 1.**Overview of the presented workflow: After a set of suitable criteria for a planned grid expansion is identified by start and end point, the modelling of the study area and optimisation criteria is performed by the implemented ArcMap add-in (client). Processed data is transferred to the optimisation server by means of a RESTful web service. A discrete structure (grid graph) is derived from preprocessed spatial data and the optimisation process is started. After an approximation of the Pareto-front (a set of suitable paths) is calculated, results are transferred back to the client for analysis.

**Figure 2.**Criteria generation with the developed ArcMap Add-In: ⓐ definition of start and end point and study area; ⓑ feature layers from the ArcMap data frame added to the list of criteria; ⓒ classified in an arbitrary amount of criteria categories (groups); ⓓ by defining an priority value for each layer, an inter-group weighting of the criterion is achieved; ⓔ criteria with positive impact are flagged as bundling criteria; ⓕ definition of the length of graph edges in metres; ⓖ visualisation of the criteria layers in the ArcMap map view. Data copyright by GeoBasis-DE/BKG 2017.

**Figure 3.**Creation of the grid graph: (

**a**) spatial data is preprocessed using GIS; (

**b**) objective function is modelled (visualisation of three exemplary weight layers) and (

**c**) view of the resulting graph structure. Colour mapping from high values (red) to low values (green) is used.

**Figure 4.**Interactive Visualisation System: (

**a**,

**c**): spider-plot as a graphical control element to support navigation through the set of Pareto-optimal solutions. Criteria are classified into groups (visualised by different colours of sliders and labels). The blue polygon outlines the current slider positions and thus restrictions in the accompanying solution space dimension. The magenta coloured inner polygon shows the minimum possible values for each criterion induced by the current constraints. In the centred circular area of the widget, the current length restriction of the highlighted criterion is shown (in map units, here metre). (

**b**,

**d**): resulting paths for different solution space restrictions are visualised in GIS.

**Figure 5.**Criteria used to model the impact of power-line routings in the study area. Criteria are categorised into four categories of protective goods. Data copyright by GeoBasis-DE/BKG 2017. (

**a**) 200 $\mathrm{m}$ buffers of linear infrastructures (positive impact); (

**b**) Regional Planning Regulations (negative impact); (

**c**) Nature and Environmental Protection areas (negative impact); (

**d**) Settlement Structures and Urban Land Use (negative impact).

**Figure 6.**(

**a**) overview of the resulting 4667 Pareto-optimal paths; (

**b**) statistically identified paths of interest. Visualisation of the paths minimising each of the five criteria. The path with minimal length is also the path with minimal crossing of priority areas (regional planning regulations). The Nearest-To-Ideal classified path is the one with minimum Euclidean distance to the approximation of the ideal point (see Section 3.4). Data copyright by GeoBasis-DE/BKG 2017.

**Figure 7.**Crossing length for the identified alternatives (cf. Figure 9). Criteria with zero crossings were omitted. (

**a**) scenario 1 “Settlement” with Alternatives A, B, C; (

**b**) scenario 2 “Environment” with Alternatives D, E, F; (c) scenario 3 “Bundling” with Alternatives G, H, I.

**Figure 8.**Using the interactive visualisation tool to set constraints on the approximation of the Pareto-front: (

**a**) Minimum Settlement Impact Constraints: Maximum crossing length for mining sites, waste deposition sites, cemeteries and sensitive structures are set to zero. Maximum crossing length of urban settlement buffers is restricted to 1.8 km; (

**b**) Minimum Nature and Environmental Impact Constraints: Crossing of habitats directive areas, water bodies greater than 10 ha, protected biotopes and wildlife areas are constrained to zero. The impact on forests is limited to crossing length below 500 m and crossing length with land conservation areas is limited to 8 km.

**Figure 9.**Visualisation of exemplary results from interaction with the approximated Pareto-front. Data copyright by GeoBasis-DE/BKG 2017.

**Table 1.**Evaluated criteria for finding optimised transmission line routes and their impact classes.

Category | ID | Description | Impact Class |
---|---|---|---|

bundling with linear infrastructure (+ 200 $\mathrm{m}$ buffer) | ${o}_{1}$ ${o}_{2}$ ${o}_{3}$ | concentration along existing power-lines concentration along motorways concentration along main roads | high moderate low |

regional planning regulations | ${o}_{4}$ ${o}_{5}$ ${o}_{6}$ ${o}_{7}$ ${o}_{8}$ | priority areas for urban development priority areas for farming priority areas for forestry priority areas for industrial development priority areas for surface water bodies | lowest lowest lowest lowest lowest |

nature and environmental protection | ${o}_{9}$ ${o}_{10}$ ${o}_{11}$ ${o}_{12}$ ${o}_{13}$ ${o}_{14}$ ${o}_{15}$ ${o}_{16}$ ${o}_{17}$ | habitats directive areas nature conservation areas protected wildlife areas protected biotopes forests water bodies > 10 $\mathrm{h}\mathrm{a}$ landscape conservation areas natural parks biotope networks | high moderate moderate low low low lowest lowest lowest |

settlement structures and urban land use | ${o}_{18}$ ${o}_{19}$ ${o}_{20}$ ${o}_{21}$ ${o}_{22}$ ${o}_{23}$ ${o}_{24}$ | urban settlement areas + 400 $\mathrm{m}$ buffer rural settlement areas + 200 $\mathrm{m}$ buffer sensitive structures (e.g., hospitals) cemeteries industrial sites waste deposition sites mining sites | high high moderate moderate moderate moderate moderate |

length | ${o}_{25}$ | length | high |

**Table 2.**Overview of the resulting cost values for the 4667 Pareto-optimal solutions. Groups ${g}_{1},\cdots ,{g}_{4}$ are weighted sums of the criteria depicted in Table 1. ${g}_{5}$ represents the lengths of the paths and thus equals ${o}_{25}$ (see Table 3). Note: ${g}_{1}$ is a bundling criterion and thus represents the accumulated lengths along which no linear infrastructure corridors are crossed.

${\mathit{g}}_{1}$ | ${\mathit{g}}_{2}$ | ${\mathit{g}}_{3}$ | ${\mathit{g}}_{4}$ | ${\mathit{g}}_{5}$ | |
---|---|---|---|---|---|

mean | 262,215.54 | 135,263.14 | 94,531.76 | 94,083.08 | 27,052.36 |

std | 40,486.08 | 8393.63 | 27,074.91 | 38,241.67 | 1678.49 |

min | 176,490.00 | 118,364.00 | 34,113.70 | 25,723.70 | 23,672.79 |

25% | 232,537.00 | 129,646.00 | 74,141.05 | 64,968.20 | 25,929.22 |

50% | 265,687.00 | 133,836.00 | 94,012.90 | 87,675.10 | 26,767.26 |

75% | 289,193.50 | 139,407.00 | 112,216.50 | 115,919.00 | 27,881.48 |

max | 367,991.00 | 180,637.00 | 192,218.00 | 247,791.00 | 36,127.42 |

**Table 3.**Overview of the resulting crossing lengths for the 4667 Pareto-optimal solutions (corresponding to 12 of the 25 criteria). All values are in metres. Note: ${o}_{1}$ is a bundling criterion and thus represents the length along which no linear infrastructure corridors (existing power-lines) are crossed.

${\mathit{o}}_{1}$ | ${\mathit{o}}_{9}$ | ${\mathit{o}}_{10}$ | ${\mathit{o}}_{12}$ | ${\mathit{o}}_{13}$ | ${\mathit{o}}_{15}$ | ${\mathit{o}}_{17}$ | ${\mathit{o}}_{18}$ | ${\mathit{o}}_{19}$ | ${\mathit{o}}_{20}$ | ${\mathit{o}}_{22}$ | ${\mathit{o}}_{25}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

mean | 16,400.10 | 650.24 | 814.71 | 259.98 | 2861.54 | 19,135.67 | 7663.80 | 6760.39 | 11,519.39 | 35.15 | 670.53 | 27,052.36 |

std | 6928.15 | 934.87 | 867.86 | 230.42 | 2288.32 | 3369.19 | 3384.64 | 5043.95 | 3071.71 | 58.76 | 471.50 | 1678.49 |

min | 77.25 | 0.00 | 0.00 | 0.00 | 91.75 | 5920.21 | 1068.14 | 736.38 | 4180.24 | 0.00 | 67.17 | 23,672.79 |

25% | 11,851.90 | 0.00 | 243.48 | 75.00 | 1011.57 | 17,226.39 | 4858.99 | 3311.09 | 9263.85 | 0.00 | 244.71 | 25,929.22 |

50% | 17,725.41 | 250.00 | 565.56 | 187.07 | 2348.32 | 19,533.72 | 7667.46 | 5398.64 | 11,302.53 | 14.14 | 723.30 | 26,767.26 |

75% | 21,447.03 | 730.42 | 1058.01 | 396.75 | 3932.75 | 21,431.00 | 10,167.91 | 8057.41 | 13,985.11 | 28.28 | 883.42 | 27,881.48 |

max | 30,281.46 | 5652.94 | 6022.24 | 1279.33 | 11,141.00 | 27,013.01 | 16,518.35 | 28,585.28 | 19,947.25 | 316.92 | 4283.53 | 36,127.42 |

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## Share and Cite

**MDPI and ACS Style**

Bachmann, D.; Bökler, F.; Kopec, J.; Popp, K.; Schwarze, B.; Weichert, F. Multi-Objective Optimisation Based Planning of Power-Line Grid Expansions. *ISPRS Int. J. Geo-Inf.* **2018**, *7*, 258.
https://doi.org/10.3390/ijgi7070258

**AMA Style**

Bachmann D, Bökler F, Kopec J, Popp K, Schwarze B, Weichert F. Multi-Objective Optimisation Based Planning of Power-Line Grid Expansions. *ISPRS International Journal of Geo-Information*. 2018; 7(7):258.
https://doi.org/10.3390/ijgi7070258

**Chicago/Turabian Style**

Bachmann, Daniel, Fritz Bökler, Jakob Kopec, Kira Popp, Björn Schwarze, and Frank Weichert. 2018. "Multi-Objective Optimisation Based Planning of Power-Line Grid Expansions" *ISPRS International Journal of Geo-Information* 7, no. 7: 258.
https://doi.org/10.3390/ijgi7070258