Flowty

Flowty is a network optimization solver for multi-commodity flow (MCF), resource-constrained MCF (RCMCF), fixed-charge MCF (FCMCF), vehicle routing (VRPTW), and related problems. It uses column generation with branch-and-bound, where subproblems are resource-constrained shortest path problems solved over user-defined graphs. Written in C++ with a Python interface.

Installation

System dependencies (Ubuntu/Debian):

sudo apt-get install libopenblas0 libtbb12

Then install the package:

pip install flowty

Quick Start

Multi-Commodity Flow

Use McfModel for MCF problems:

import flowty

model = flowty.McfModel(flowty.McfModel.Type.Path)

# Network with 4 edges: sources, targets, costs, capacities
model.addEdges([0, 1, 0, 2], [1, 3, 2, 3], [1.0, 1.0, 1.0, 2.0], [10.0, 10.0, 10.0, 10.0])

# Two commodities: origins, destinations, demands
model.addCommodities([0, 0], [1, 3], [3.0, 2.0])

status = model.solve()
solution = model.getSolution()
print(f"Status: {status}, Cost: {solution.cost}")
print(f"Edge flows: {solution.edgeFlows}")

Vehicle Routing with Time Windows

Use Model for VRPTW and other resource-constrained problems:

import flowty

model = flowty.Model()

# Graph: depot(0) -> customer(1) -> depot(2)
edges = [(0, 1), (1, 2)]
costs = [1.0, 1.0]

# Resources: time windows and capacity
resources = [
    ({"V": [[0, 0, 0], [10, 10, 10]], "E": [[1, 1]]}, "time"),
    ({"V": [[0, 1, 0]], "G": [2]}, "capacity"),
]

graph = model.addGraph(edges, costs, [], resources, flowty.Graph.PathSense.Simple)
rules = [("Window", ["time"]), ("Capacity", ["capacity"])]
model.addSubproblem(graph, 0, 2, 0.0, 1.0, 1.0, "B", rules)

# Each customer must be visited at least once
model += graph.vertices[1] >= 1.0

status = model.solve()
solution = model.getSolution()
print(f"Status: {status}, Cost: {solution.cost}")

Documentation

Full documentation at docs.flowty.ai.

License

The solver ships with a Non-Commercial License. For commercial licenses, contact license@flowty.ai.

Issues & Contact

Report issues at github.com/flowty/flowty.

For inquiries contact info@flowty.ai.