Unrestricted wind-farm layout optimization (compact continuous seed)

A citation-backed continuous wind-farm layout benchmark derived from Quan and Kim’s unrestricted MILP formulation, packaged as a compact seven-turbine seed instance.

See Optimization Problem Catalog for the optimization family index.

Quick Facts

Field	Value
Problem ID	wind_farm_unrestricted_deficit_min
Problem Family	optimization
Implementation	design_research_problems.problems.optimization._wind_farm_unrestricted:UnrestrictedWindFarmLayoutOptimizationProblem
Capabilities	baseline-solver, bounded-variables, citation-backed, statement-markdown
Study Suitability	none
Tags	optimization, continuous, layout, wind-farm, milp-inspired, citation-backed

Taxonomy

Formulation

continuous_optimization

Convexity

not_guaranteed

Design Variable Type

continuous

Is Dynamic

no

Orientation

engineering-practical

Feasibility Ratio Hint

0.02

Objective Mode

single

Constraint Nature

hard

Bounds Summary

fourteen continuous variables representing seven planar turbine coordinates inside a 650 m square field

Tags

optimization, continuous, layout, wind-farm, milp-inspired, citation-backed

Statement

This packaged optimization problem is a compact, citation-backed seed derived from Quan and Kim’s unrestricted wind-farm layout formulation (2015). The original paper introduces a mixed-integer linear programming model for placing wind turbines continuously inside a rectangular field while minimizing the worst wake-interference penalty across several wind directions.

The in-package benchmark preserves the paper’s seven-turbine 650 m x 650 m case data, the directional wind table, and the paper’s Manhattan-style exclusion-zone constraint. To keep the benchmark lightweight and reproducible, the package evaluates layouts with the paper’s exact wake-deficit curve instead of reconstructing the full MILP linearization and branch-and-bound workflow. Each design variable is one turbine coordinate, so the optimizer searches over continuous turbine positions rather than a fixed candidate grid.

Problem Shape

Field	Value
Design Variable Count	14
Bound Summary	fourteen continuous variables representing seven planar turbine coordinates inside a 650 m square field
Total Constraint Count	21
Equality Constraint Count	0
Inequality Constraint Count	21

Variable Bounds

Variable	Lower Bound	Upper Bound
x[0]	0	650
x[1]	0	650
x[2]	0	650
x[3]	0	650
x[4]	0	650
x[5]	0	650
x[6]	0	650
x[7]	0	650
x[8]	0	650
x[9]	0	650
x[10]	0	650
x[11]	0	650
x[12]	0	650
x[13]	0	650

Manifest Parameters

Key	Value
direction_profile_name	quan_kim_2015_reduced
edge_length_m	650
minimum_l1_spacing_m	350
rotor_diameter_m	77
thrust_coefficient	0.8
turbine_count	7
wake_expansion_coefficient	0.075
wake_membership_alpha	1

Library Interface

• generate_initial_solution(seed=None)

• objective(x)

• evaluate(x)

• solve(initial_solution=None, seed=None, maxiter=200)

Sources

Key	Summary
quan2015unrestricted	Kim and Quan (2015).

Raw Citation Records

Kim, H., and Quan, N. (2015). A Mixed Integer Linear Programming Formulation for Unrestricted Wind Farm Layout Optimization. Proceedings of the ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2015-46876.