Real World¶

Practical applications with realistic constraints.

Nurse Scheduling¶

Assign nurses to shifts while respecting regulations and preferences.

Constraints¶

Each shift must be covered
Maximum shifts per nurse per week
Minimum rest between shifts
No more than N consecutive days
Skill requirements

Approach¶

Uses CP-SAT model with all_different and sum constraints.

from solvor import Model

def schedule_nurses(nurses, shifts, days):
    m = Model()

    # x[nurse][day][shift] = 1 if nurse works shift on day
    x = {}
    for n in nurses:
        for d in range(days):
            for s in shifts:
                x[n, d, s] = m.bool_var(f'{n}_{d}_{s}')

    # Each shift covered by exactly one nurse
    for d in range(days):
        for s in shifts:
            m.add(sum(x[n, d, s] for n in nurses) == 1)

    # Max 5 shifts per nurse per week
    for n in nurses:
        m.add(sum(x[n, d, s] for d in range(days) for s in shifts) <= 5)

    return m.solve()

School Timetabling¶

Assign classes to rooms and time slots without conflicts.

Uses ITC 2007 competition format.

Approaches¶

Multiple solver approaches compared:

timetabling_sat.py - SAT
timetabling_cp.py - CP-SAT
timetabling_milp.py - MILP
timetabling_anneal.py - Simulated annealing
timetabling_genetic.py - Genetic algorithm
timetabling_tabu.py - Tabu search

Constraints¶

No teacher teaches two classes at once
No room hosts two classes at once
Class-room compatibility (capacity, equipment)
Teacher availability
Curriculum requirements

Machine Learning¶

Linear Regression¶

Gradient descent for least squares regression.

linear_regression.py

from solvor import adam

def grad(weights):
    # Compute gradient of MSE loss
    return gradient

result = adam(grad, x0=initial_weights, lr=0.01)

Logistic Regression¶

Binary classification with Adam optimizer.

logistic_regression.py