Artelys Knitro Modeling Examples
Nonlinear optimization models solved with Artelys Knitro, each built step by step as a standalone example in several interfaces:
AC Optimal Power Flow
Dispatch generators over a transmission network at minimum cost while respecting the nonlinear AC power-flow physics, voltage limits, and line ratings.
Hydro Unit Commitment
Schedule the water discharge of several turbines sharing one reservoir to maximize the revenue from selling generated hydropower, a non-convex MIQCQP.
Water Network Design
Pick commercial pipe diameters for a fixed water-network layout, at the lowest cost that still meets every demand and the nonlinear Hazen-Williams head loss.
Wastewater Treatment Network
Route wastewater through splitters, mixers and treatment units so that the least possible flow goes through costly treatment and the discharge still meets its quality limits.
Polygon Clustering
Arrange two polygons without overlap inside the smallest possible bounding rectangle, using convex decomposition to express the non-overlap constraints.
Single-Row Facility Layout
Order facilities of given lengths along a line to minimize the weighted traffic between them, a nonconvex binary quadratic program over the pairwise ordering.
k-Means Clustering
Partition observations into k clusters by minimizing the within-cluster squared distance, a nonconvex model that, unlike the classical algorithm, also accepts must-link, cannot-link and cluster-size constraints.
Pivot Irrigators
Place and size non-overlapping center-pivot irrigation machines across a field to maximize the net present value of the investment.
Largest Diameter
Find the two points of a closed shape that lie furthest apart, when the shape is a black box the solver can only evaluate.
Aircraft Deconfliction
Adjust aircraft headings and speeds by the smallest amount that keeps every pair separated, a nonconvex problem over continuous trajectories.
Portfolio Optimization
Allocate capital across assets to minimize risk at a target return, the convex Markowitz model, then extend it with diversification, cardinality and transaction-cost constraints.