The target site of this study is the Southwest Sea region between Wido and Anmado in Jeollabuk-do, Republic of Korea, which is considered one of the candidate sites for large-scale offshore wind farm development. According to previous assessments, the mean wind speed in the target area corresponds to wind class 3, ranging from 6.8 to 7.5 m/s (KIER, 2025). This indicates sufficient resource potential for commercial-scale offshore wind farm development. However, seasonal and directional variability remain significant, and therefore long-term data-based detailed statistics are essential for reliable AEP estimation and establishing wake-minimizing layout strategies.

For wind resource assessment, ERA5 reanalysis data from the ECMWF covering the OWF target area were used, as shown in Fig. 1 (Hersbach et al., 2023). ERA5 provides hourly mean reanalysis data on a global grid and is well suited for constructing long-term statistics for large-scale offshore wind candidates owing to its temporal consistency, gap-filling capability, and standardized variables. A representative point for the target area was defined at 35.5° N and 126° E, and hourly time series data were collected over a 20-year period from 00:00 on January 1, 2005 to 23:00 on December 31, 2024. A total of 175,320 samples were obtained. The u- and v-components of wind at 100 m above sea level from ERA5 single-level data were directly used to derive wind resources at that height.

In this study, the specifications and performance characteristics of the IEA 15 MW reference wind turbine (RWT) were adopted as input data (Gaertner et al., 2020). This publicly available model provides comprehensive design information, including rated power, cut-in, rated, and cut-out wind speeds, rotor diameter, hub height, as well as power output (P) and thrust coefficient (C_T). These features make the model suitable for direct integration into the AEP estimation module and wake modeling. Table 1 summarizes the main specifications of the selected turbine, and Fig. 2 presents the power and thrust coefficient curves. The power output P was calculated by linearly interpolating the discretized power curve data provided by the RWT using spline interpolation to evaluate the output at specific wind speeds. The thrust coefficient C_T was subsequently used in wake modeling to estimate the effective incident wind speed and deficits for each wind speed and direction.

Hourly time-series data of the 100 m wind components from ECMWF ERA5, consisting of the eastward u and northward v components, were used to calculate wind speed and direction at 100 m above sea level. The wind speed V and wind direction θ at 100 m were calculated following the ERA5 guidelines (ECMWF, 2025).

To convert the wind speed from the reference height z_ref of 100 m to the hub height of 150 m, the power law introduced in IEC 61400-3-2 (Clause 3.96) was applied (IEC, 2025).

The power law exponent σ is treated as a constant that reflects the long-term vertical wind shear characteristics of the target area. The increase in wind speed with height arises from surface roughness effects, and modeling this behavior requires wind speed data at multiple heights at the same location. Therefore, data from the Global Wind Atlas (GWA), which provided mean wind speeds at multiple heights (10, 50, 100, 150, and 200 m), were utilized (DTU, 2019). In this study, σ was estimated using linear regression across these height-dependent wind speeds implemented in MATLAB (MathWorks, 2025a), yielding σ = 0.1050 with a coefficient of determination R² = 0.9977, as shown in Fig. 3. This value was then applied to the power law equation to construct the hub-height wind speed time series.

In summary, ERA5 reanalysis data were used as the primary data source for hourly wind speed and direction time series, while GWA data were employed solely to estimate the power law exponent σ based on long-term multi-height mean wind speeds. Consequently, GWA mean values were used only for vertical correction through σ estimation, and the time-resolved hub-height wind speed series was directly used for subsequent AEP calculations. In addition, unlike onshore conditions, offshore environments were characterized by a very small surface roughness, assumed to be 0.2 mm, resulting in negligible wind veer with height. Therefore, the wind direction obtained at the reference height was assumed to be identical to that at the hub height in this study.

Using the preprocessed hub-height wind speed time series at 150 m, the wind speed and direction characteristics of the target offshore area were analyzed. First, a wind rose was constructed based on the 20-year long-term wind data to identify the dominant directional patterns. Subsequently, three-parameter Weibull distributions were fitted for each of the N_WD directional sectors to quantitatively describe the wind speed distribution. Fig. 4 presents the wind rose, confirming that winds from the north-northwest to north sector constitute the prevailing wind directions, together with the joint distribution of wind direction and speed.

For probabilistic statistical analysis of wind resources, the wind speed distribution for each direction was modeled using a three-parameter Weibull distribution.

Here, a denotes the scale parameter, b is the shape parameter, and c is the location parameter. Under the assumption that no upstream wind speed disturbance exists, the mean incident wind speed for each directional sector θ_d, d = 1, ⋯, N_WD within the OWF area is calculated using Eq. (4).

Table 2 summarizes the three-parameter Weibull coefficients for each wind direction sector (N_WD = 16), together with the wind occurrence frequency (F) and mean wind speed v_d for each direction.

To estimate the wind speed incident on downstream wind turbines affected by wakes generated by upstream turbines, the classical Jensen wake model was adopted. An OWF consisting of a total of N_T turbines was assumed to be arranged in a Cartesian coordinate system, with turbine positions defined as X = (x₁, ⋯, x_NT), Y = (y₁, ⋯, y_NT). The location of an upstream turbine j was denoted by (x_j, y_j), and that of a downstream turbine i by (x_i, y_j). For convenient representation of the longitudinal and lateral distances between turbines, the Cartesian coordinate system was rotated to align with the wind direction θ_d (d = 1, ⋯, 16), as described in previous studies (Du Pont and Cagan, 2012; Feng and Shen, 2015; Ju and Liu, 2019; Katic et al., 1987; Park et al., 2025b; Park and Sung, 2024).

Here, θ represents the counterclockwise rotation angle of the coordinate system, defined as θ = 3π/2−θ_d. The longitudinal distance between an upstream and a downstream turbine is then given by x′_ij (=x′_i − x′_j > 0), while the lateral distance is |y′_ij| (=|y′_i − y′_j|0). The overlap area between the wake generated by the upstream turbine j and rotor of the downstream turbine i is formulated as follows.

Here, W_ij denotes the wake radius, α is the wake expansion ratio, z_H is the hub height, and z₀ is the surface roughness length, which is set to 0.0002 m, a value commonly used for offshore environments (Kirchner-Bossi and Porté-Agel, 2024; Manwell et al., 2009).

For a given wind direction θ_d and incident wind speed v_d defined in Eq. (4), the effective mean wind speed incident on downstream turbine i, accounting for wind speed deficits caused by wakes from multiple upstream turbines, is expressed by Eq. (7) (Feng and Shen, 2015).

Here, C_T is the thrust coefficient shown in Fig. 2, A_S is the rotor swept area listed in Table 1, and N_WT denotes the total number of turbines. Finally, the AEP of an OWF consisting of N_WT wind turbines, accounting for wind resources, is calculated as follows (Feng and Shen, 2015; Park et al., in press).

Here, P represents the turbine power output from Fig. 2, and F denotes the wind occurrence frequency corresponding to each wind direction δ_d(d =1, ⋯, N_WD), as summarized in Table 2.

Prior to formulating the optimization objective function, recent studies on the cost structure of fixed-bottom OWFs indicate that total project costs are primarily composed of turbines (33.6 %), electrical infrastructure (17.9 %), substructures and foundations (12.8 %), assembly and installation (10.5 %), and leasing costs (4.6 %) (Stehly and Duffy, 2022). The economic performance of offshore wind farms is typically evaluated from the perspective of the LCOE. In this study, an approximate form of LCOE is first introduced to separately examine the relative impacts of layout variations on capital expenditures (CAPEX) and AEP. The LCOE for a given layout can be expressed as follows.

Here, CAPEX_fix denotes fixed capital expenditures that are independent of layout, including turbines, substructures and foundations, installation, onshore and transmission systems, and OSS. CAPEX_cbl represents the internal cable investment cost that varies with layout OPEX_fix is the annual fixed operating expenditure, and CRF is the capital recovery factor, which is a function of the discount rate r and project lifetime N.

In practice, incorporating all detailed cost components such as OSS placement, voltage drop and resistive losses, cable specifications, and voltage levels as simultaneous optimization variables would exponentially increase the design space and significantly reduce computational efficiency and convergence stability. Because the objective of this study was to quantitatively compare and interpret the effects of layout variations, the optimization variables were deliberately restricted to a minimal set that was directly sensitive to layout changes. Accordingly, fixed terms (CAPEX_fix, OPEX_fix) were treated as constants across all layouts, while only the variable terms (CAPEX_cbl, AEP) were included in the optimization objective function. This approach enables the essential effects of layout optimization to be evaluated in a reproducible manner within a practical computational budget. Under this simplification, ranking layouts by LCOE becomes equivalent to minimizing the following simplified ratio.

Here, Cost_{in − cbl} can be interpreted as the annualized or equivalent cost associated with the internal cable network. For consistency in exploration and comparison, this study adopts a length-proportional cost model, expressed as follows.

In this model, L_cbl (km) is the total length of the internal cable network for a given layout, Cost_clv ((€/d) is the daily charter cost of the cable-laying vessel, and R_inst (d/km) is the installation time required per unit cable length. Thus, Cost_{in − cbl} serves as a representative proxy for cable installation costs proportional to cable length. Identical unit costs and installation productivity were applied to all scenarios to ensure fairness in relative layout comparisons. To maintain unit consistency, AEP was converted to MWh/yr and used in the objective function calculation in €/MWh.

The total internal cable length L_cbl was calculated by connecting all turbines using a minimum spanning tree (MST) based on Prim’s algorithm, assuming the minimum total length and excluding the number and locations of OSS, electrical losses such as voltage drop and resistive losses, cable specifications and voltage ratings, and anchor-cable interference effects (MathWorks, 2025b). Representative parameters were selected based on recent design studies, with the cable-laying vessel daily charter cost Cost_clv set to 60,000 €/d and the installation time per unit length R_inst set to 1.5 d/km (Lerch et al., 2021).

In summary, by treating the fixed terms of the approximate LCOE formulation as constants and including only the variable terms, namely AEP accounting for wake effects and a proxy for cable installation cost modeled by the MST-based total internal cable length, this study evaluates the economic impact of layout variations in a simple, transparent, and reproducible form expressed in €/MWh. This constitutes a reasonable simplification to balance exploration and convergence while maintaining computational efficiency in a large design space. Future studies can progressively extend this framework toward full LCOE-based simultaneous optimization by incorporating OSS placement, electrical losses, and cable specifications and voltage levels.

This study targets layout optimization of a 1.2 GW-class OWF consisting of 80 IEA 15 MW reference wind turbines. Following practices observed in overseas OWF projects, a two-stage approach was adopted, in which the overall farm configuration was first determined, and internal layout optimization was subsequently performed. Turbines were assumed to actively respond to wind direction changes through yawing system operation. The baseline layout was defined to simultaneously ensure operational safety and wake mitigation. The minimum inter-turbine spacing was set to 5D, where D = 240 m was the rotor diameter of the IEA 15 MW RWT, resulting in a minimum spacing of 1,200 m. This value is consistent with the minimum turbine spacing recommended for the Empire Wind 1 project, which consists of 54 turbines rated at 15 MW (Empire Wind, 2025), and reflects a practical criterion that considers both navigational and operational safety and wake interference mitigation for large-capacity turbines. In addition, for the grid-based layout scenario discussed in Section 4.2, the longitudinal and lateral spacings were fixed at 10D and 5D, respectively, relative to the prevailing wind direction. The rotation angle of the grid layout was treated as a design variable and optimized to align the layout with both the project boundary and prevailing wind, thereby maximizing site utilization and AEP while maintaining the 5D and 10D spacing rule. Accordingly, the baseline inter-turbine spacing within the OWF follows the principle of a minimum lateral spacing of 5D relative to the prevailing wind direction. Although larger spacings can reduce wake overlap and improve AEP, they also increase the total length of the internal cable network. Therefore, the objective function F_obj explicitly includes an MST-based cable installation cost term to reflect the cost increase associated with wider spacing.

To select an appropriate OWF configuration, the geometries and layouts of major overseas offshore wind farms were reviewed (Owda and Badger, 2022). Representative configurations include rectangular or parallelogram layouts and convex or concave layouts. The former category includes projects such as Horns Rev 1 in Denmark, Amrumbank West in Germany, and East Anglia One in the United Kingdom, while the latter includes Anholt and Horns Rev 2 in Denmark and Butendiek in Germany. Rectangular or parallelogram layouts offer advantages such as minimized wind interference through uniform turbine spacing, adaptability to varying wind directions, ease of installation and maintenance, improved transmission efficiency, simplicity in design and construction, and expandability of the farm. Convex or concave layouts, on the other hand, provide benefits in terms of optimized turbine spacing, maximized energy production considering the prevailing wind direction, and centralized transmission design (Jin et al., 2019; Kim et al., 2024; Malisani et al., 2025; Pryor and Barthelmie, 2024). Recent comparative studies under equivalent conditions have also reported that convex or concave layouts could exhibit higher efficiency under certain wind regimes (Park and Sung, 2024), indicating that configuration selection depended on a combination of wind resource conditions, constraints, and objective functions such as cable cost. Based on this background, rather than fixing the farm geometry in absolute dimensions, this study adopted the Anholt OWF as a reference template because its layout could be easily scaled using coordinate ratios normalized by rotor diameter; it simultaneously incorporated linear alignments characteristic of rectangular grids and concave or convex contours, and its layout data were publicly available and well documented (Penã et al., 2018). An approach that simultaneously optimized a broader boundary shape, such as a rectangular envelope, was also viable, but such a formulation would require explicit consideration of permitting boundaries, seabed topography, exclusion zones, and onshore landing points. These aspects constitute a separate problem definition and are therefore beyond the scope of the present study and considered for future work.

The Anholt OWF is a 400 MW offshore wind farm located near Anholt Island in Denmark, consisting of 111 turbines rated at 3.6 MW, and widely cited as a representative early commercial project owing to the public availability of its configuration and layout data (Penã et al., 2018). In this study, the Anholt layout was first normalized using rotor diameter-based coordinates (x/D, y/D) rather than absolute distances, and then scaled by a factor of two to match the rotor diameter of the IEA 15 MW RWT (D = 240 m). Through this process, the relative spacing between turbines, such as maintaining a minimum of 5D, and the overall layout pattern were preserved, while wake calculations and AEP evaluations were newly performed using the power curve, thrust coefficient C_T, and hub height of the IEA 15 MW turbine. In other words, only the geometric layout pattern of the 3.6 MW farm was referenced, and all performance-related calculations were recomputed from scratch based on the 15 MW turbine specifications used in this study.

Two scenarios were considered for OWF configuration and internal layout candidate selection. In Candidate A, the Anholt layout coordinates were scaled based on rotor diameter ratios and reconstructed by multiplying these ratios by the rotor diameter of the IEA 15 MW turbine (240 m). As shown in Fig. 6(a), the original Anholt layout consists of 111 turbine positions, indicated by red cross markers. To increase layout flexibility and expand the search space for optimization, 20 additional candidate positions were designed by considering vacant slots within the existing pattern, resulting in a total of 131 candidate locations. The baseline layout geometry follows the Anholt arrangement pattern, while the relative positions of turbines are fixed and the entire farm is treated as a rigid body that can be rotated to optimally align with the prevailing wind direction. This preselection procedure involves evaluating an alignment score, defined in Section 4.1.1, which quantitatively measures wake overlap weighted by wind direction frequency. Among various rotation angle candidates, the farm orientation that minimizes the alignment score, corresponding to minimal wake accumulation, is selected. This step preserves the geometric advantages of the Anholt configuration while adapting the layout to the wind characteristics of the target area, and provides a more favorable initial configuration for the subsequent layout optimization using CACO.

Candidate B, shown in Fig. 6(b), fixes the project boundary polygon and automatically generates a rotated rectangular grid with a lateral spacing of 5D and a longitudinal spacing of 10D based on the rotor diameter D = 240 m. The boundary coordinates are first imported, and the centroid of the boundary polygon is used as the pivot point. After translating the coordinate system so that the pivot coincides with the origin, a predefined rotation angle is applied to define local coordinate axes. Grid points are then generated over a sufficiently wide area in the local coordinate system, and multiple combinations of starting offsets along both axes are tested by varying the offset from 0 to 1 rotor diameter at small intervals. The combination that yields the maximum number of grid points within the project boundary is selected. To maximize space utilization, the minimum clearance between turbine locations and the boundary was set to zero, allowing candidate points to lie directly on the boundary. The selected grid points are then transformed back into the global coordinate system and assigned consistent candidate indices based on angular and radial ordering. Through this procedure, internal candidate locations that naturally satisfied the minimum spacing constraints of 5D laterally and 10D longitudinally while aligning well with both the prevailing wind direction and the boundary geometry were constructed. A total of 121 candidate locations were ultimately obtained and used for constraint checking and generation of initial solutions for optimization.

In both scenarios, turbine placement satisfies the constraints of remaining within the project boundary and maintaining a minimum inter-turbine spacing of at least 5D. CACO is then applied to derive the final layout by minimizing the objective function that simultaneously considers wake-affected AEP and MST-based internal cable cost. By contrast, simultaneous optimization that treats the boundary geometry itself as a design variable is a topic for future research.

In this section, layout optimization is performed for two cases: layout candidate A shown in Fig. 8, which represents initial configurations with minimum and maximum wake accumulation, and the boundary-fixed grid configuration shown in Fig. 6(b) as candidate B. In both cases, the OWF consists of 80 IEA 15 MW reference wind turbines, corresponding to a total installed capacity of 1.2 GW. The input data include the preprocessed hub-height wind resource information at 150 m, comprising wind occurrence frequency and wind speed distributions by direction, the power curve and thrust coefficient of the IEA 15 MW RWT, and the project boundary and layout constraints, including placement within the boundary and minimum inter-turbine spacing. The objective function integrates wake-affected AEP and internal cable cost.

CACO was employed as the optimization method. The maximum number of iterations ℓ_max was set to 500, at which point the optimization terminated. The number of newly generated candidate solutions per iteration, defined as the population size m, was set to 2N_WT, corresponding to 160, to ensure sufficient exploration diversity. The archive size k was set to 80, and at each iteration l, candidate solutions were sorted in ascending order of the objective function value f^(ℓ) (S), with the top k solutions retained in the archive. The reference solution selection bias parameter q was set to 0.1, providing a moderate bias toward higher-ranked solutions when forming the rank-based weight distribution in Eq. (13). The search radius contraction coefficient ξ was set to 0.85, scaling the standard deviation used in Gaussian sampling to allow wide exploration in the early stages and accelerated convergence in the later stages of the optimization (Dorigo et al., 2006; Omran and Al-Sharhan, 2019; Socha and Dorigo, 2008).

Randomness was initialized by setting the seed of the MATLAB uniform random number generator. Initial layouts were generated using uniform random sampling within the project boundary, and only solutions satisfying the layout constraints, including boundary inclusion and minimum inter-turbine spacing, were accepted. During the optimization process, solution selection was performed using a roulette-wheel mechanism. Specifically, at each iteration, rank-based weights representing probabilistic pheromones were assigned to the solutions in the k-best archive after sorting by objective function value. These weights were normalized to form a cumulative distribution, and a single uniform random number in the range [0, 1] was used to select the index of the reference solution. This procedure was applied for each newly generated variable or candidate solution, ensuring that higher-quality solutions were more frequently referenced while all solutions retained a non-zero probability of selection, thereby preserving exploration diversity. After merging and sorting, the order of solutions in the archive was randomly permuted once to mitigate path-dependent bias. Gaussian sampling was then performed around the selected reference solution, with the standard deviation controlled by the contraction coefficient ξ to promote broad exploration initially and faster convergence in later iterations.

To assess the robustness of the overall search process, 10 independent runs were conducted, each performing a single-objective optimization independently. The objective function was defined, as in Eq. (12), to minimize the ratio of internal cable installation cost to AEP, directly favoring solutions that reduced the additional unit energy cost attributable to the cable network. Among all evaluated solutions, the solution with the lowest final objective function value f(S) was selected as the optimal layout.

Fig. 9(a) presents the optimization results for layout candidate A with minimum wake accumulation. The first image shows the convergence history of the layout optimization objective function F_obj over iterations for 10 independent runs (runs 1–10) performed with different initial random seeds. In all runs, a rapid decrease in F_obj is observed within the first 1–50 iterations, followed by a characteristic stepwise improvement pattern in which exploratory phases alternate with convergence after approximately 50 iterations. In the later stage of the optimization, between 300 and 500 iterations, the performance differences among runs diminish, and the dispersion of the final objective function values remains limited. Among the runs, run 4 achieved the lowest final F_obj of 2.660 €/MWh and exhibited stable improvements in the mid to late stages. Accordingly, the result of run 4 was selected as the optimal layout solution.

The second image of Fig. 9(a) illustrates the optimized layout obtained from run 4. The resulting AEP is 3,874.93 GWh. Out of the 131 candidate turbine locations, the optimized configuration places 80 turbines primarily along the concave boundaries on both sides of the OWF, with a subset of turbines forming central connections between the two sides. In the figure, red lines represent the internal cable connections based on the MST between turbine nodes, with a total cable length of 114.51 km. The wake shapes shown correspond to the prevailing wind direction, with wake expansion modeled using the wake expansion coefficient α defined in Eq. (6) and illustrated up to a downstream distance of 33.0D, consistent with maxL_D in Eq. (16). This visualization indirectly confirms that the optimized layout tends to place turbines toward the outer edges of the farm to mitigate wake effects.

The third image shows the AEP of each turbine in the optimized layout. The results indicate that turbines located in the left outer row, which first encounter the prevailing wind in the aligned configuration, achieve higher AEP values. Moving downstream toward the interior and then to the opposite outer row, AEP gradually decreases. In particular, when comparing turbines 2 and 3, which are aligned along the prevailing wind direction, the downstream turbine 3 experiences an AEP reduction of approximately 21.3 % relative to the upstream turbine 2 owing to wake effects.

Fig. 9(b) presents the optimization results obtained by applying the same procedure to the initial layout with maximum wake accumulation. The first image shows the convergence behavior of the objective function over 500 iterations, with run 5 yielding the best objective function value of 2.801 €/MWh. The second image shows the final optimized layout, which achieves an AEP of 3,663.37 GWh and a total internal cable length of 114.01 km. The resulting layout exhibits concave boundaries on both sides, similar to the result in Fig. 9(a). This outcome can be interpreted as the result of central candidate locations being largely excluded during optimization because their alignment with the prevailing wind direction leads to increased wake overlap. For example, among turbines aligned approximately with the prevailing wind, turbine 67 produces 35.87 GWh annually, representing a 22.8 % reduction compared with the upstream turbine 64, which produces 46.46 GWh. Despite these losses, the optimized layout converges toward a configuration that preferentially utilizes the lateral edges of the farm to avoid wake losses associated with alignment along the prevailing wind. From a wake minimization perspective, this represents a reasonable optimal solution.

Fig. 10 shows the layout optimization results for layout candidate B, which adopts the fixed OWF geometry shown in Fig. 6(b). In this case, the best convergence was obtained in run 7, with a minimum objective function value of 2.686 €/MWh. The corresponding AEP is 3,739.47 GWh, and the total internal cable length is 111.60 km. In comparison with the results for layout candidate A, this configuration concentrates turbine placement within the boundary-defined candidate locations. Owing to the staggered arrangement of turbines, wake interactions are relatively mitigated, resulting in a higher AEP than that obtained for the maximum wake accumulation case of layout candidate A.

In this study, layout selection is based on minimizing a single optimization objective function F_obj composed of internal cable installation cost, represented by the total internal cable length L_cbl, and AEP. Accordingly, performance comparisons among scenarios are primarily interpreted in terms of the relative magnitude of F_obj. As shown in the comparison in Table 4, layout A with minimum wake accumulation achieved the lowest F_obj, despite a somewhat longer internal cable length, because it delivered a substantially higher AEP of 3,874.93 GWh. By contrast, layout A initialized from the maximum wake accumulation configuration exhibited a lower AEP of 3,663.37 GWh, even though its internal cable length was comparable. This indicates that the disadvantage of the initial configuration with severe wake accumulation, as identified by the alignment score, cannot be fully offset through subsequent layout optimization. Layout B reduced the cost numerator through a shorter L_cbl, thereby improving F_obj, but its relatively lower AEP resulted in an intermediate F_obj value. Nevertheless, layout B achieved an AEP of 3,739.47 GWh and could be regarded as a practically attractive compromise solution in situations where installation constraints, routing simplicity, or CAPEX limitations were emphasized. Relative to layout B, layout A with minimum wake accumulation achieved an AEP improvement of 3.62 %.

L_cbl in this study serves as a cost proxy derived by multiplying the MST-based total internal cable length by a unit coefficient, Cost_clv×R_inst in Eq. (9), under simplifying assumptions that exclude OSS number and location, electrical losses, and cable specification differences. As such, L_cbl is not an independent optimization objective but rather a component of F_obj. Therefore, within this single-objective framework, the final decision metric is F_obj, while AEP and L_cbl are interpreted as diagnostic indicators used to analyze the physical and economic tendencies of the results. In future studies that incorporate detailed electrical network models, including OSS placement, voltage drop, resistive losses, and cable specifications and voltage levels, the realism of the cost term will be enhanced, further strengthening both the absolute and relative interpretability of F_obj.

From an operations and maintenance (O&M) perspective, layout A with minimum wake accumulation predominantly features turbines aligned along the outer edges of the OWF. This configuration simplifies access and egress routes for crew transfer vessels (CTVs) and service operation vessels (SOVs), making work distances more predictable and facilitating annual maintenance planning. In addition, reduced wake accumulation is expected to lower turbulence intensity, thereby mitigating fatigue damage to blades and towers and potentially extending component replacement intervals over the long term. In contrast, layout candidate B benefits from the regularity of turbine spacing, which allows consistent minimum clearances between blades, vessels, and equipment. This regularity supports standardization of components, personnel deployment, and vessel operations, leading to higher repetitive efficiency in routine O&M activities (Sickler et al., 2023).

Consequently, if long-term operational reliability, higher energy yield, and reduced fatigue loading are prioritized, layout A with minimum wake accumulation is advantageous. Conversely, if simplification of cabling and associated CAPEX constraints are of greater importance, layout candidate B is relatively more favorable. In practical projects, it is therefore reasonable to select the final layout by balancing annual energy production, internal cable installation cost, and operational considerations, including workability and safety, while accounting for site-specific wind resources, navigational constraints, grid limitations, and maintenance strategies.