How spatial policies can leverage energy transitions − Finding Pareto-optimal solutions for wind turbine locations with evolutionary multi-objective optimization

. The identification of possible sites for on-shore wind


Introduction
In 2019, the global electricity consumption was 25,027 TWh, supplied mainly by coal (40%), natural gas (25%) and hydro power (17%) (IEA, 2022). To secure the electricity supply and simultaneously reach the 2015 Paris climate targets, requires focused actions and concentrated initiatives (i.e., green deal strategies). Increasing the share of renewable energy is a key goal in many of these initiatives at national or transnational levels (Smol, 2022). To reach the European Green Deal, the installed onshore wind energy capacity has to grow from 174 GW in 2020 up to 750 GW in 2050(WindEurope, 2020. However, achieving this goal is a major challenge, as it has been shown that the allocation of renewable energy systems involves sustainability trade-offs between energy production, ecological and social objectives (Lehmann et al., 2021). For instance in Europe, the wind turbines (WT) have been placed in the most cost effective locations in the past, but there is significant potential for affecting less people in future allocation scenarios . Therefore, energy resource assessments  and coordinated allocation strategies for various renewable energy systems are critical to reach climate targets and secure social welfare (Drechsler et al., 2017). However, capacity planning and allocation strategies for renewable energy systems and WT in particular, remain complex tasks, including uncertainties about multiple technical or non technical constraints and various stakeholder interests (Drechsler et al., 2017;Savvidis et al., 2019).

Wind turbine allocation − a multi objective problem
To support policy makers and planners in this complex decision space, spatially explicit multi-criteria analysis (MCA) has been frequently used to determine the most suitable areas for wind energy production (Baseer et al., 2017;Eichhorn et al., 2019;Gigović et al., 2017;Harper et al., 2019;Mahdy and Bahaj, 2018). The combined spatial criteria used in this type of analysis mainly encompass the potential wind energy yield (Lu et al., 2009) and impacts of WT on various ecosystem services (Eichhorn et al., 2017;Hastik et al., 2015;Kienast et al., 2017;Sliz-Szkliniarz and Vogt, 2011). MCA aggregates the various planning criteria into a single suitability indicator to directly inform policy makers with spatial explicit, optimal solutions  or to determine low-conflicting areas between the multiple criteria .
In a participatory process, in which stakeholders express their interests in the weighting of planning criterias, MCA in combination with maps, are essential tools and comprehensible communication instruments (Higgs et al., 2008). However, MCA methods for WT allocation have been shown to lack global performance since WT are treated individually and not related to each other (Asadi et al., 2023). In addition, the obtained solutions may not always be unequivocal. For example, it can be challenging to involve all relevant stakeholders, stakeholders may find it difficult to express their preferences for a given problem and there can be substantial disagreement between stakeholders on preferences and associated weights given to the different planning criteria (Lehmann et al., 2021). Consequently, the suitable or low-conflict areas for WT are strongly determined by the interests of a subset of stakeholders that are not guaranteed to be fully representative and their expression of preferences which is subject to uncertainties (Eichhorn et al., 2019;Lehmann et al., 2021;McKenna et al., 2022;Song and Chen, 2018a). Thus, instead of primarily focusing on weighing different criteria, it can have advantages to explore a wide range of possible solutions and scenarios in trade-off space (Schwaab et al., 2018). To analyze trade-offs between multiple criteria for only optimal solutions, multi-objective optimization can be used to explore a set of non-dominated or Pareto-optimal solutions (i.e., the Pareto Front) in the n-dimensional target space (Song and Chen, 2018b). A Pareto-optimal solution is impossible to further enhance on one target dimension without reducing the quality of another target (Charpentier, 2015;Drechsler et al., 2017). The set of Pareto solutions facilitates an unbiased trade-off analysis between the targets (Charpentier, 2015;Coello, 2006). Consequently, a trade-off analysis of WT planning targets provides insights beyond optimal allocation solutions towards a better understanding of interdependencies between different constraints and targets.

Genetic multi-objective optimization
Contrary to MCA, multi-objective (MO) optimization techniques do not require predefined weights for the objectives to derive Paretooptimal solutions, rather it is possible to rate and discuss the resulting Pareto solutions with different stakeholders in a participatory a posteriori process (Roberts et al., 2011;Seppelt et al., 2013). Thus, it revealed promising to use an MCA after an MO to find the final best solution from the pareto-optimal solutions (Ridha et al., 2021). Genetic algorithms (GAs) are heuristic MO optimization algorithms which have been shown to handle nonlinear, multi-objective optimization problems efficiently (Coello, 2006;Song and Chen, 2018b). GAs are capable of generating discontinuous or concave Pareto Fronts including spatial dependencies of optimization objectives (Song and Chen, 2018a). Therefore, GAs have been used for various spatial allocation problems such as water resource management (Sahebgharani, 2016), land use planning (Schwaab et al., 2017) or energy system planning (Fischer et al., 2020;Kachirayil et al., 2022). In order to better understand trade-offs of planning olicies in multi-objective spatial allocation problems, Seppelt et al. (2013) combine MO optimization with scenario approaches. Scenarios represent a set of plausible future contexts and can be used to support the distillation of policy implications (Shearer, 2005). Although finding Pareto-optimized solutions for land allocation problems is technically possible, it is often not clear how existing policy instruments influence these optimal solutions (Seppelt et al., 2013). Additionally, a recent review of McKenna et al. (2022) highlights the need for further elaborate holistic models that include multiple aspects of wind energy planning beyond costs and analyze interactions and trade-offs of planning targets. Up to now only few studies have applied data mining algorithms for WT location selection (Asadi et al., 2023). Asadi et al. (2023) used a support vector regression with spatial layers to find suitable locations for wind parks in Iran. Others applied a principle component analysis on suitability indicators, followed by a multiple regression analysis to determine the best WT locations (Shareen and Kahn, 2016). Therefore, with this study we contribute with a framework that combines a spatial explicit MO with scenarios of WT planning policies. We directly derive the optimization goals from national wind energy policies to examine trade-offs and influences of these policies on optimal WT allocation. Finally, we aim to understand the sensitivity of the optimal WT allocation solution on different weights of planning policies. In order to guide the methods and analysis, we ask the following research questions. Using the case study area of Switzerland, we identify national policy options to leverage spatial opportunities for wind energy development. The policy scenarios (2.2) are based on a review of national policies influencing the spatial allocation of WT. We assess the implications of the different policy scenarios for Pareto-optimized WT allocation using a multi-objective optimization algorithm (2.3). We then identify the spatial and non-spatial trade-offs between WT planning targets, considering different policy scenarios. Finally, we outline the spatial opportunities to reach the national wind energy production goal of 4.3 TWh/y.

Case study area
We use Switzerland as a case study area since the country has decided to phase out nuclear power and cover 93% of its electricity demand with renewable resources by 2050 (25 TWh/y; Swiss Federal Office of Energy, 2018). In order to bridge the winter gap in electricity production from hydropower or solar energy, the Swiss energy strategy, sets out to produce 4.3 TWh/y of wind energy by 2050. However, the identification of suitable areas to reach this wind energy production target remains challenging. Due to the high diversity of land cover, land use, topography and population density within a relatively small area, land-use conflicts with wind energy production are highly probable. For Switzerland, Kienast et al. (2017) calculated that 5 TWh/y of wind energy could be produced in Switzerland within areas of marginal competing land-use interests.
Within the scope of the Swiss national energy turnaround, a spatial explicit wind energy strategy has been developed (Swiss Federal Office for Spatial Development, 2017). The strategy coordinates the planning of WT between the Swiss cantons (subnational administrative units) and defines areas where other national interests are prioritized over wind energy production. In this policy framework, forests, areas of crop rotation farming and buffer zones around scenic townscapes are, however, not strictly protected by federal law (Swiss Federal Office for Spatial Development, 2017). In these areas, wind energy production might conflict with other ecosystem services (Egli et al., 2017;Kienast et al., 2017;Egli et al., 2017;Kienast et al., 2017), and a weighting of interests needs to be conducted. Moreover, the wind energy strategy encompasses strategic planning targets from a national perspective to allocate WT. The strategic planning targets are formulated to minimize the impacts on ecosystem services, mounting and operational costs and to ultimately foster positive public perceptions. The latter is crucial in reaching the outlined wind energy production goal, especially in countries such as Switzerland with bottom-up decision-making processes and high landscape awareness.

Optimization goals and constraints
The three optimization goals were derived from the Swiss national wind energy strategy (Table 1). From a total of nine strategic planning targets, three directly affect the spatial allocation of WT and were thus integrated in the MO optimization procedure.
The first goal aims at reducing the number of WT to reach the energy target. The second goal tackles the spatial distribution of WT aiming at clustering rather than dispersing them. We used the Clark-Evans index to determine the clustering of a WT allocation solution. The Clark-Evans index is calculated as the ratio between the observed and the expected distance of nearest neighbors (Clark and Evans, 1954). In our case, the observed distance represents the closest distance between two WT locations, averaged over all selected WT. The expected distance refers to a random distribution of WT within a specific area (the total area of Switzerland in our case; Clark and Evans, 1954). The index ranges from zero to infinity, whereby 0 represents perfect clustering, and values higher than 1 trend towards dispersion.
The third goal prioritizes areas with high energy production potential and low impact on ecosystem services. We operationalized this goal by calculating the energy density as the ratio between energy production [MWh/y] and the visibility [ha] of each turbine. Section 2.3 describes in detail the calculations for energy production and the viewshed analysis for each WT.
The first optimization constraint was determined by the Swiss wind energy target of 4.3 TWh/y electricity production as a minimal boundary of each optimization solution. The second constraint was given by the different areas for allocating the WT, generated under the planning policy scenarios (2.3).

Reference scenario (REF)
To identify the influence of different planning policy scenarios on WT locations, we established a spatially explicit WT allocation model for Switzerland. First, the model excludes all areas that are technically impossible to establish WT (Appendix A), resulting in spatial points representing the geographical wind energy potential . Second, each spatial point is the centroid of a hexagon with a specific circumcircle radius dependent on the rotor diameter of the considered WT types (Table 2, Fig. 1). Since turbine characteristics are often not considered in WT allocation studies (McKenna et al., 2021), our model includes three different WT types in order to roughly account for the diverse topography and varying wind conditions in the study area. The distribution of the WT types was guided by the three main types of landscapes in Switzerland ( Fig. 1): firstly, the flat plateau with large settlement areas and agricultural production, including the large Alpine valley bottoms; secondly, the hilly Jura and Prealps with moderate slopes and small valleys, larger forests up to 1200 m.s.l.; thirdly, the Alpine areas with steeper slopes, elevations between 1200 and 3000 m.s.l., stony ground and deglaciated areas, touristic villages in high inner alpine valleys.
To create a reference scenario, we further removed sites that fall into national restricted, non-focus or low priority areas as defined in the planning guidelines from the Swiss wind energy strategy (Appendix A, Swiss Federal Office of Energy, 2018). The reference scenario (REF) additionally rigorously excludes forest, regions of crop rotation farming and surrounding zones of scenic townscapes. Thus, REF represents a very restrictive planning scenario of N = 1745 possible WT locations.

Policy scenarios
To analyze the effects of different WT planning policies on optimal WT allocations and the spatial trade-offs between planning targets, we derived seven policy scenarios based on the REF scenario. Compared to REF, all seven policy scenarios relax some of the national spatial constraints (Table 3).
The first scenario group (A) refers to policies that separately relax forests, areas designated for crop rotation farming or areas around townscapes of outstanding scenic beauty for WT development. The second policy group (B) relaxes two areas simultaneously, and in the third group (C), all three areas are relaxed for WT development (ALL). We provide the spatial distribution of potential WT for each scenario in appendix A.1.

Site-specific WT attributes
To develop the optimization procedure (2.3), we calculated the sitespecific WT energy output, the view shed and further attributes, for all spatial points in the various policy scenarios.
2.3.3.1. Spatial explicit energy production. The potential energy output of a WT is a function of the turbine type and the specific physical wind condition at the turbine location. Eq. (1) shows the calculation of yearly energy production P w [MWh/y] for a WT at a specific location (Zafirakis et al., 2012). The total energy production is the sum of all mean wind speeds U between cut-in and cut-off windspeed, multiplied with the weibull distribution as shown in Eq. (3).   (2)), A: rotor swept area as a function of the wind turbine model (Table 2), U: mean wind speed at turbine hub height cp: power curve dependent on turbine model and wind speed (see Eq. (3)) ef: Efficiency factor of ~80% due to losses, (Pw multiplied with 8760 h and divided by 10^3 to get MWh/y).
Especially for high elevation, the air density parameter p has been shown as crucial (Jung and Schindler, 2019). Therefore, we approximated p with Eq. (2), derived particularly for Switzerland https://wind-data.ch/tools/luftdichte.php), based on a digital elevation model (DEM 200 m resolution; Federal Office of Topography).
z: Elevation in meter above sea level.
The cp of a WT type have been calculated with the site-specific parameters a and k, the mean wind speed U at a given location, derived from the wind distribution model of Switzerland (Koller and Humar, 2016). These parameters follow a weibull distribution according to Eq.
(3). The wind speed dependent cp U was extracted from WT performance data provided by (https://www.wind-turbine-models.com).
U: mean wind speed at turbine hub height, k: Mean Weibull shape parameter of wind distribution at hub height, A: Mean Weibull scale parameter of wind distribution at hub height, cp_U: power curve of specific WT type according to manufacturer, dependent on wind speed U.
Subsequently, P w is reduced through several losses resulting in the efficiency parameter ef. By the help of two WT planning engineers, we accounted for icing losses based on the turbine location (Appendix B.1). We conservatively assumed that each day of expected icing leads to a 0.25% loss in total energy production. In addition to the spatial explicit icing losses, we generally assumed further reductions of the electricity output due to revisions (5%), electric losses (4%), wake-effects (5%), deactivation because of birds and bats (3%) and deactivation hours to reduce shadow flickering and noise (3%). For each type of WT, this resulted in a raster of 200 m x 200 m, where the cells contained the electricity production in MWh/y. Subsequently, we averaged the electricity production for each hexagonal raster with zonal statistics and added these values as a production estimate [MWh/y] to the corresponding spatial point, representing a WT.

Visibility analysis.
We calculated the viewshed in hectares [ha] as an approximation for the visibility of each of the potential WT locations. Specifically, the viewshed gives the area from which the WT is visible. We used the ArcPy function (ArcMap V.10.7.1) '3d_view_shed' with a digital elevation model, an observer height of 1.6 m and the hub heights according to the WT types (Table 2). We considered hub heights instead of total heights since this decreases the visibility slightly and corrects for the fact that the visibility of a WT depends on the angle to the observer and, thus, might be overestimated using the total height (Wróżyński et al., 2016). In addition, we used an outer radius, which represents the maximal visibility of the turbine. According to Wrozynski (2016), these distances are dependent on the WT height: We assumed 11 km for the E82, 14 km for the E138 and 16 km for the V150 WT type.

The optimization algorithm NSGA-3
To calculate Pareto optimal WT locations, considering multiple optimization goals (i.e., planning targets) and various constraints, we used a genetic optimization algorithm (GA). In principle, a GA starts with an initial population consisting of several individuals. In our case, an individual represents randomly distributed WT locations that sum up to 4.3 TWh/y electricity productions, sampled from a respective policy scenario. Thus, the selected WT in an individual cannot be located in areas that are restricted by the respective policies. In addition, for each individual, the degree of optimization target (Table 1) achievement is calculated (i.e., fitness value). Iteratively, the populations of individual WT are changed by selection, crossover and mutation in order to reach better fitness values in the subsequent generation (Coello, 2006). We used the 'Elitist Non Dominated Sorting Algorithm' (NSGA-3; Jain and Deb, 2014) to solve the optimization problem. The algorithm was implemented in python with the package 'Distributed Evolutionary Algorithms' (Fortin et al., 2012). The NSGA-3 efficiently finds Pareto optimal solutions considering three or more objectives (Jain and Deb, 2014). In the  initial population, we included three individuals that each have been optimized based on a single objective. Hence, before starting with the multi-objective procedure, we optimized each of the three WT planning targets separately. Including these solutions improved the spread of the Pareto Front. During the optimization we tracked the hypervolume and the fitness values of the three optimization goals for every generation. In addition, we updated the Pareto archive with the non-dominated solutions after each iteration. Subsequently, we calculated the relative frequency of occurrence in the Pareto Front (RFOP) for every single WT in a scenario. RFOP ranges from 0 to 1 and indicates a certain robustness with which each WT contributes to an optimal allocation solution. In order to perform a sensitivity analysis and investigate the effect of different parameter settings (Appendix C.1), we ran the optimization for each policy scenario several times. With a multilinear regression, we investigated the effect of the different model parameterizations and the scenarios on the Pareto optimal WT allocation solutions. It revealed that the effect of model parameterization was considerably smaller compared to the effect of different scenarios (Appendix C.2). Consequently, we selected the best parameter settings for each scenario. We did so by applying a rank (1 =best, 4 = worst) for each fitness value comparing a policy scenario between the four model runs. We then selected the model run for each policy scenario according to the minimal rank-sum (Appendix C.3. indicated with*). The descriptive and inferential statistics were calculated in R (V. 4.2.1; R Core Team, 2020) using RStudio (V.1.1.447).
To analyze trade-offs between optimization targets we used the Kmedoids cluster algorithm. The procedure grouped the solutions in the Pareto Front in clusters which are similar for all three fitness values (Obayashi and Sasaki, 2003). We did so by the use of the 'pamk' algorithm, implemented in the R-package fpc. Subsequently, we extracted the representative WT allocation solution for each cluster (medoid) and, thus, reduced the size of the Pareto Front noticeably (Zatarain Salazar et al., 2016).

Influence of planning policy on spatial distribution of WT
To answer the research question Q1, we show the most robust (highest RFOP values) Pareto-optimal WT allocation in the three different landscape types and for each policy scenario in Fig. 2. In addition, Table 4 provides the corresponding wind energy production.
In the REF scenario, the optimal WT locations are concentrated in the northeast, east and central Switzerland (Fig. 2a). Compared to the REF policy, the FOR policy scenario concentrates the WT in the western Plateau while removing some in the eastern alpine areas (Fig. 2B). The spatial distribution under the ISOS policy changes only marginally compared to the restrictive REF scenario (Fig. 2C). In addition, the CRF policy leads to a strong concentration of WT in the western Plateau (Fig. 2D). Following a very restrictive planning scenario (REF) leads to a drastic increase of wind energy production in the alpine areas (Table 4). In addition, the absolut number of WT in alpine areas is higher compared to the other scenarios. However, producing more than 0.8 TWh/y wind energy in alpine regions (REF scenario, Table 4) remains challenging since construction and operational costs tend to be higher than in flat areas. In addition, natural alpine landscapes are often of high scenic value (Kienast et al., 2015), consequently the public perceives WT in these areas as more disruptive than in areas of lower scenic value (Salak et al., 2021;Spielhofer et al., 2021a). However, in policy scenarios where the Alps significantly contribute to the national wind energy target, potential locations can be found in touristic alpine areas. These landscapes are already developed with touristic infrastructure, and, thus, WT present higher functional coherence and less visual disruption compared to natural landscapes, which tends to higher  Fig. 3. Distribution of number of WT (a), clustering (b) and energy density (c) N for pareto-optimized solutions from each policy scenario.
acceptance (Spielhofer et al., 2021a(Spielhofer et al., , 2021b. Contrarily, allowing WT in areas for crop rotation farming (CRF) of forests (FOR), would substantially decrease the need for alpine wind energy production (Table 4). We explain this by the fact that CRF retains more possibilities to develop the large (Vestas V150) WT in the western Plateau with mainly good wind conditions. However, while the REF and the ISOS scenario distribute the WT in all three landscape types and through more regions, the FOR and the CRF policies concentrate the WT within fewer areas. This regional inequality might be compensated with less WT to achieve the production target of 4.3 TWh/y (Section 3.2). The scenarios in which two (FOR_ISOS, CRF_FOR, ISOS_CRF) or three (ALL) policies are relaxed show similar Pareto-fronts and distribution patterns. Hence, for all subsequent Sections (3.2-3.4), we integrated the solutions of the double relaxed policy scenarios into Appendix G.

Trade-off analysis of planning targets
In the following section, we examined the optimization targets with Fig. 3a-c. In addition Fig. 3 shows the number (N) of solutions found as pareto optimal solution for each policy scenario. As proposed by Ashbolt et al. (2017), potential trade-offs between the optimization targets were analyzed using the Pareto front (Fig. 4a-c) and the parallel coordinates plot (Fig. 5).

Number of WT
The restrictive REF policy scenario leads in general to the highest amount of necessary WT to reach the wind energy production target of 4.3 TWh/y. If areas around scenic townscapes (ISOS) are relaxed the number of WT is only marginally affected (Fig. 3a). The relaxation of forests and areas for crop rotation farming leads to a drastic decrease of WT. Particularly the CRF policy provides areas in the flat part of Switzerland to mount the large Vestas V150 (Fig. 2d) under relatively good wind conditions and therefore decreases the number of WT in general.

Clustering
As already shown for the most robust solutions in Section 3.1, the REF is generally lower clustered compared to the policy scenarios FOR, ISOS and CRF (Fig. 3b). Allowing forests (FOR) or areas for crop rotation farming (CRF) leads to similar clustered solutions. From a local perspective, clustered WT allocation solution could be perceived as inequitable, forcing the affected regions to bear all the negative impacts of the national wind energy strategy (Jørgensen et al., 2020). On the other hand, clustered solutions tend to have lower operational costs compared to evenly distributed allocations . The optimization results show that restricting certain areas for WT development might influence the general distribution of WT significantly.

Energy density
The energy density, the ratio between the energy production and the view shed of a WT (MWh/yha) is highest in the REF policy scenario (Fig. 3c). Under the REF policy, more but smaller WT are placed in the Alps (Fig. 2a). As these alpine WT are less visible due to their smaller scale and the steep topography which narrows their visibility, the produced MWh/visible hectare are high. Contrarily, when implementing CRF and FOR, less but larger WT (V 150) are placed in the flat areas of Switzerland, which generally leads to higher visibility. Interestingly, for Switzerland, policy makers need to be aware that if areas in the flat part are allowed for WT (FOR, CRF) results in more visual impact per produced MWh electricity compared to scenarios where alpine areas contribute to the wind energy production.
In the FOR and the CRF scenario we can observe a synergy between reducing the amount of WT and enhancing the clustering (lower CLUS values). The FOR and the CRF policies lead to edges in the Pareto fronts with very low numbers of WT and very clustered spatial aggregation (Fig. 4a). Thus, these solutions would be optimal if only the clustering and the number of WT are considered. However, policies that lead to a reduction in WT (e.g., CRF or FOR) result in only a few regions that produce wind energy. By contrast, the REF and ISOS scenario result in wide u-shaped pareto fronts. Restricting all the areas of national interest (REF) leads to a trade-off between reducing the number of WT and better clustered solutions.
The steep front of the FOR and the CRF policies show solutions in the Pareto-Front that increase the energy density without reducing clustering significantly (4b). However, more clustered solutions lead to less energy density, particularly in the REF and the ISOS policies. Fig. 4c shows a partial trade-off between lowering the number of WT and maximizing energy density [MWh/ha]. The relatively sharp shapes of the Pareto Fronts in Fig. 4c indicate that the targets to reduce the number of WT and enhance energy density are relatively independent from the clustering target. By contrast, Fig. 4a and b show more distributed two-dimensional Pareto Fronts. This indicates a greater influence of the respective third optimization target on the other two.
Due to the simultaneous interactions of all three planning targets, the analysis of trade-offs in the two-dimensional space is critical. Therefore, we applied a K-medoids cluster algorithm to the Pareto Fronts for each policy scenario. Based on Ashbolt et al. (2017), we plotted the normalized fitness values (y-axis) with parallel coordinates to compare the three planning targets simultaneously (Fig. 5). Fig. 5 reveals two trade-offs that appear in all four policy scenarios considering all three planning targets. Firstly, most of the medoids (gray, thin lines) show a low number of WT (high performance in Fig. 5) resulting in low energy density or vice versa. This indicates a general trade-off between minimizing the number of WT and maximizing the energy density of the WT allocation solutions. Secondly, there is a tradeoff between the clustering and the energy density. The better-clustered solutions show in general worse energy densities and vice versa. This indicates that the alpine WT locations, with generally higher energy densities, are mainly isolated locations with limited possibilities for other WT in the neighborhood. Interestingly, we cannot see a distinct trade-off between the low number of WT and their clustering across all four policies. While in the CRF and FOR policies, a low number of WT generally leads to intermediate clustering values, in the ISOS and REF policies, the high number of WT additionally leads to worse clustered solutions. It seems that the REF and ISOS policies restrict too many areas for WT development and thereby prevent clustering of the turbines. The FOR policy tends to produce optimal WT allocation solutions with less trade-offs compared to other policy scenarios.

Wind energy potential within areas of national interest
With regard to the fact that CRF and FOR policies strongly influence the spatial distribution of WT (3.1) and the planning targets (3.2), Section 3.3 focuses on these two policies. Particularly, this section highlights the energy production potential in the areas designated for crop rotation farming and forests. Both areas are protected under the REF policy and would be made available for wind energy development in the CRF and FOR policies, respectively. The FOR policy leads to a noticeable shift of produced MWh/y from the areas without national interest to the forests. Under such a policy, 71% of the most robust WT locations can be found in forests and 29% in areas without further national interest. The CRF policy redistributes wind energy production even more. About 86% of the wind energy is produced in the areas designated for crop rotation farming and only 14% remains in areas without any national interest. Together with the findings from the previous sections, it can be concluded that forests and especially areas designated for crop rotation farming contain substantial physical potential for wind energy production.

Fig. 5.
Cluster representatives (gray). Best solution to reduce the number of WT (magenta), best solution to improve clustering (orange) and best solution to enhance energy density (blue).
However, relaxing either forests or areas for crop rotation farming entirely for WT development might not be conducive to the broad acceptance of a national wind energy strategy. Exemplarily, Suškevičs et al. (2019) showed that defining priority areas for WT on a national strategic planning level can help to overcome local concerns. Therefore, we show the most important WT locations common under the ALL and the REF policy scenario (Fig. 6a). First, we compared the very restrictive REF policy with the ALL policy, in which the forests, the areas around scenic townscapes and the areas for crop rotation farming are relaxed for WT development. The 36 robust (high RFOP) WT locations that are common in the REF and ALL policy summing up to 0.21 TWh/y of electricity production cover app. 4.8% of the wind energy target (Fig. 6a). In the plateau (blue) 0.14 TWh/y are produced and in the Alps (orange) 0.07 TWh/y. From a national perspective, these locations contribute substantially to an optimized WT allocation solution. The locations are important, independently of whether areas for crop rotation farming, forests and areas around scenic townscapes are allowed in WT development. Consequently, the designated locations might be defined as high-priority areas for wind energy development in Switzerland.
Further, we identified the most important WT locations in forests by comparing the ALL with the FOR policy. From the robust WT locations common in both policies, we subsequently selected the locations within forests. The production of the resulting 79 WT locations amounts to 0.83 TWh/y of wind energy. Fig. 6b shows that the important WT within forests are mainly located in the western Plateau of Switzerland (blue). In the same manner, we identified the robust WT locations within areas designated for crop rotation farming. This leads to 227 WT, amounting to 2.46 TWh/y of electricity and covering 57% of the wind energy target (Fig. 6c). The most robust WT locations in areas designated for crop rotation farming are located exclusively in the Plateau (blue) of Switzerland. Consequently, national planning authorities could restrict forests and areas for crop rotation farming in general while partly relaxing these areas with subnational authorities in the western part of Switzerland.

Spatial effects of different weights of WT planning targets
Planning WT considering multiple planning targets might be embedded in a participatory process incorporating different stakeholders. Different stakeholders assign different weights and priorities to the planning targets. To support the negotiation regarding the prioritization of these targets, it is valuable to analyze the spatial and nonspatial effects under different target weights. Therefore, we calculated for each point on the Pareto Front the distance to a hypothetical ideal WT allocation (Ballestero, 2007). The hypothetically best WT allocation solution has the smallest amount of WT, the best clustering and the highest energy density found for all Pareto Fronts. The distance measure considers an adjustable weighting factor for each target. Exemplarily, we used 80%, 10%, and 10% in the different combinations for the weighting of the three targets. However, this represents merely a showcase for the spatial effects of different weights (Fig. 7) and is not based on expert ratings which will most likely be quite different. The numerical results of all points can be found in Appendix F.
Comparing the WT distribution of the equal weights (7a) with the weighted targets (7b-c), we can conclude for Q4, that the weights have noticeable influence on the spatial WT allocation. Weighting the reduction of WT and enhancing the clustering as the most important targets, the optimal WT allocation solutions tend to be clustered in the western part of Switzerland (Fig. 7b & c). Consequently, the discussion about the numbers of WT and spatial clustering should consider the possibility of combining areas for crop rotation farming and wind energy production. Emphasizing on maximizing the energy density results in a more distributed pattern that removes WT from the west to the east and from the flat parts to the Alps (Fig. 7d). However, the emphasis on enhancing the energy density results in more than 250 additional WT compared to a solution that equally balances the weights (Appendix F).

Policy implications
Based on the results, we have identified the following implications for the design of policies that support a wind energy strategy on a Off-site effects of WT planning: Policy makers should be aware that restricting certain areas for wind energy development directly influences other areas. Thus, before elaborating policies that limit the development of WT in specific areas, interregional dependencies and off-site effects need to be considered. This might come with the development of compensation schemes between WT affected and nonaffected regions. For Switzerland, such a specific off-site effect can be observed when restricting forests and areas for crop rotation farming in the lowlands, simultaneously leading to more WT in alpine regions. Communicating off-site effects might help to harmonize national and local perspectives on wind energy development.
Trade-offs in planning targets: WT planning targets should be analyzed with regard to their trade-offs. In the case of Switzerland we found a general trade-off between minimizing the number of WT and maximizing the energy density of the WT allocation. Policy makers must keep in mind that trade-offs might change under certain policies. In general, spatial policies that restrict a lot of areas narrow the optimal solution space and tend to show allocation solutions with stronger tradeoffs.
Common WT sites in different scenarios: The designation of common WT locations, optimal within two or more policy scenarios, helps to prioritize areas for wind energy within a spatial action plan. Additionally, such an analysis discloses regional potential in areas that might not be seen as high priority areas on national scales. Further, the spatially explicit quantification of the energy potential within areas of lower priority support regional decisions about changes in local policies to make these potentials available. However, such a decision about a local change in the planning policy might include further local analysis of the social, ecological and economic impacts of specific WT locations. Finally, before defining absolute restriction zones, the energy production potential in these zones should be analyzed. Such an analysis helps to estimate the monetary and non-monetary costs and gains of restricting specific areas for WT development.  McKenna et al. (2022) highlights the need for more holistic models and approaches contributing to the field of finding and analyzing sites for wind turbines considering a complex decision space with uncertainties. Besides few other studies which make a step towards such holistic approaches (Shaheen and Khan, 2016;Asadi et al., 2023), our study contributes with a multi-objective, genetic optimization algorithm. The proposed algorithm (NSGA-III) simultaneously considered three main WT planning objectives, derived from the Swiss wind energy policies. The NSGA-III, combined with different policy scenarios led to hundreds of pareto-optimal, spatially explicit solutions to distribute WT within the study area. In accordance with Lehman et al. (2021) we conclude that the WT pattern is highly sensitive to applied weights of different planning objectives (optimization targets). Since preference ratings of stakeholders are subject to uncertainties (Lehmann et al., 2021;McKenna et al., 2022;Eichhorn et al., 2019;Song & Chen, 2018), our method is capable of showing the spatial and non-spatial effects of weighting planning targets. By overlaying Pareto optimal allocation solutions of different policy scenarios, we uncovered common optimal locations for siting wind turbines. Such common 'robust' places can be further used as a minimal solution of consensus between opposing stakeholder interests.

Conclusion
For the case study of Switzerland we aimed to better understand the leverages of different planning policies for the development of wind energy. We can conclude that particularly areas designated for crop rotation farming are optimal sites for wind energy production. Thus, in Switzerland the combination of food production with energy production can play a crucial role in the energy transition and help to avoid wind turbines in the alpine areas, if this is a desired scenario. However, such off-site effects are rarely accounted for, in the design and communication of planning policies. Further, our results revealed a trade-off between reducing the number of WT and enhancing the energy density. Consequently, less wind turbines leads to larger, more clustered and better visible turbines in the flat and urbanized areas of Switzerland. Such a scenario might lower the installation and operational costs, since fewer turbines are operated closer together, but the allocation solution is unevenly distributed across Switzerland. In general this result supports the findings of Sasse and Trutnevyte (2019) who conclude that policies focussing on cost-efficiency, lead to strong regional disparities in the distribution of renewable energy in Switzerland. On the one hand spatial clustering of WT, which we integrated as an optimization target, might be beneficial regarding cost-efficiency and cumulative visual impact. On the other hand the spatial patterns derived when including the clustering objective, lack distributional justice or regional equality and can trigger local oppositions . The multi-objective optimization approach employed in this study does not lead to the formulation of wind energy strategies but it helps identify spatial patterns and effects that support the development of such strategies. In our opinion, the multi-objective optimization method is adjustable and transferable to a variety of applications in the field of infrastructure planning and policy implementation under complex restrictions.

Study limitations
There are certain limitations and assumptions involved in the design of this study that should be noted. First, to optimize the allocation of wind turbines, we rely on a discrete grid with potential locations, from which we select optimal subsets. The definition of this grid is somewhat arbitrary and makes the allocation of wind turbines slightly inflexible. However, it has been shown that particularly in complex terrain the wind characteristics of a stand-alone and a parked turbine are quite similar (Kozmar et al., 2021). Thus, selecting the location of wind turbines based on a continuous definition of space could improve the allocation process, but may also add substantial complexity to the optimization problem. A sensitivity analysis with slightly shifted, discrete grids might be a first step to better understand the influence of the exact WT position.
Second, in the context of WT, the technical assumptions of future development are crucial for the output of the optimized WT locations. Although we used three different, currently available types of WT to account for the diversity in topography and wind conditions in Switzerland, the selection of WT types should be further refined and adapted to future technical development.
Third, in this study, we included three objectives which we deem highly relevant when identifying optimal solutions for WT allocation. Nevertheless, as in many infrastructure planning problems, it could be important to include more objectives (Seyedashraf et al., 2021). The NSGA-III algorithm has been shown to perform well for several many-objective optimization problems (Deb and Jain, 2014) and would allow to include more objectives. However, the visualization and interpretation of high-dimensional results can become challenging (Koochaksaraei et al., 2017). In addition, it should be noted that it is not guaranteed that the algorithm converges towards global optimal solutions when applied to the optimization to higher dimensional objectives.
Fourth, in our analysis we applied the spatial clustering target for each optimization run. However, the WT locations in our solutions are more or less independent from each other, and not grouped into a larger wind park. This simplification can be further assessed through the integration of wind farm layout parameters into optimization algorithms (Kirchner-Bossi and Porté-Agel, 2018).
Finally, we want to highlight that policies are not exclusively spatially explicit as it was the case in this study. Often, planning policies include non-spatial aspects that need to be included in planning processes. Therefore, the optimization procedure can be seen as a tool to develop strategic targets with a certain spatial resolution, but this needs to be combined with other assessments at different scales.

Outlook
Our results provide crucial insights for policy-and decision-makers and could further profit from an interactive and iterative decisionmaking process. For example, preferences expressed by stakeholders and decision-makers could be used to rerun the multi-objective optimization with a focus on a specific scenario and a specific part of the Pareto Front (Wicki et al., 2021). Another promising possibility is to further explore the optimization results with a MCA approach as proposed by Ridha et al. (2021). Including preferences is a prerequisite for selecting a solution on the Pareto Front and defining the pathway that should be followed to reach this solution. Ideally, an interactive optimization process in close collaboration with stakeholders will not only result in the selection of specific Pareto optimal solutions, but also in an adapted formulation of the objectives and constraints. In addition, all pathways are subject to uncertainties that may also be considered. For example, changing preferences and policies within a certain timeframe, such as a switch from one to another scenario (i.e., FOR to CRF), could be included by adding a temporal dimension to the modeling framework. Identifying frequently occurring sub-patterns (i.e., WT locations that are part of many Pareto-optimal solutions) is a key way to identify solutions that are robust in uncertain contexts, such as changing preferences. They may also provide decision-makers with some more time before they have to state their preferences and select a certain pathway. Finally, we encourage further research to apply the proposed method to further investigate sensitivity of different input parameters in order to better address uncertainties .