Solvor all your optimization needs.

What's in the box?

Category	Solvors	Use Case
Linear/Integer	solve_lp, solve_lp_interior, solve_milp, solve_cg, solve_bp	Resource allocation, cutting stock
Constraint	solve_sat, Model	Sudoku, puzzles, and that one config problem that's been bugging you
Combinatorial	solve_knapsack, solve_bin_pack, solve_job_shop, solve_vrptw	Packing, scheduling, routing
Local Search	anneal, tabu_search, lns, alns	TSP, combinatorial optimization
Population	evolve, differential_evolution, particle_swarm	Global search, nature-inspired
Gradient	gradient_descent, momentum, rmsprop, adam	ML, curve fitting
Quasi-Newton	bfgs, lbfgs	Fast convergence, smooth functions
Derivative-Free	nelder_mead, powell, bayesian_opt	Black-box, expensive functions
Pathfinding	bfs, dfs, dijkstra, astar, astar_grid, bellman_ford, floyd_warshall	Shortest paths, graph traversal
Graph	max_flow, min_cost_flow, kruskal, prim, topological_sort, strongly_connected_components, pagerank, louvain, articulation_points, bridges, kcore_decomposition	Flow, MST, dependency, centrality, community detection
Assignment	solve_assignment, solve_hungarian, network_simplex	Matching, min-cost flow
Exact Cover	solve_exact_cover	N-Queens, tiling puzzles
Utilities	FenwickTree, UnionFind	Data structures for algorithms

---

Quickstart

uv add solvor

from solvor import solve_lp, solve_tsp, dijkstra, solve_hungarian

# Linear Programming
result = solve_lp(c=[1, 2], A=[[1, 1], [2, 1]], b=[4, 5])
print(result.solution)  # optimal x

# TSP with tabu search
distances = [[0, 10, 15], [10, 0, 20], [15, 20, 0]]
result = solve_tsp(distances)
print(result.solution)  # best tour found

# Shortest path
graph = {'A': [('B', 1), ('C', 4)], 'B': [('C', 2)], 'C': []}
result = dijkstra('A', 'C', lambda n: graph.get(n, []))
print(result.solution)  # ['A', 'B', 'C']

# Assignment
costs = [[10, 5], [3, 9]]
result = solve_hungarian(costs)
print(result.solution)  # [1, 0] - row 0 gets col 1, row 1 gets col 0

---

Solvors

Linear & Integer Programming

solve_lp

For resource allocation, blending, production planning. Finds the exact optimum for linear objectives with linear constraints.

# minimize 2x + 3y subject to x + y >= 4, x <= 3
result = solve_lp(
    c=[2, 3],
    A=[[-1, -1], [1, 0]],  # constraints as Ax <= b
    b=[-4, 3]
)

solve_milp

When some variables must be integers. Diet problems, scheduling with discrete slots, set covering.

# same as above, but x must be integer
result = solve_milp(c=[2, 3], A=[[-1, -1], [1, 0]], b=[-4, 3], integers=[0])

solve_cg

Column generation for problems with exponentially many variables. Cutting stock, bin packing, vehicle routing, crew scheduling.

# Cutting stock: minimize rolls to cut required pieces
result = solve_cg(
    demands=[97, 610, 395, 211],
    roll_width=100,
    piece_sizes=[45, 36, 31, 14],
)
print(result.objective)  # 454 rolls

solve_bp

Branch-and-price for optimal integer solutions. Combines column generation with branch-and-bound for proven optimality.

# Cutting stock with guaranteed integer optimality
result = solve_bp(
    demands=[97, 610, 395, 211],
    roll_width=100,
    piece_sizes=[45, 36, 31, 14],
)
print(result.objective)  # Integer optimal

Constraint Programming

solve_sat

For "is this configuration valid?" problems. Dependencies, exclusions, implications - anything that boils down to boolean constraints.

# (x1 OR x2) AND (NOT x1 OR x3) AND (NOT x2 OR NOT x3)
result = solve_sat([[1, 2], [-1, 3], [-2, -3]])
print(result.solution)  # {1: True, 2: False, 3: True}

Model

Constraint programming for puzzles and scheduling with "all different", arithmetic, and logical constraints. Sudoku, N-Queens, timetabling.

m = Model()
cells = [[m.int_var(1, 9, f'c{i}{j}') for j in range(9)] for i in range(9)]

# All different in each row
for row in cells:
    m.add(m.all_different(row))

result = m.solve()

Metaheuristics

anneal

Simulated annealing, sometimes you have to go downhill to find a higher peak.

result = anneal(
    initial=initial_solution,
    objective_fn=cost_function,
    neighbors=random_neighbor,
    temperature=1000,
    cooling=0.9995
)

tabu_search

Greedy local search with a "don't go back there" list. Simple but surprisingly effective.

result = tabu_search(
    initial=initial_solution,
    objective_fn=cost_function,
    neighbors=get_neighbors,  # returns [(move, solution), ...]
    cooldown=10
)

lns / alns

Large Neighborhood Search, destroy part of your solution and rebuild it better. ALNS learns which operators work best.

result = lns(initial, objective_fn, destroy_ops, repair_ops, max_iter=1000)
result = alns(initial, objective_fn, destroy_ops, repair_ops, max_iter=1000)  # adaptive

evolve / differential_evolution / particle_swarm

Population-based global search. Let a swarm of candidates explore for you. DE and PSO work on continuous spaces.

result = evolve(objective_fn=fitness, population=pop, crossover=cx, mutate=mut)
result = differential_evolution(objective_fn, bounds=[(0, 10)] * n, population_size=50)
result = particle_swarm(objective_fn, bounds=[(0, 10)] * n, n_particles=30)

Continuous Optimization

Gradient-Based

gradient_descent, momentum, rmsprop, adam - follow the slope. Adam adapts learning rates per parameter.

def grad_fn(x):
    return [2 * x[0], 2 * x[1]]  # gradient of x^2 + y^2

result = adam(grad_fn, x0=[5.0, 5.0])

Quasi-Newton

bfgs, lbfgs - approximate Hessian for faster convergence. L-BFGS uses limited memory.

result = bfgs(objective_fn, grad_fn, x0=[5.0, 5.0])
result = lbfgs(objective_fn, grad_fn, x0=[5.0, 5.0], memory=10)

Derivative-Free

nelder_mead, powell - no gradients needed. Good for noisy, non-smooth, or "I have no idea what this function looks like" situations.

result = nelder_mead(objective_fn, x0=[5.0, 5.0])
result = powell(objective_fn, x0=[5.0, 5.0])

bayesian_opt

When each evaluation is expensive. Builds a surrogate model to sample intelligently. Perfect for hyperparameter tuning or when your simulation takes 10 minutes per run.

result = bayesian_opt(expensive_fn, bounds=[(0, 1), (0, 1)], max_iter=30)

Pathfinding

bfs / dfs

Unweighted graph traversal. BFS finds shortest paths (fewest edges), DFS explores depth-first. Both work with any state type and neighbor function.

# Find shortest path in a grid
def neighbors(pos):
    x, y = pos
    return [(x+1, y), (x-1, y), (x, y+1), (x, y-1)]

result = bfs(start=(0, 0), goal=(5, 5), neighbors=neighbors)
print(result.solution)  # path from start to goal

dijkstra

Weighted shortest paths. Classic algorithm for when edges have costs. Stops early when goal is found.

def neighbors(node):
    return graph[node]  # returns [(neighbor, cost), ...]

result = dijkstra(start='A', goal='Z', neighbors=neighbors)

astar / astar_grid

A* with heuristics. Faster than Dijkstra when you have a good distance estimate. astar_grid handles 2D grids with built-in heuristics.

# Grid pathfinding with obstacles
grid = [[0, 0, 1, 0], [0, 0, 1, 0], [0, 0, 0, 0]]
result = astar_grid(grid, start=(0, 0), goal=(2, 3))

bellman_ford

Handles negative edge weights. Slower than Dijkstra but detects negative cycles, which is useful when costs can go negative.

result = bellman_ford(start=0, edges=[(0, 1, 5), (1, 2, -3), ...], n_nodes=4)

floyd_warshall

All-pairs shortest paths. O(n³) but gives you every shortest path at once. Worth it when you need the full picture.

result = floyd_warshall(n_nodes=4, edges=[(0, 1, 3), (1, 2, 1), ...])
# result.solution[i][j] = shortest distance from i to j

Network Flow & MST

max_flow

"How much can I push through this network?" Assigning workers to tasks, finding bottlenecks.

graph = {
    's': [('a', 10, 0), ('b', 5, 0)],
    'a': [('b', 15, 0), ('t', 10, 0)],
    'b': [('t', 10, 0)],
    't': []
}
result = max_flow(graph, 's', 't')

min_cost_flow / network_simplex

"What's the cheapest way to route X units?" Use min_cost_flow for simplicity, network_simplex for large instances.

# network_simplex for large min-cost flow
arcs = [(0, 1, 10, 2), (0, 2, 5, 3), (1, 2, 15, 1)]  # (from, to, cap, cost)
supplies = [10, 0, -10]  # positive = source, negative = sink
result = network_simplex(n_nodes=3, arcs=arcs, supplies=supplies)

kruskal / prim

Minimum spanning tree. Connect all nodes with minimum total edge weight. Kruskal sorts edges, Prim grows from a start node.

edges = [(0, 1, 4), (0, 2, 3), (1, 2, 2)]  # (u, v, weight)
result = kruskal(n_nodes=3, edges=edges)
# result.solution = [(1, 2, 2), (0, 2, 3)] - MST edges

Assignment

solve_assignment / solve_hungarian

Optimal one-to-one matching. solve_hungarian is O(n³), direct algorithm for assignment problems.

costs = [
    [10, 5, 13],
    [3, 9, 18],
    [10, 6, 12]
]
result = solve_hungarian(costs)
# result.solution[i] = column assigned to row i
# result.objective = total cost

# For maximization
result = solve_hungarian(costs, minimize=False)

Exact Cover

solve_exact_cover

For "place these pieces without overlap" problems. Sudoku, pentomino tiling, N-Queens, or any puzzle where you stare at a grid wondering why nothing fits.

# Tiling problem: cover all columns with non-overlapping rows
matrix = [
    [1, 1, 0, 0],  # row 0 covers columns 0, 1
    [0, 1, 1, 0],  # row 1 covers columns 1, 2
    [0, 0, 1, 1],  # row 2 covers columns 2, 3
    [1, 0, 0, 1],  # row 3 covers columns 0, 3
]
result = solve_exact_cover(matrix)
# result.solution = (0, 2) or (1, 3) - rows that cover all columns exactly once

Combinatorial Solvers

solve_knapsack

The classic "what fits in your bag" problem. Select items to maximize value within capacity.

values = [60, 100, 120]
weights = [10, 20, 30]
result = solve_knapsack(values, weights, capacity=50)
# result.solution = (1, 2) - indices of selected items

solve_bin_pack

Bin packing heuristics. Minimize bins needed for items.

items = [4, 8, 1, 4, 2, 1]
result = solve_bin_pack(items, bin_capacity=10)
# result.solution = (1, 0, 0, 1, 0, 0) - bin index for each item
# result.objective = 2 (number of bins)

solve_job_shop

Job shop scheduling. Minimize makespan for jobs on machines.

# jobs[i] = [(machine, duration), ...] - operations for job i
jobs = [[(0, 3), (1, 2)], [(1, 2), (0, 4)]]
result = solve_job_shop(jobs, n_machines=2)

solve_vrptw

Vehicle Routing with Time Windows. Serve customers with capacity and time constraints.

from solvor import Customer, solve_vrptw

customers = [
    Customer(1, 10, 10, demand=10, tw_start=0, tw_end=50, service_time=5),
    Customer(2, 20, 20, demand=10, tw_start=0, tw_end=50, service_time=5),
    Customer(3, 30, 30, demand=10, tw_start=0, tw_end=50, service_time=5),
]
result = solve_vrptw(customers, vehicles=2, vehicle_capacity=30)

---

Result Format

All solvors return a consistent Result dataclass:

Result(
    solution,     # best solution found
    objective,    # objective value
    iterations,   # solver iterations (pivots, generations, etc.)
    evaluations,  # function evaluations
    status,       # OPTIMAL, FEASIBLE, INFEASIBLE, UNBOUNDED, MAX_ITER
    error,        # error message if failed (None on success)
    solutions,    # multiple solutions when solution_limit > 1
)

---

When to use what?

Problem	Solvor
Linear constraints, continuous	solve_lp, solve_lp_interior
Linear constraints, integers	solve_milp
Cutting stock, crew scheduling	solve_cg, solve_bp
Boolean satisfiability	solve_sat
Discrete vars, complex constraints	Model
Knapsack, subset selection	solve_knapsack
Bin packing	solve_bin_pack
Job shop scheduling	solve_job_shop
Vehicle routing	solve_vrptw
Combinatorial, local search	tabu_search, anneal
Combinatorial, destroy-repair	lns, alns
Global search, continuous	differential_evolution, particle_swarm
Global search, discrete	evolve
Smooth, differentiable, fast	bfgs, lbfgs
Smooth, differentiable, ML	adam, rmsprop
Non-smooth, no gradients	nelder_mead, powell
Expensive black-box	bayesian_opt
Shortest path, unweighted	bfs, dfs
Shortest path, weighted	dijkstra, astar
Shortest path, negative weights	bellman_ford
All-pairs shortest paths	floyd_warshall
Minimum spanning tree	kruskal, prim
Dependency ordering	topological_sort
Circular dependencies	strongly_connected_components
Node importance	pagerank
Community detection	louvain
Single points of failure	articulation_points, bridges
Core vs periphery	kcore_decomposition
Maximum flow	max_flow
Min-cost flow	min_cost_flow, network_simplex
Assignment, matching	solve_hungarian, solve_assignment
Exact cover, tiling	solve_exact_cover

---

Performance

Have your cake and eat it too. solvOR gives you both:

• Readable Python - Every algorithm is implemented in clear, documented Python you can study and modify
• Rust Performance - Optional drop-in Rust backends with 5-60x speedup for compute-heavy algorithms

from solvor import floyd_warshall

# "auto" (default) - Uses Rust if available, falls back to Python
result = floyd_warshall(n_nodes, edges)

# "python" - Force pure Python (for learning, debugging, or extending)
result = floyd_warshall(n_nodes, edges, backend="python")

Pre-built wheels include Rust extensions for Linux, macOS, and Windows. If Rust isn't available, solvOR falls back to Python automatically.

See the Performance docs for which algorithms have Rust backends and benchmarks.

---

Philosophy

1. Readable first: every algorithm in clear Python you can actually understand
2. Performance when needed: optional Rust backends, zero-copy where possible
3. Consistent: same Result format, same minimize/maximize convention
4. Practical: solves real problems (and AoC puzzles)

---

Documentation

Full docs at solvOR.ai: getting started, algorithm reference, cookbook with worked examples, and troubleshooting.

---

Contributing

See CONTRIBUTING.md for development setup and guidelines.

License

Apache 2.0 License, free for personal and commercial use.

Background of solvOR

A little bit of history..

I learned about solvers back in 2011, working with some great minds at a startup in Paris. I started writing python myself around 2018, always as a hobby, and in 2024 I got back into solvers for an energy management system (EMS) and wrote a few tools (simplex, milp, genetic) myself mainly to improve my understanding.

Over time this toolbox got larger and larger, so I decided to publish it on GitHub so others can use it and improve it even further. Since I am learning Rust, I will eventually replace some performance critical operations with a high performance Rust implementation. But since I work on this project (and others) in my spare time, what and when is uncertain. The name solvOR is a mix of solver(s) and OR (Operations Research).

Disclaimer; I am not a professional software engineer, so there are probably some obvious improvements possible. If so let me know, or create a PR!