Grid-based wind-farm layout optimization (compact QKP seed)

A citation-backed binary wind-farm layout benchmark that packages the Quan and Kim grid-based quadratic-knapsack formulation as a compact fixed-count seed instance.

See Optimization Problem Catalog for the optimization family index.

Quick Facts

Field	Value
Problem ID	wind_farm_grid_qkp_power_max
Problem Family	optimization
Implementation	design_research_problems.problems.optimization._wind_farm_layout:WindFarmLayoutOptimizationProblem
Capabilities	baseline-solver, bounded-variables, citation-backed, equality-constraint, statement-markdown
Study Suitability	none
Tags	optimization, binary, layout, wind-farm, quadratic-knapsack, citation-backed

Taxonomy

Formulation

binary_optimization

Convexity

not_guaranteed

Design Variable Type

discrete

Is Dynamic

no

Orientation

engineering-practical

Feasibility Ratio Hint

0.1

Objective Mode

single

Constraint Nature

hard

Bounds Summary

one binary variable per grid node on a compact 4 x 4 fixed-count wind-farm layout seed

Tags

optimization, binary, layout, wind-farm, quadratic-knapsack, citation-backed

Statement

This packaged optimization problem is a compact, citation-backed seed derived from the grid-based wind-farm layout formulation reported by Quan and Kim (2016). The original paper studies large mixed-integer and quadratic-knapsack instances. This in-package benchmark keeps the same binary layout structure and greedy baseline spirit, but fixes a much smaller 4 x 4 square grid so the problem is fully specified and reproducible in a lightweight Python package.

Each binary design variable decides whether one turbine is placed on one grid node. The packaged instance uses a deterministic directional wake-loss proxy to convert the paper’s pairwise interaction idea into a compact expected-power objective. Exactly four turbines must be placed, and any pair of turbines that violates the minimum spacing threshold is infeasible.

Problem Shape

Field	Value
Design Variable Count	16
Bound Summary	one binary variable per grid node on a compact 4 x 4 fixed-count wind-farm layout seed
Total Constraint Count	25
Equality Constraint Count	1
Inequality Constraint Count	24

Variable Bounds

Variable	Lower Bound	Upper Bound
x[0]	0	1
x[1]	0	1
x[2]	0	1
x[3]	0	1
x[4]	0	1
x[5]	0	1
x[6]	0	1
x[7]	0	1
x[8]	0	1
x[9]	0	1
x[10]	0	1
x[11]	0	1
x[12]	0	1
x[13]	0	1
x[14]	0	1
x[15]	0	1

Manifest Parameters

Key	Value
base_power_mw	1.5
direction_profile_name	east_skewed_seed
edge_length_m	960
grid_cols	4
grid_rows	4
minimum_spacing_m	450
pairwise_loss_scale_mw	0.42
rotor_diameter_m	80
turbine_count	4
wake_expansion_coefficient	0.075

Library Interface

• generate_initial_solution(seed=None)

• objective(x)

• evaluate(x)

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

Sources

Key	Summary
quan2016windfarm	Quan and Kim (2016).

Raw Citation Records

Quan, N., and Kim, H. (2016). A Tight Upper Bound for Grid-Based Wind Farm Layout Optimization. Proceedings of the ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2016-59712.