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Integer and mixed-integer programming skill for combinatorial optimization problems with discrete decision variables.
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Reference for querying the Atlas knowledge graph through its MCP tools — the SECONDARY enrichment/comparison layer that adds best-practice context to systems you have ALREADY scanned from your real sources (`az`, repos, dirs). Use when you need to look up nodes, edges, kinds, clusters, stats, or wiki pages in Atlas to compare against your real inventory. (atlas graph, query atlas, atlas mcp, search the graph, graph neighbors, atlas record, atlas kinds, enrichment layer)
Atlas turns your STATED NEED into a real systems atlas by SCANNING your actual sources (Azure via `az`, git repos, local dirs) and process/data mining them, THEN enriching against the Atlas knowledge graph. Use this skill when asked to inventory/map your real systems, scan your cloud + repos + directories, mine the real processes or data they contain, or collect their real constraints/gotchas. (atlas, scan my systems, inventory our azure account, map my repos, real systems atlas, process mining, data mining, collect nuances, system discovery)
This skill should be used when the user asks to "find skills in the wild", "assimilate popular workflows", "discover SKILL.md files in repos", "research external skills", "find workflow patterns", "survey the skill landscape", "what skills exist out there", or wants to investigate public repositories for extractable processes, babysitter plugins, and reusable procedural insights. Searches GitHub for SKILL.md files, classifies repos by archetype, and maintains structured research under docs/reference-repos/.
SOC 職業分類に基づく
| name | integer-program-solver |
| description | Integer and mixed-integer programming skill for combinatorial optimization problems with discrete decision variables. |
| allowed-tools | Bash(*) Read Write Edit Glob Grep WebFetch |
| metadata | {"author":"babysitter-sdk","version":"1.0.0","category":"operations-research","backlog-id":"SK-IE-002"} |
| graph | {"domains":["domain:industrial-engineering"],"skillAreas":["skill-area:statistical-analysis","skill-area:organizational-design","skill-area:data-analysis"],"roles":["role:operations-analyst","role:research-engineer"]} |
You are integer-program-solver - a specialized skill for formulating and solving integer and mixed-integer programming models for combinatorial optimization problems.
This skill enables AI-powered integer programming including:
from ortools.linear_solver import pywraplp
def facility_location():
solver = pywraplp.Solver.CreateSolver('SCIP')
# Binary variables: open facility j?
facilities = range(5)
customers = range(10)
y = {j: solver.BoolVar(f'y_{j}') for j in facilities}
x = {(i,j): solver.BoolVar(f'x_{i}_{j}')
for i in customers for j in facilities}
# Each customer assigned to exactly one facility
for i in customers:
solver.Add(sum(x[i,j] for j in facilities) == 1)
# Can only assign to open facilities
for i in customers:
for j in facilities:
solver.Add(x[i,j] <= y[j])
# Objective: minimize total cost
fixed_cost = [100, 120, 110, 130, 90]
transport_cost = [[...]] # cost matrix
solver.Minimize(
sum(fixed_cost[j] * y[j] for j in facilities) +
sum(transport_cost[i][j] * x[i,j]
for i in customers for j in facilities)
)
return solver
# If-then constraints using Big-M
def big_m_constraints(solver, x, y, M=1e6):
"""
Model: if x > 0 then y = 1
Linearization: x <= M * y
"""
solver.Add(x <= M * y)
# Either-or constraints
# Either constraint1 OR constraint2
# c1: a*x <= b + M*(1-z)
# c2: c*x <= d + M*z
z = solver.BoolVar('z')
solver.Add(a*x <= b + M*(1-z))
solver.Add(c*x <= d + M*z)
def logical_constraints(solver, y1, y2, y3):
"""
Common logical constraints
"""
# AND: z = y1 AND y2
z_and = solver.BoolVar('z_and')
solver.Add(z_and <= y1)
solver.Add(z_and <= y2)
solver.Add(z_and >= y1 + y2 - 1)
# OR: z = y1 OR y2
z_or = solver.BoolVar('z_or')
solver.Add(z_or >= y1)
solver.Add(z_or >= y2)
solver.Add(z_or <= y1 + y2)
# Implication: y1 => y2
solver.Add(y1 <= y2)
# At most one: sum(y) <= 1
solver.Add(y1 + y2 + y3 <= 1)
# Exactly one: sum(y) == 1
solver.Add(y1 + y2 + y3 == 1)
def solve_with_gap_tracking(solver, time_limit=300):
solver.SetTimeLimit(time_limit * 1000)
# Set MIP gap tolerance
solver.SetSolverSpecificParametersAsString(
"limits/gap = 0.01" # 1% optimality gap
)
status = solver.Solve()
result = {
"status": status,
"objective": solver.Objective().Value(),
"best_bound": solver.Objective().BestBound(),
"gap": (solver.Objective().Value() -
solver.Objective().BestBound()) /
solver.Objective().Value() * 100,
"nodes_explored": solver.nodes(),
"time": solver.WallTime() / 1000
}
return result
def generate_solution_pool(model, max_solutions=10):
"""
Generate multiple near-optimal solutions
"""
solutions = []
for i in range(max_solutions):
status = model.solve()
if status == pywraplp.Solver.OPTIMAL:
solution = {
"objective": model.Objective().Value(),
"variables": {v.name(): v.solution_value()
for v in model.variables()}
}
solutions.append(solution)
# Add constraint to exclude this solution
exclude = sum(v if v.solution_value() > 0.5 else (1-v)
for v in binary_vars)
model.Add(exclude <= len(binary_vars) - 1)
else:
break
return solutions
This skill integrates with the following processes:
linear-programming-model-development.jstransportation-route-optimization.jswarehouse-layout-slotting-optimization.js{
"model_name": "Facility_Location",
"status": "optimal",
"objective_value": 4520.0,
"mip_gap": 0.0,
"solve_time_seconds": 12.5,
"nodes_explored": 1547,
"solution": {
"open_facilities": [0, 2, 4],
"assignments": {
"customer_0": "facility_2",
"customer_1": "facility_0"
}
},
"solution_pool_size": 5
}
| Library | Description | Use Case |
|---|---|---|
| Google OR-Tools | Open source | General MIP |
| Gurobi | Commercial | High performance |
| CPLEX | Commercial | Enterprise |
| SCIP | Open source | Research |
| CBC | Open source | General purpose |