pycsp3-scheduling
Scheduling extension for pycsp3 with interval variables, sequence variables, and scheduling constraints.
Features
- Interval Variables: Represent tasks/activities with start, end, size, length, and optional presence
- Intensity Functions: Stepwise intensity metadata with granularity scaling for size/length
- Sequence Variables: Ordered sequences of intervals on disjunctive resources
- Precedence Constraints:
end_before_start, start_at_start, etc.
- Grouping Constraints:
span, alternative, synchronize
- Sequence Constraints:
SeqNoOverlap, first, last, before, previous, same_sequence
- Forbidden Time Constraints:
forbid_start, forbid_end, forbid_extent
- Presence Constraints:
presence_implies, presence_or, presence_xor, chain
- Overlap Constraints:
must_overlap, overlap_at_least, disjunctive
- Aggregate Expressions:
count_present, earliest_start, latest_end, makespan
- Cumulative Functions:
pulse, step_at_start, step_at_end for resource modeling
- State Functions: Model resource states with transitions
- XCSP3 Extension: Output scheduling models in extended XCSP3 format
- Visualization: Gantt charts and resource profiles
Installation
pip install pycsp3-scheduling
For development:
git clone https://github.com/sohaibafifi/pycsp3-scheduling.git
cd pycsp3-scheduling
pip install -e ".[dev]"
Quick Start
from pycsp3 import *
from pycsp3_scheduling import *
# Create interval variables for tasks
task1 = IntervalVar(size=10, name="task1")
task2 = IntervalVar(size=15, name="task2")
task3 = IntervalVar(size=8, name="task3")
# Precedence: task1 must finish before task2 starts
satisfy(end_before_start(task1, task2))
# No overlap: task2 and task3 cannot overlap
satisfy(SeqNoOverlap([task2, task3]))
# Minimize makespan
minimize(max(end_time(task1), end_time(task2), end_time(task3)))
Example: Job Shop Scheduling
from pycsp3 import *
from pycsp3_scheduling import *
# Data
n_jobs, n_machines = 3, 3
durations = [[3, 2, 2], [2, 1, 4], [4, 3, 3]]
machines = [[0, 1, 2], [0, 2, 1], [1, 0, 2]]
# Create interval variables for each operation
ops = [[IntervalVar(size=durations[j][o], name=f"op_{j}_{o}")
for o in range(n_machines)] for j in range(n_jobs)]
# Sequences for each machine
sequences = [SequenceVar(
intervals=[ops[j][o] for j in range(n_jobs)
for o in range(n_machines) if machines[j][o] == m],
name=f"machine_{m}"
) for m in range(n_machines)]
# Precedence within jobs
satisfy(
end_before_start(ops[j][o], ops[j][o+1])
for j in range(n_jobs) for o in range(n_machines-1)
)
# No overlap on machines
satisfy(SeqNoOverlap(seq) for seq in sequences)
# Minimize makespan
minimize(Maximum(end_time(ops[j][-1]) for j in range(n_jobs)))
Example: RCPSP (Resource-Constrained Project Scheduling)
from pycsp3 import *
from pycsp3_scheduling import *
# Data
durations = [3, 2, 5, 4, 2]
demands = [[2, 1], [1, 2], [3, 0], [2, 1], [1, 3]]
capacities = [4, 3]
precedences = [(0, 2), (1, 3), (2, 4)]
# Interval variables
tasks = [IntervalVar(size=durations[i], name=f"task_{i}")
for i in range(len(durations))]
# Precedence constraints
satisfy(end_before_start(tasks[p], tasks[s]) for p, s in precedences)
# Cumulative resource constraints
for r in range(len(capacities)):
resource = sum(pulse(tasks[i], demands[i][r])
for i in range(len(tasks)) if demands[i][r] > 0)
satisfy(resource <= capacities[r])
# Minimize makespan
minimize(Maximum(end_time(t) for t in tasks))
API Reference
Variables
| Function |
Description |
IntervalVar(size, start, end, length, intensity, granularity, optional, name) |
Create an interval variable |
IntervalVarArray(size, ...) |
Create array of interval variables |
SequenceVar(intervals, types, name) |
Create a sequence variable |
Expressions
| Function |
Description |
start_of(interval, absent_value=0) |
Start time of interval |
end_of(interval, absent_value=0) |
End time of interval |
size_of(interval, absent_value=0) |
Size/duration of interval |
length_of(interval, absent_value=0) |
Length of interval |
presence_of(interval) |
Boolean presence status |
overlap_length(interval1, interval2, absent_value=0) |
Overlap duration between two intervals |
expr_min(*args) |
Minimum of scheduling expressions |
expr_max(*args) |
Maximum of scheduling expressions |
Element Expressions (Array Indexing)
| Function |
Description |
element(array, index) |
Access array element by interval expression index |
element2d(matrix, row, col) |
Access 2D matrix element by interval expressions |
ElementMatrix(matrix) |
Wrapper for 2D indexing with [] operator |
Interop Helpers
| Function |
Description |
start_time(interval) |
pycsp3 variable for start time |
end_time(interval) |
pycsp3 expression for end time |
presence_time(interval) |
pycsp3 variable for presence (optional intervals) |
interval_value(interval) |
Get solved interval values (start, end, size, present) |
model_statistics() |
Get model statistics (variables, constraints counts) |
solution_statistics() |
Get solution statistics after solving |
Precedence Constraints
| Constraint |
Semantics (when both present) |
start_before_start(a, b, delay) |
start(b) >= start(a) + delay |
start_before_end(a, b, delay) |
end(b) >= start(a) + delay |
end_before_start(a, b, delay) |
start(b) >= end(a) + delay |
end_before_end(a, b, delay) |
end(b) >= end(a) + delay |
start_at_start(a, b, delay) |
start(b) == start(a) + delay |
start_at_end(a, b, delay) |
start(b) == end(a) + delay |
end_at_start(a, b, delay) |
end(a) == start(b) + delay |
end_at_end(a, b, delay) |
end(b) == end(a) + delay |
Grouping Constraints
| Constraint |
Description |
span(main, subtasks) |
Main interval spans all present subtasks |
alternative(main, alts, card=1) |
Select card alternatives matching main |
synchronize(main, intervals) |
All present intervals sync with main |
Sequence Constraints
| Constraint |
Description |
SeqNoOverlap(sequence, transition_matrix, is_direct) |
Non-overlap with optional transition times |
first(sequence, interval) |
Constrain interval to be first in sequence |
last(sequence, interval) |
Constrain interval to be last in sequence |
before(sequence, interval1, interval2) |
interval1 must end before interval2 starts |
previous(sequence, interval1, interval2) |
interval1 immediately precedes interval2 |
same_sequence(seq1, seq2) |
Common intervals have same position in both |
same_common_subsequence(seq1, seq2) |
Common intervals have same relative order |
Sequence Accessor Expressions
| Function |
Description |
start_of_next(sequence, interval, absent_value) |
Start time of next interval in sequence |
end_of_next(sequence, interval, absent_value) |
End time of next interval |
size_of_next(sequence, interval, absent_value) |
Size of next interval |
length_of_next(sequence, interval, absent_value) |
Length of next interval |
type_of_next(sequence, interval, absent_value) |
Type of next interval |
start_of_prev(sequence, interval, absent_value) |
Start time of previous interval |
end_of_prev(sequence, interval, absent_value) |
End time of previous interval |
size_of_prev(sequence, interval, absent_value) |
Size of previous interval |
length_of_prev(sequence, interval, absent_value) |
Length of previous interval |
type_of_prev(sequence, interval, absent_value) |
Type of previous interval |
Cumulative Functions
| Function |
Description |
pulse(interval, height) |
Constant consumption during interval |
step_at(time, height) |
Step at fixed time point |
step_at_start(interval, height) |
Step at interval start |
step_at_end(interval, height) |
Step at interval end |
height_at_start(interval, cumul) |
Cumulative height at interval start |
height_at_end(interval, cumul) |
Cumulative height at interval end |
cumul_range(cumul, min, max) |
Constrain cumul to [min, max] |
always_in(cumul, interval, min, max) |
Cumul in range during interval |
SeqCumulative(sequence, heights, capacity) |
Cumulative on sequence with per-interval heights |
State Functions
| Function |
Description |
StateFunction(transition_matrix) |
Create state function with optional transitions |
TransitionMatrix(n_states) |
Create transition matrix for state function |
always_equal(func, interval, value) |
State equals value during interval |
always_constant(func, interval) |
State constant during interval |
always_no_state(func, interval) |
No state assigned during interval |
Forbidden Time Constraints
| Constraint |
Description |
forbid_start(interval, periods) |
Interval cannot start during forbidden periods |
forbid_end(interval, periods) |
Interval cannot end during forbidden periods |
forbid_extent(interval, periods) |
Interval cannot overlap forbidden periods |
Presence Constraints
| Constraint |
Description |
presence_implies(a, b) |
If a is present, b must be present |
presence_or(a, b) |
At least one must be present |
presence_xor(a, b) |
Exactly one must be present |
all_present_or_all_absent(intervals) |
All-or-nothing group |
if_present_then(interval, constraint) |
Apply constraint only when present |
at_least_k_present(intervals, k) |
At least k must be present |
at_most_k_present(intervals, k) |
At most k can be present |
exactly_k_present(intervals, k) |
Exactly k must be present |
Chain Constraints
| Constraint |
Description |
chain(intervals, delays) |
Intervals execute in sequence with optional delays |
strict_chain(intervals, delays) |
Intervals execute back-to-back (equality) |
Overlap Constraints
| Constraint |
Description |
must_overlap(a, b) |
Two intervals must share some time |
overlap_at_least(a, b, min_overlap) |
Intervals must overlap by at least min_overlap |
no_overlap_pairwise(intervals) |
Simple pairwise no-overlap |
disjunctive(intervals, transition_times) |
Unary resource (at most one active) |
Aggregate Expressions
| Expression |
Description |
count_present(intervals) |
Count of present intervals |
earliest_start(intervals) |
Minimum start time among present intervals |
latest_end(intervals) |
Maximum end time among present intervals |
span_length(intervals) |
Total span (latest_end - earliest_start) |
makespan(intervals) |
Alias for latest_end |
Requirements
- Python >= 3.10
- pycsp3 >= 2.5
- lxml >= 4.9
- matplotlib >= 3.7 (optional, for visualization)
- java >= 8 (optional, for solving with ACE/Choco)
License
MIT License - see LICENSE file.
References
