Pith. sign in

REVIEW 3 major objections 5 minor 38 references

Offshore wind farm layout optimization using mathematical programming techniques

T0 review · 3 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A two-stage optimizer—random feasible starts plus gradient-based nonlinear programming—keeps turbine coordinates continuous and finds a KKT-optimal Alpha Ventus layout with 3.758% higher expected annual energy than the installed grid.

desk verdict The multistart NLP approach is a reasonable idea, but the wake-deficit equation as printed has the wrong sign, so the headline 3.758% AEP gain is not credible as stated. read the letter →

arxiv 2502.00476 v1 pith:EECBHYLA submitted 2025-02-01 cs.CE

Beatriz Perez , Roberto Minguez , Raul Guanche This is my paper · ORCID
classification cs.CE
keywords layoutoptimizationoffshorewindfarmwakeeffectheuristicnonlinearprogrammingKarush-Kuhn-TuckerconditionsannualenergyproductionAlphaVentus
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that offshore wind farm layout optimization need not rely on heuristic searches over a discretized grid: a two-step procedure—random feasible initial layouts generated by a spreading heuristic, followed by gradient-based nonlinear programming—can locate high-quality continuous turbine positions that satisfy the Karush-Kuhn-Tucker optimality conditions. Applied to the 12-turbine Alpha Ventus farm in the North Sea, the procedure raises expected annual energy production from 293.274 GWh to 304.809 GWh, a 3.758% gain over the real grid layout, while reducing modeled wake losses from 4.440% to 0.682%. If the wake model used in the objective is trustworthy, the result shows that existing farms could gain roughly one million euros per year simply by rearranging turbine positions, and that the optimization is robust to rotations of the wind rose.

What carries the argument

The load-bearing mechanism is the two-stage optimizer. Stage one draws uniformly random points in a reference square, maps them into the farm's quadrilateral boundary with bilinear shape functions, and then solves a small maximization of Delaunay triangle areas to spread the turbines across the whole site while keeping constraints (4) and (5) feasible; this supplies diverse starting points that explore nonconvex subregions. Stage two runs nonlinear programming solvers (KNITRO/ktrlink to find a local maximum quickly, then fmincon to polish it) on the objective (7), the expected annual energy production computed from 12 directional sectors, Weibull wind fits, the power and thrust curves, and the cumulative wake deficit (10). The wake deficit itself is the N.O. Jensen model with partial rotor-area intersection, Eq. (9), and a linear constraint set of minimum-distance and inside-quadrilateral inequalities. Because coordinates remain continuous decision variables, the feasible region is not reduced to a grid.

What would settle it

Recompute both the existing and optimized Alpha Ventus layouts with the standard Jensen deficit term $(1-\sqrt{1-C_t})$ and with a decay factor $k$ calibrated from measured wind data, or compare the model's predicted AEP for the as-built grid against actual SCADA production; if the corrected model shows the optimized layout gaining less than 3.758%—or losing—the central claim falls.

Watch

Extended reading notes

Core claim

On its own terms, the paper claims that there exists a layout of the 12 Alpha Ventus turbines, inside the original farm boundary and respecting a four-rotor-diameter minimum spacing, whose expected annual energy production is 304.809 GWh under the paper's N.O. Jensen wake model, versus 293.274 GWh for the as-built grid layout. The claimed 3.758% improvement is achieved not by moving to a bigger area or another turbine model, but by re-positioning the same NREL 5 MW machines continuously within the existing site; the optimized layout cuts per-sector wake losses almost to zero for the most productive wind directions. The paper further claims that the solution is a pseudo-global optimum in the sense that repeated random restarts followed by local nonlinear programming converge to it, and that it satisfies the Karush-Kuhn-Tucker conditions—something heuristic-only methods do not guarantee.

Load-bearing premise

The entire comparison rests on the N.O. Jensen wake model, as printed in Eqs. (1) and (9), correctly predicting how much each turbine slows the wind reaching the others; if that velocity-deficit formula or its decay factor is wrong for Alpha Ventus, the optimized layout and the 3.758% gain are artifacts of the model.

Editorial extensions

If this is right

  • Because turbine coordinates stay continuous and the final point satisfies KKT conditions, the same framework can add extra constraints or objective terms—bathymetry, foundations, cable routing—without changing the solution flow.
  • At 12 turbines on Alpha Ventus, expected AEP rises from 293.274 to 304.809 GWh and modeled wake loss falls from 4.440% to 0.682%, worth about €0.99 million per year at the stated prices.
  • Rotating the wind rose by 90°, 180°, or 270° still leaves the optimized layout outperforming the actual grid, so the gain is not an artifact of one particular directional distribution.
  • As turbine count per area grows, optimization gains shrink and optimal layouts approach the grid layout; with 23 turbines the constraints become infeasible, so capacity is limited by spacing rather than by wake tuning.
  • The optimized 12-turbine layout reaches 99.25% efficiency versus 95.51% for the grid, and the method can also refine layouts produced by other heuristics.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper does not test it, but the same random-feasible-start plus KKT local-search recipe should transfer to other continuous nonconvex design problems, such as cable routing or substation siting, whenever a cheap feasible-point generator exists.
  • The paper's observation that 23 turbines are infeasible implies that for a fixed area there is a hard density ceiling; an economic optimum will usually sit below that ceiling, so treating turbine count as a decision variable, as Section 5.1 begins to do, is the natural next step.
  • Because the no-wake ceiling is 306.9 GWh, the optimized layout already captures nearly all of the modeled resource; further gains on this site would require changing the turbine type, adding controls, or enlarging the allowed footprint rather than more layout tuning.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper formulates the offshore wind farm layout problem as a continuous nonlinear program: maximize expected annual energy production (AEP) subject to minimum-spacing and area constraints, using the N.O. Jensen wake model with Weibull wind-direction sectors. It solves the problem with a multistart heuristic (uniform random points, Delaunay triangulation spreading, then local NLP) using KNITRO and fmincon. The method is applied to Alpha Ventus with 12 NREL 5MW turbines. The authors report an optimal AEP of 304.809 GWh versus 293.274 GWh for the actual layout (3.758% increase), a reduction in modeled wake loss from 4.44% to 0.682%, and about EUR 0.99M/year profit gain, along with sensitivity, capacity-efficiency, and computational-time analyses.

Significance. The proposed sequential random-restart strategy is a sensible and potentially useful way to combine heuristic global exploration with local NLP refinement for continuous wind-farm layout problems, and the paper is explicit about many of its assumptions. The rotated-wind-rose sensitivity analysis (Table 3) and the saturation study (Section 5.2) are useful extensions. If the numerical results were reproducible, the claimed continuous (non-gridded) optimization with KKT-satisfying solutions and easy parallelization would be a contribution to the layout-optimization literature. However, the central quantitative claim is not currently reliable: the printed wake-deficit formula is physically inconsistent and the reported AEP values cannot be reproduced from it, and the smoothness assumptions behind the KKT claim are not addressed.

major comments (3)
  1. [Section 2, Eq. (1); Section 3.4, Eq. (9)] The wake-deficit equations use the wrong sign in the numerator. The standard N.O. Jensen/Katic model is Dvij = (1 - sqrt(1 - Ctj))/(1 + k*dij/R)^2, but Eqs. (1) and (9) print (1 + sqrt(1 - Ctj)) in the numerator. With the plus sign, the deficit at zero distance exceeds unity (for Ct = 0.8, Dv = 1.447), so Eq. (11) can produce negative wind speeds. For a typical downstream distance of 4D (d/R = 8) and k = 0.038, a fully overlapping wake would have a deficit of about 0.85, which is irreconcilable with the wake losses of at most 1.5% per sector in Table 1. Either the implementation uses the correct minus sign and the paper misprints the model, or the code implements a different model; in either case the reported AEP values and the 3.758% improvement cannot be reproduced from the equations as written. The authors must correct the formula and rerun (or verify) all reported optimizations.
  2. [Section 3.4 and Section 4] The objective function is not smooth, so the claim that the final solution satisfies KKT conditions is not established. For each directional sector, the algorithm sorts turbines by their rotated y' coordinate and defines the upstream set Omega_i as {1,...,i-1}; this set changes discontinuously when two turbines cross in y' as x varies. The area intersection Aij is also only piecewise smooth. The paper does not provide a differentiable reformulation, a smoothing approximation, or a generalized-gradient treatment. Since fmincon and ktrlink are gradient-based NLP solvers, the KKT statement in Section 4 (item 5) and the 'pseudo-global optimum' characterization in Table 2 require additional justification.
  3. [Section 5, Tables 1-2] The claimed improvement is an in-sample value of the same AEP objective used for optimization, and no comparison with measured Alpha Ventus production or independent wake-model validation is provided. The wake decay coefficient k is derived from an assumed roughness length z0 = 0.0002 m with no calibration (Section 2, Eq. (2); Section 5). Without at least one out-of-sample check—measured production, SCADA data, or a second wake model—the 3.758% economic gain cannot be distinguished from an artifact of the chosen model. At minimum, the authors should report the optimized turbine coordinates and the no-wake baseline so readers can recompute the AEP with another model.
minor comments (5)
  1. [Abstract vs. Section 5] The abstract reports a 3.52% increase while the body and conclusions report 3.758% (Section 5, observation 5); these should be reconciled.
  2. [Section 4.1, Eq. (13)] In Eq. (13), the y-coordinate transformation uses xL_l on the right-hand side; it should presumably be yL_l.
  3. [Section 3.3] Section 3.3 describes constraints (4) and (5) as linear, but Eq. (4) is a quadratic inequality in (xi, yi); the problem is a nonlinearly constrained NLP, not a linearly constrained one.
  4. [Section 5, Table 3] The 'Random' row in Table 3 is not defined in the text; it should state what wind rose was used and how the random case was constructed.
  5. [Section 5.1] The reported efficiency values (95.51% and 99.25%) differ slightly from the AEP ratios in Table 2 (293.274/306.9 = 95.56% and 304.809/306.9 = 99.32%); the rounding should be explained or corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the reported AEP gain is the value of the same explicit objective used for optimization, not a fitted parameter or independent prediction; the few self-citations only tune numerical discretization settings.

full rationale

The paper's derivation chain is self-contained as an optimization study: it defines the objective AEP in Eq. (7) using the wake model in Eq. (9), maximizes it over turbine positions subject to constraints (4) and (5), and then reports AEP(x*) = 304.809 GWh for the optimized layout. The 3.758% improvement over the existing layout is therefore an in-sample property of the optimized layout under the same model, not a separate 'prediction' that is fitted from data or renamed from an input. The wind data, turbine curves, roughness length, and wake-model constants are all fixed before optimization; no fitted parameter is later relabeled as a predicted result. The only self-citations are to the first author's thesis [29] for numerical choices (12 wind sectors and trapezoidal quadrature step), and these tune discretization settings rather than carrying the central claim; they are also said to be in accordance with external reference [17]. The apparent sign issue in Eq. (9) is a correctness/validation concern, not a circularity, because the same formula is used consistently as both the objective and the reporting metric. There is no imported uniqueness theorem and no known empirical result merely renamed as a contribution.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The result rests on standard engineering models and data assumptions rather than on newly invented entities. The main free parameters are the site-roughness/decay factor, the per-sector Weibull fits, numerical discretization choices, and the unstated number of random restarts. No new physical objects are introduced.

free parameters (4)
  • Weibull sector parameters (lambda_s, delta_s) = not reported in paper
    For each of 12 direction sectors, shape and scale are fitted from SeaWind hourly reanalysis (1989-2009); the AEP objective depends on these fits, but the fitted values and goodness-of-fit statistics are not given.
  • Wake decay factor k via surface roughness z0 = z0 = 0.0002 m; k ~ 0.038 from Eq. (2)
    The offshore roughness length is taken from literature rather than measured at Alpha Ventus; it controls wake expansion and all deficit calculations, and the result is sensitive to it.
  • Numerical discretization (ns, delta_v) = ns = 12, delta_v = 0.1 m/s
    The number of direction sectors and the trapezoidal step are chosen from the author's thesis [29] with claimed error bounds below 0.5% and 0.01%, respectively; these are algorithmic hyperparameters, not site data.
  • Number of random restarts M = unspecified
    The quality of the pseudo-global optimum and the run time both depend on M, the number of heuristic initial solutions tried, but the paper never states what value of M was used for the reported results.
assumptions (5)
  • domain assumption N.O. Jensen wake model with Katic quadratic superposition predicts turbine velocity deficits (Eqs. 1, 9, 10).
    Adopted on the recommendation of [17] without site-specific calibration; as printed, the deficit formula appears to have a sign error relative to the standard Jensen form.
  • domain assumption Wind speed conditional on direction follows a Weibull distribution in each 30-degree sector (Eq. 6).
    Standard wind-energy modeling assumption, used to compute AEP in Eq. (7); no goodness-of-fit tests are reported.
  • domain assumption SeaWind reanalysis at 10 m height over 1989-2009 represents the long-term wind climate at Alpha Ventus.
    Section 5 uses hourly reanalysis on a 15 km grid and a logarithmic profile; no comparison with in-situ measurements from Alpha Ventus is shown.
  • domain assumption All 12 turbines are identical NREL 5 MW units with the given power and thrust curves.
    Section 5 states this simplification, but the real Alpha Ventus uses Multibrid M5000 and REpower 5M turbines, so the 'actual configuration' is a surrogate rather than the real farm.
  • standard math Nonlinear solvers ktrlink and fmincon converge to local maxima satisfying KKT conditions.
    The paper relies on the numerical behavior of these solvers to claim that final solutions hold KKT optimality; this is not formally verified here.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Offshore wind farm layout optimization using mathematical programming techniques." pith.science (2026). https://pith.science/paper/EECBHYLA

@misc{pith2026250200476,
  author       = {Pith},
  title        = {Pith review of: Offshore wind farm layout optimization using mathematical programming techniques},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EECBHYLA}},
  note         = {Machine review of arXiv:2502.00476}
}
read the original abstract

Offshore wind power is a renewable energy of growing relevance in current electric energy systems, presenting favorable wind conditions in comparison with the sites on land. However, the higher energy yield has to compensate the increment in installation and maintenance costs, thus the importance of optimizing resources. One relevant aspect to increase profitability is the wind farm layout. The aim of this paper is to propose a new method to maximize the expected power production of offshore wind farms by setting the appropriate layout, i.e. minimizing the wake effects. The method uses a sequential procedure for global optimization consisting of two steps: i) an heuristic method to set an initial random layout configuration, and ii) the use of nonlinear mathematical programming techniques for local optimization, which use the random layout as an initial solution. The method takes full advantage of the most up-to-date mathematical programming techniques while performing a global optimization approach, which can be easily parallelized. The performance of the proposed procedure is tested using the German offshore wind farm Alpha Ventus, located in the North Sea, yielding an increment of expected annual power production of 3.52% with respect to the actual configuration. According to current electricity prices in Germany, this constitutes an expected profit increment of almost 1 M per year.

Figures

Figures reproduced from arXiv: 2502.00476 by the authors.

Figure 1
Figure 1. Flow diagram: calculating the Annual Energy Production (A [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Renumbering of the turbines after the base change. [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Different possibilities for cross sectional intersection pro [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Initial and optimal Delaunay triangulations. [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]
Figure 5
Figure 5. Figure 5: Graphical interpretation of the combined heuristic-grad [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]
Figure 6
Figure 6. Figure 6: Characteristic curves of 5MW NREL Turbine: a) Power out [PITH_FULL_IMAGE:figures/full_fig_p019_6.png]
Figure 7
Figure 7. Figure 7: Wind rose for the Alpha Ventus location. [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]
Figure 8
Figure 8. Figure 8: Evolution of the wakes for a 15 m/s wind in sector 3 (75 [PITH_FULL_IMAGE:figures/full_fig_p022_8.png]
Figure 9
Figure 9. Figure 9: Evolution of the wakes for a 15 m/s wind in sector 2 (45 [PITH_FULL_IMAGE:figures/full_fig_p022_9.png]
Figure 10
Figure 10. Figure 10: Efficiency vs. installed power capacity per km [PITH_FULL_IMAGE:figures/full_fig_p024_10.png]
Figure 11
Figure 11. Figure 11: Combined box-plots: AEP and root mean square distance [PITH_FULL_IMAGE:figures/full_fig_p025_11.png]
Figure 12
Figure 12. Figure 12: Running time as a function of turbines. It is important to note that the above experimental time values for the different number of turbines were measured during the development of the program, so not all the simulations began under the exact same conditions. Therefor…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

38 extracted references · 36 canonical work pages

  1. [2]

    Mosetti, C

    G. Mosetti, C. Poloni, B. Diviacco, Optimization of wind turbine po- sitioning in large wind farms by means of a genetic algorithm, Journal 27 of Wind Engineering and Industrial Aerodynamics 51 (1) (1994) 105 –

    work page 1994

  2. [3]

    Ozturk, B

    U. Ozturk, B. Norman, Heuristic methods for wind energy conve rsion system positioning, Electric Power Systems Research 70 (3) (2004 ) 179 – 185. doi:10.1016/j.epsr.2003.12.006

    work page doi:10.1016/j.epsr.2003.12.006 2004

  3. [4]

    S. A. Grady, M. Y. Hussaini, M. M. Abdullah, Placement of wind tur- bines using genetic algorithms, Renewable Energy 30 (2) (2005) 259 –

    work page 2005

  4. [5]

    C. N. Elkinton, J. F. Manwell, J. G. McGowan, Offshore wind farm layout optimization (owflo), project: Preliminary results, Tech. re p., University of Massachusetts (2006)

    work page 2006

  5. [6]

    L. W. M. M. Rademakers, H. Braam, M. B. Zaaijer, G. J. W. Van Bu ssel, Assessment and optimization of operation and maintenance of offsh ore wind turbines, in: Proceedings of the European Wind Energy Confer - ence (EWEC), Madrid, Spain, 2003

    work page 2003

  6. [8]

    Donovan, H

    S. Donovan, H. D. Sherali, J. C. Smith, Wind farm optimization, Tec h. rep., University of Auckland, Engineering science department (200 5)

    work page

  7. [9]

    Kusiak, Z

    A. Kusiak, Z. Song, Design of wind farm layout for maximum wind energy capture, Renewable Energy 35 (3) (2010) 685–694. doi:10.1016/j.renene.2009.08.019

    work page doi:10.1016/j.renene.2009.08.019 2010

  8. [10]

    Chowdhury, J

    S. Chowdhury, J. Zhang, A. Messac, L. Castillo, Unrestricted wind farm layout optimization (UWFLO): Investigating key factors influe nc- ing the maximum power generation, Renewable Energy 38 (2012) 16– 30. doi:10.1016/j.renene.2011.06.033

    doi:10.1016/j.renene.2011.06.033 2012

Show all 38 references
  1. [11]

    C. N. Elkinton, J. F. Manwell, J. G. McGowan, Algorithms for offsh ore wind farm layout optimization, Wind Engineering 32 (1) (2008) 67–84. doi:10.1260/030952408784305877. 28

    2008 doi

  2. [12]

    Serrano, A

    J. Serrano, A. G. Gonz´ alez, J. Castro, J. Riquelme, M. Bur- gos, Optimization of wind farm turbines layout using an evo- lutive algorithm, Renewable Energy 35 (2010) 1671–1681. doi:10.1016/j.renene.2010.01.010

    2010 doi

  3. [13]

    Saavedra-Moreno, S

    B. Saavedra-Moreno, S. Salcedo-Sanz, A. Paniagua-Tineo, A . Portilla- Figueras, Seeding evolutionary algorithms with heuristics for optima l wind turbines positioning in wind farms, Renewable Energy 36 (2011) 2338–2844. doi:10.1016/j.renene.2011.04.018

    2011 doi

  4. [14]

    Ero˘ glu, Y

    Y. Ero˘ glu, Y. Ulusam, Design of wind farm layout using ant colony algorithm, Renewable Energy 44 (2012) 53–62. doi:10.1016/j.renene.2011.12.013

    2012 doi

  5. [15]

    G. N. Vanderplaats, Numerical Optimization Techniques for Eng ineering Design, McGraw-Hill, New York, 1984

    1984

  6. [16]

    M. S. Bazaraa, H. D. Sherali, C. M. Shetty, Nonlinear Programm ing. Theory and Algorithms, 2nd Edition, John Wiley & Sons, New York, 1993

    1993

  7. [17]

    D. R. Vanluvanee, Investigation of observed and modelled wake effects at horns rev using windpro, Report, Technical University of Denma rk, MEK Department, Fluid Mechanics Section, Denmark (2006)

    2006

  8. [18]

    Sorensen, M

    T. Sorensen, M. L. Thogersen, P. Nielsen, Adapting and calibra tion of existing wake models to meet the conditions inside offshore wind farms , Report, EMD International A/S, Denmark (2008)

    2008

  9. [19]

    URL http://www.emd.dk/

    Windpro, EMD International A/S (2011). URL http://www.emd.dk/

    2011

  10. [20]

    J. R. Douwe, Validation of wind turbine wake models. using wind far m data and wind tunnel measurements, Master’s thesis, Delft Univer sity of Technology. Faculty of Aerospace Engineering, Netherlands (2 007)

  11. [21]

    Wind Energy Department (2011)

    Wasp wind atlas analysis and application program, Risø National La b- oratory. Wind Energy Department (2011). URL http://www.wasp.dk/ 29

    2011

  12. [22]

    M. L. Thogersen, Wind turbine wake modelling and wake generate d turbulence, Report, EMD International A/S, Denmark (2011)

    2011

  13. [23]

    N. O. Jensen, A note on wind generator interaction, Report, R iso Na- tional Laboratory, Roskilde, Denmark (1984)

    1984

  14. [24]

    Katic, J

    I. Katic, J. Hostrucp, N. O. Jensen, A simple model for cluster ef- ficiecy, European wind energy association conference and exhibitio n, Rome, 1986

    1986

  15. [25]

    Hassan, P

    G. Hassan, P. Ltd., GH WindFarmer Theroy Manual (2004)

    2004

  16. [26]

    Castillo, A

    E. Castillo, A. J. Conejo, P. Pedregal, R. Garc ´ ıa, N. Alguacil, Bu ild- ing and Solving Mathematical Programming Models in Engineering and Science, John Wiley & Sons Inc., New York, 2001, pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs a nd Tracts

    2001

  17. [27]

    A. J. Conejo, E. Castillo, R. M ´ ınguez, R. Garc ´ ıa-Bertrand, Decomposi- tion techniques in mathematical programming. Engineering and scien ce applications, Springer-Verlag Berlin Heidelberg, New York, 2006

    2006

  18. [28]

    Men´ endez, A

    M. Men´ endez, A. Tom´ as, P. Camus, M. Garc ´ ıa-D ´ ıez, L. Fita , J. Fern´ andez, F. J. M´ endez, I. J. Losada, A methodology to ev aluate regional-scale offshore wind energy resources, in: OCEANS, 2011 I EEE - Spain, 2011, pp. 1–8. doi:10.1109/Oceans-Spain.2011.6003595

    2011

  19. [29]

    P´ erez, Estrategia de optimizaci´ on del layout de parques e ´ olicos off- shore, Master’s thesis, Environmental Hydraulics Institute, Can tabria University, Santander (2012)

    B. P´ erez, Estrategia de optimizaci´ on del layout de parques e ´ olicos off- shore, Master’s thesis, Environmental Hydraulics Institute, Can tabria University, Santander (2012)

    2012

  20. [30]

    B. A. Murtagh, M. A. Saunders, MINOS 5.5 User’s Guide, Report SOL 83-20R SOL 83-20R, Department of Operations Research, Stanf ord Uni- versity, Stanford, California (1998)

    1998

  21. [31]

    Drud, CONOPT: A system for large scale nonlinear optimization , Reference manual for CONOPT subroutine library, ARKI Consulting and Development A/S, Bagsvaerd, Denmark (1996)

    A. Drud, CONOPT: A system for large scale nonlinear optimization , Reference manual for CONOPT subroutine library, ARKI Consulting and Development A/S, Bagsvaerd, Denmark (1996)

    1996

  22. [32]

    Brooke, D

    A. Brooke, D. Kendrick, A. Meeraus, R. Raman, GAMS: A user’s guide, GAMS Development Corporation, Washington, 1998. 30

    1998

  23. [33]

    T. F. Coleman, Y. Li, On the convergence of reflective newton m ethods for large-scale nonlinear minimization subject to bounds, Mathemat ical Programming 67 (2) (1994) 189–224

    1994

  24. [34]

    T. F. Coleman, Y. Li, An interior, trust region approach for non lin- ear minimization subject to bounds, SIAM Journal on Optimization 6 (1996) 418–445

    1996

  25. [35]

    R. H. Byrd, J. Nocedal, R. A. Waltz, KNITRO: An integrated pac kage for nonlinear optimization, in: G. di Pillo, M. Roma (Eds.), Large-Scale Nonlinear Optimization, 2006, pp. 35–59

    2006

  26. [36]

    C. B. Barber, D. P. Dobkin, H. T. Huhdanpaa, The quickhull algo rithm for convex hulls, ACM Transactions on Mathematical Software 22 ( 4) (1996) 469–483

    1996

  27. [37]

    URL http://www.alpha-ventus.de,

    Alpha ventus (2011). URL http://www.alpha-ventus.de,

    2011

  28. [38]

    Jonkman, S

    J. Jonkman, S. Butterfield, W. Musial, G. Scott, Definition of a 5 -mw reference wind turbine for offshore system development, Report , Na- tional Renewable Energy Laboratory (2009). 31

    2009

  29. [116]

    doi:10.1016/0167-6105(94)90080-9

    doi

  30. [270]

    doi:10.1016/j.renene.2004.05.007

    2004 doi

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.