### Abstract

the model, the method used, and the political process and impact, we refer to these papers. In the Netherlands, dike rings, consisting of dunes, dikes, and

structures, protect a large part of the country against flooding. After the catastrophic flood in 1953, a cost-benefit model was developed by D. van Danzig [1956] to determine optimal dike heights. The objective of the cost-benefit analysis (CBA) is to find an optimal balance between investment costs and the benefit of reducing flood damages, both as a result of heightening dikes. The question then becomes when and how much to invest in the dike ring. In Eijgenraam et al. [2014b] we improve and extend D. van Danzig’s

model. In that paper we show how to properly include economic growth in the cost-benefit model, and how to address the question when to invest in dikes. All these models consider dike rings that consist of a homogeneous dike. This means that all parts in the dike ring have the same characteristics with respect to investment costs, flood probabilities, water level rise, etc. Many dike rings in the Netherlands, however, are nonhomogeneous, consisting of different segments that each have different characteristics. Differences occur, for instance, if along a dike ring in the delta area a river dominated regime changes into a sea dominated regime, or if a dike ring contains a large sluice complex. Currently, there are dike rings with up to ten segments in the Netherlands. In

this nonhomogeneous case, it is not necessary and not desirable to enforce that all these segments are heightened simultaneously and by exactly the same amount. Hence, the decision problem for the nonhomogeneous case concerns when and how much to invest in each individual dike segment. In the current article, we consider the extension of the homogeneous case in Eijgenraam et al. [2014b] to the nonhomogeneous case. The research has been carried out as part of a project initiated by the government. The project’s main goal is to support decision making with respect to setting new flood protection standards for

the dike rings in the Netherlands. Figure 1 shows the main dike rings and the current legal protection standard for each dike ring. Efficient flood protection standards can be derived from the optimal investment strategy and the resulting flood probabilities. How this can be done is explained in Eijgenraam et al. [2014a]. Here we confine ourselves to a description of the first stage: finding the optimal investment strategy. In order to lay a firm base for the new standards, the 53 larger dike rings in the Netherlands need to be analyzed thoroughly. This requires that particular scenarios can be analyzed within a reasonable amount of time, where each scenario represents a certain instance of the model parameters such as economic growth, interest rate, water level rise, flood characteristics,

investment costs and so on. It is shown in Eijgenraam et al. [2014b] that the homogeneous case can be solved analytically. Unfortunately, we did not succeed

in solving the nonhomogeneous case analytically. In this article we show how the nonhomogeneous dike height optimization problem can be modeled as a Mixed Integer Nonlinear Programming (MINLP) problem. In addition to the MINLP formulation of the decision problem, we constructed an iterative optimization algorithm that speeds up the solution time considerably. The algorithm has been implemented in AIMMS, which has subsequently been integrated in user-friendly

software to perform the dike ring analysis [Duits 2009a,b]. The final

results have had a big impact in the political decision making process.

Original language | English |
---|---|

Number of pages | 6 |

Journal | Optima: Mathematical Optimization Society Newsletter |

Issue number | 94 |

Publication status | Published - Apr 2014 |

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### Cite this

*Optima: Mathematical Optimization Society Newsletter*, (94).

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*Optima: Mathematical Optimization Society Newsletter*, no. 94.

**A mixed integer nonlinear optimization approach to optimize dike heights in the Netherlands.** / Brekelmans, Ruud; Eijgenraam, C.; den Hertog, Dick; Roos, C.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - A mixed integer nonlinear optimization approach to optimize dike heights in the Netherlands

AU - Brekelmans, Ruud

AU - Eijgenraam, C.

AU - den Hertog, Dick

AU - Roos, C.

PY - 2014/4

Y1 - 2014/4

N2 - This article is based on the material in two earlier papers, Brekelmans et al. [2012] and Eijgenraam et al. [2014a] that were published in the journals Operations Research and Interfaces, respectively. It describes the optimization model that has been developed to optimize dike heights in the Netherlands. Moreover, it briefly describes the high impact of the results of this project on political decision making in the Netherlands. The project was awarded the INFORMS Franz Edelman 2013 Award. For more details on the validation ofthe model, the method used, and the political process and impact, we refer to these papers. In the Netherlands, dike rings, consisting of dunes, dikes, andstructures, protect a large part of the country against flooding. After the catastrophic flood in 1953, a cost-benefit model was developed by D. van Danzig [1956] to determine optimal dike heights. The objective of the cost-benefit analysis (CBA) is to find an optimal balance between investment costs and the benefit of reducing flood damages, both as a result of heightening dikes. The question then becomes when and how much to invest in the dike ring. In Eijgenraam et al. [2014b] we improve and extend D. van Danzig’smodel. In that paper we show how to properly include economic growth in the cost-benefit model, and how to address the question when to invest in dikes. All these models consider dike rings that consist of a homogeneous dike. This means that all parts in the dike ring have the same characteristics with respect to investment costs, flood probabilities, water level rise, etc. Many dike rings in the Netherlands, however, are nonhomogeneous, consisting of different segments that each have different characteristics. Differences occur, for instance, if along a dike ring in the delta area a river dominated regime changes into a sea dominated regime, or if a dike ring contains a large sluice complex. Currently, there are dike rings with up to ten segments in the Netherlands. Inthis nonhomogeneous case, it is not necessary and not desirable to enforce that all these segments are heightened simultaneously and by exactly the same amount. Hence, the decision problem for the nonhomogeneous case concerns when and how much to invest in each individual dike segment. In the current article, we consider the extension of the homogeneous case in Eijgenraam et al. [2014b] to the nonhomogeneous case. The research has been carried out as part of a project initiated by the government. The project’s main goal is to support decision making with respect to setting new flood protection standards forthe dike rings in the Netherlands. Figure 1 shows the main dike rings and the current legal protection standard for each dike ring. Efficient flood protection standards can be derived from the optimal investment strategy and the resulting flood probabilities. How this can be done is explained in Eijgenraam et al. [2014a]. Here we confine ourselves to a description of the first stage: finding the optimal investment strategy. In order to lay a firm base for the new standards, the 53 larger dike rings in the Netherlands need to be analyzed thoroughly. This requires that particular scenarios can be analyzed within a reasonable amount of time, where each scenario represents a certain instance of the model parameters such as economic growth, interest rate, water level rise, flood characteristics,investment costs and so on. It is shown in Eijgenraam et al. [2014b] that the homogeneous case can be solved analytically. Unfortunately, we did not succeedin solving the nonhomogeneous case analytically. In this article we show how the nonhomogeneous dike height optimization problem can be modeled as a Mixed Integer Nonlinear Programming (MINLP) problem. In addition to the MINLP formulation of the decision problem, we constructed an iterative optimization algorithm that speeds up the solution time considerably. The algorithm has been implemented in AIMMS, which has subsequently been integrated in user-friendlysoftware to perform the dike ring analysis [Duits 2009a,b]. The finalresults have had a big impact in the political decision making process.

AB - This article is based on the material in two earlier papers, Brekelmans et al. [2012] and Eijgenraam et al. [2014a] that were published in the journals Operations Research and Interfaces, respectively. It describes the optimization model that has been developed to optimize dike heights in the Netherlands. Moreover, it briefly describes the high impact of the results of this project on political decision making in the Netherlands. The project was awarded the INFORMS Franz Edelman 2013 Award. For more details on the validation ofthe model, the method used, and the political process and impact, we refer to these papers. In the Netherlands, dike rings, consisting of dunes, dikes, andstructures, protect a large part of the country against flooding. After the catastrophic flood in 1953, a cost-benefit model was developed by D. van Danzig [1956] to determine optimal dike heights. The objective of the cost-benefit analysis (CBA) is to find an optimal balance between investment costs and the benefit of reducing flood damages, both as a result of heightening dikes. The question then becomes when and how much to invest in the dike ring. In Eijgenraam et al. [2014b] we improve and extend D. van Danzig’smodel. In that paper we show how to properly include economic growth in the cost-benefit model, and how to address the question when to invest in dikes. All these models consider dike rings that consist of a homogeneous dike. This means that all parts in the dike ring have the same characteristics with respect to investment costs, flood probabilities, water level rise, etc. Many dike rings in the Netherlands, however, are nonhomogeneous, consisting of different segments that each have different characteristics. Differences occur, for instance, if along a dike ring in the delta area a river dominated regime changes into a sea dominated regime, or if a dike ring contains a large sluice complex. Currently, there are dike rings with up to ten segments in the Netherlands. Inthis nonhomogeneous case, it is not necessary and not desirable to enforce that all these segments are heightened simultaneously and by exactly the same amount. Hence, the decision problem for the nonhomogeneous case concerns when and how much to invest in each individual dike segment. In the current article, we consider the extension of the homogeneous case in Eijgenraam et al. [2014b] to the nonhomogeneous case. The research has been carried out as part of a project initiated by the government. The project’s main goal is to support decision making with respect to setting new flood protection standards forthe dike rings in the Netherlands. Figure 1 shows the main dike rings and the current legal protection standard for each dike ring. Efficient flood protection standards can be derived from the optimal investment strategy and the resulting flood probabilities. How this can be done is explained in Eijgenraam et al. [2014a]. Here we confine ourselves to a description of the first stage: finding the optimal investment strategy. In order to lay a firm base for the new standards, the 53 larger dike rings in the Netherlands need to be analyzed thoroughly. This requires that particular scenarios can be analyzed within a reasonable amount of time, where each scenario represents a certain instance of the model parameters such as economic growth, interest rate, water level rise, flood characteristics,investment costs and so on. It is shown in Eijgenraam et al. [2014b] that the homogeneous case can be solved analytically. Unfortunately, we did not succeedin solving the nonhomogeneous case analytically. In this article we show how the nonhomogeneous dike height optimization problem can be modeled as a Mixed Integer Nonlinear Programming (MINLP) problem. In addition to the MINLP formulation of the decision problem, we constructed an iterative optimization algorithm that speeds up the solution time considerably. The algorithm has been implemented in AIMMS, which has subsequently been integrated in user-friendlysoftware to perform the dike ring analysis [Duits 2009a,b]. The finalresults have had a big impact in the political decision making process.

M3 - Article

JO - Optima: Mathematical Optimization Society Newsletter

JF - Optima: Mathematical Optimization Society Newsletter

IS - 94

ER -