## 3 Relevant Research in Wind Farm Design and Optimization
### Sub-Modeling
#### 3.2.3 Civil Engineering and Electrical Infrastructure  
The layout of the civil engineering infrastructure of a wind farm can be considered as an embedded problem, where the main objectives are: (1) minimizing the distance, or costs, of the roads accessing the WTs and (2) minimize the costs associated to WT foundations. The wind farm road design problem has been treated previously, within the scope of WFDO problem, by translating the problem into a minimum spanning tree problem [135,278] and into a Steiner tree problem [167]. The assumptions in both approaches were that the wind farm was planar (e.g., flat terrain), and that the cost per kilometerof road was constant and independent of the WT positions. The Steiner tree problem implementation allowed to find shorter road paths involving nodes (Steiner points), that were not necessarily active WT locations, when compared with the output of the minimum spanning tree approach. However, the Steiner tree problem is significantly more difficult to solve than the minimum spanning tree problem, requiring specialized solution procedures [167]. Although several algorithms have been developed to solve the minimum spanning tree problem, the most widely used are the Prim-Jarnik and the Kruskal greedy algorithms [304,305]. The problem of deciding the kind of WT foundation to use is significantly more complex for offshore wind projects than for onshore wind projects in both economic and pathologic terms. For offshore cases, the problem has been treated by [PERSON] _et al._[55,234], within the OWFLO framework, [PERSON] _et al._[166], within the TOPFARM framework [306], and by [PERSON] _et al._[307, 308, 309, 310]. In all cases, cost functions that depend on the WT individual locations, as discussed in Section 3.2.6, were developed to model cost of foundations due to seabed depth. The most robust approach was proposed by [PERSON] [55], who considered the selection of the kind of tower, type of sub-structure and type of foundation during the optimization process while accounting for wind and wave loads and validated cost functions obtained from different real offshore wind farms. A detailed description of the commonly used offshore foundation technologies and its costs can be found in [55,83]. For onshore cases, the problem has been treated by [PERSON] [167], and [PERSON] _et al._[135,278,280]. Both approaches assumed that foundation costs are an exclusive function of the soil bearing capacity. In addition to the civil engineering infrastructure, the wind farm electrical grid layout, which is mainly composed of substations and power lines of different types and capacities, must be designed with the aim of minimizing the overall costs, as mentioned in Section 2.2.2. The electrical layout design is significantly different between offshore wind farms and onshore wind farms. For offshore cases, the problem has been treated by: (1) [PERSON] [55], who considered a validated model, based on transmission line theory, to quantity the HVAC transmission cable losses and the MVAC collection cable losses and while accounting for its finite capacity; (2) by [PERSON] _et al._[309,310], who proposed a capacitated internal collection network design based on a minimum spanning tree procedure while accounting for Joule-based power losses; (3) by [PERSON] _et al._[166], who proposed a deterministic heuristic procedure based on clustering of non-capacitated power lines, which is similar to the minimum spanning tree approach; (4) by [PERSON] and [PERSON] [84], who developed models accounting for the cost, loss and reliability of the transmission and collection power lines and proposed an optimization strategy for the electrical layout design based on geometric programing; and (5) by [PERSON] and [PERSON] [168], who proposed a vehicle route problem approach, which minimized the total cable cost subject to capacity and physical constraints (e.g., cables did not cross each other in the final optimized electric implementation).