Constraint programming skill for scheduling, configuration, and assignment problems
Solves scheduling, configuration, and assignment problems using constraint programming techniques.
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The Constraint Satisfaction Solver skill provides capabilities for solving constraint satisfaction problems (CSPs) and constraint optimization problems (COPs). It excels at scheduling, configuration, assignment, and combinatorial problems where finding feasible solutions is as important as optimization.
# Define CSP
csp_problem = {
"name": "Employee Scheduling",
"variables": {
"shift_mon_morning": {"domain": ["Alice", "Bob", "Carol", "David"]},
"shift_mon_afternoon": {"domain": ["Alice", "Bob", "Carol", "David"]},
"shift_tue_morning": {"domain": ["Alice", "Bob", "Carol", "David"]},
"shift_tue_afternoon": {"domain": ["Alice", "Bob", "Carol", "David"]},
# ... more shifts
},
"constraints": [
{
"type": "all_different",
"scope": ["shift_mon_morning", "shift_mon_afternoon"],
"description": "Different employees on same day"
},
{
"type": "not_equal",
"variables": ["shift_mon_afternoon", "shift_tue_morning"],
"condition": "employee",
"description": "No back-to-back closing/opening"
},
{
"type": "count",
"variable": "Alice",
"min": 3,
"max": 5,
"description": "Alice works 3-5 shifts per week"
}
]
}
# Job shop scheduling
scheduling_problem = {
"jobs": [
{
"id": "Job1",
"tasks": [
{"id": "J1_T1", "machine": "M1", "duration": 3},
{"id": "J1_T2", "machine": "M2", "duration": 2, "after": "J1_T1"}
]
},
{
"id": "Job2",
"tasks": [
{"id": "J2_T1", "machine": "M2", "duration": 2},
{"id": "J2_T2", "machine": "M1", "duration": 3, "after": "J2_T1"}
]
}
],
"constraints": {
"no_overlap": "tasks on same machine cannot overlap",
"precedence": "tasks must respect ordering within job",
"deadline": {"Job1": 10, "Job2": 8}
},
"objective": "minimize_makespan" # or "minimize_tardiness"
}
# Product configuration
config_problem = {
"components": {
"engine": {"options": ["V6", "V8", "Electric"]},
"transmission": {"options": ["Manual", "Automatic", "CVT"]},
"wheel_size": {"options": [17, 18, 19, 20]},
"color": {"options": ["Red", "Blue", "Black", "White"]}
},
"constraints": [
{
"type": "implication",
"if": {"engine": "Electric"},
"then": {"transmission": ["Automatic", "CVT"]},
"description": "Electric engines don't support manual transmission"
},
{
"type": "incompatible",
"values": [{"engine": "V6"}, {"wheel_size": 20}],
"description": "V6 not available with 20-inch wheels"
}
]
}
| Constraint | Description | Example Use |
|---|---|---|
| AllDifferent | All variables take distinct values | Sudoku, assignment |
| Cumulative | Resource usage over time | Scheduling |
| Circuit | Variables form a Hamiltonian circuit | TSP, routing |
| Table | Allowed/forbidden combinations | Configuration |
| Regular | Sequence matches automaton | Shift patterns |
| Cardinality | Count of value occurrences | Workload balance |
{
"problem_type": "csp|cop|scheduling|configuration",
"variables": {
"var_name": {
"domain": "array or range",
"type": "integer|boolean|set"
}
},
"constraints": [
{
"type": "string",
"scope": ["string"],
"parameters": "object"
}
],
"objective": {
"type": "minimize|maximize",
"expression": "string"
},
"search_config": {
"strategy": "default|first_fail|min_domain",
"time_limit": "number",
"all_solutions": "boolean",
"max_solutions": "number"
}
}
{
"status": "Satisfied|Optimal|Infeasible|Unknown",
"solution": {
"variable_name": "value"
},
"objective_value": "number (if COP)",
"all_solutions": [
{"variable_name": "value"}
],
"statistics": {
"nodes_explored": "number",
"propagations": "number",
"backtracks": "number",
"solve_time": "number"
},
"explanation": {
"unsatisfied_constraints": ["string"],
"conflict_set": ["string"]
}
}
| Strategy | Description | Best For |
|---|---|---|
| First Fail | Choose variable with smallest domain | General CSPs |
| Min Domain | Same as first fail | General CSPs |
| Impact | Choose by constraint propagation impact | Large problems |
| Activity | Choose frequently changed variables | Restart searches |
| Random | Random variable/value selection | Diversification |
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