Built-in Models

PyEPO includes built-in models for several classic problems. Each model is built by a factory that takes a backend keyword (default "gurobi"). Pair a model with generated data (Data Generators) and an optDataset (Datasets):

import pyepo
from pyepo import model

grid = (5, 5)
x, c = pyepo.data.shortestpath.genData(1000, 5, grid, deg=4, seed=135)
optmodel = model.shortestPathModel(grid)                  # default Gurobi
dataset = pyepo.data.dataset.optDataset(optmodel, x, c)

Switch the solver with backend. The generic backends take a solver= argument that names the solver to run:

model.shortestPathModel(grid, backend="copt")
model.shortestPathModel(grid, backend="pyomo", solver="glpk")
model.shortestPathModel(grid, backend="mpax")             # LP on GPU

Note

In end-to-end training, pyepo.func modules call setObj and solve during the forward pass.

Shortest Path Model

Minimum-cost path from the northwest to the southeast corner of an (h, w) grid, formulated as a minimum-cost-flow LP. Supported backends: gurobi, copt, pyomo, ortools, mpax.

pyepo.model.shortestPathModel(grid, *, backend='gurobi', **kwargs)

Shortest path on a grid network.

Parameters:

  • grid (tuple) – grid size (h, w)

  • backend (str) – solver backend; one of "gurobi", "copt", "pyomo", "ortools", "mpax"

Knapsack Model

Multi-dimensional 0/1 knapsack: maximize value subject to per-dimension capacities. weights has shape (dim, n_items) and capacity has length dim. Supported backends: gurobi, copt, pyomo, ortools, mpax (LP relaxation).

weights = [[3, 4, 3, 6, 4], [4, 5, 2, 3, 5], [5, 4, 6, 2, 3]]
capacity = [12, 10, 15]
optmodel = model.knapsackModel(weights, capacity)
pyepo.model.knapsackModel(weights, capacity, *, backend='gurobi', **kwargs)

Multi-dimensional knapsack.

Parameters:

  • weights (ndarray) – item weights with shape (dim, n_items)

  • capacity (ndarray) – per-dimension capacity with length dim

  • backend (str) – solver backend; one of "gurobi", "copt", "pyomo", "ortools", "mpax"

Traveling Salesperson Model

Shortest tour visiting each city once. formulation is "DFJ" (lazy subtour elimination), "GG", or "MTZ". Supported backends: gurobi and copt (all three formulations), and pyomo (GG, MTZ). On gurobi, recycle_cuts=True keeps subtour cuts found in one solve for later solves.

optmodel = model.tspModel(20, formulation="DFJ", recycle_cuts=True)
pyepo.model.tspModel(num_nodes, *, backend='gurobi', formulation='DFJ', **kwargs)

Traveling salesperson.

Parameters:

  • num_nodes (int) – number of nodes

  • backend (str) – solver backend; one of "gurobi", "copt", "pyomo"

  • formulation (str) – ILP formulation; one of "DFJ", "GG", "MTZ" ("DFJ" on gurobi and copt only)

Capacitated Vehicle Routing Model

Shortest vehicle routes from a depot that serve every customer within capacity. formulation is "RCI" (lazy rounded-capacity cuts) or "MTZ". Supported backends: gurobi and copt (both formulations), and pyomo (MTZ). On gurobi, "RCI" also accepts recycle_cuts=True to keep cuts found in one solve for later solves.

optmodel = model.vrpModel(10, demands=[2, 1, 3, 2, 1, 2, 1, 3, 2],
                          capacity=5.0, num_vehicle=3, formulation="RCI")
pyepo.model.vrpModel(num_nodes, demands, capacity, num_vehicle, *, backend='gurobi', formulation='RCI', **kwargs)

Capacitated vehicle routing.

Parameters:

  • num_nodes (int) – number of nodes, with the depot as node 0

  • demands (list) – per-customer demands with length num_nodes - 1

  • capacity (float) – vehicle capacity

  • num_vehicle (int) – number of vehicles

  • backend (str) – solver backend; one of "gurobi", "copt", "pyomo"

  • formulation (str) – ILP formulation; "RCI" or "MTZ" ("RCI" on gurobi and copt only)

Portfolio Model

Mean-variance allocation that maximizes return under a risk budget. Supported backends: gurobi, copt, pyomo.

import numpy as np
covariance = np.cov(np.random.randn(1000, 50), rowvar=False)
optmodel = model.portfolioModel(50, covariance)
pyepo.model.portfolioModel(num_assets, covariance, *, backend='gurobi', **kwargs)

Mean-variance portfolio optimization.

Parameters:

  • num_assets (int) – number of assets

  • covariance (ndarray) – covariance matrix of the asset returns

  • backend (str) – solver backend; one of "gurobi", "copt", "pyomo"