Khalid Abdulla - 8 months ago 212

Python Question

I'm using the

`PuLP`

`MIP start`

`PuLP`

Details on how to set

`MIP start`

And the developer of the

`PuLP`

`PuLP`

Pasted below are two complete models. I have made these as small as possible whilst preventing the gurobi solver from finding the optimal value using a heuristic.

I have attempted to set an initial solution (to the optimal values) in both models, but in the

`PuLP`

`gurobipy`

How do you set an initial solution for the Gurobi solve via the PuLP interface?

`from pulp import *`

prob = LpProblem("min example",LpMinimize)

x1=LpVariable("x1",0,None,LpInteger)

x2=LpVariable("x2",0,None,LpInteger)

x3=LpVariable("x3",0,None,LpInteger)

x4=LpVariable("x4",0,None,LpInteger)

# Objective function

prob += 3*x1 + 5*x2 + 6*x3 + 9*x4

# A constraint

prob += -2*x1 + 6*x2 -3*x3 + 4*x4 >= 2, "Con1"

prob += -5*x1 + 3*x2 + x3 + 3*x4 >= -2, "Con2"

prob += 5*x1 - x2 + 4*x3 - 2*x4 >= 3, "Con3"

# Choose solver, and set it to problem, and build the Gurobi model

solver = pulp.GUROBI()

prob.setSolver(solver)

prob.solver.buildSolverModel(prob)

# Attempt to set an initial feasible solution (in this case to an optimal solution)

prob.solverModel.getVars()[0].start = 1

prob.solverModel.getVars()[1].start = 1

prob.solverModel.getVars()[2].start = 0

prob.solverModel.getVars()[3].start = 0

# Solve model

prob.solve()

# Status of the solution is printed to the screen

print "Status:", LpStatus[prob.status]

# Each of the variables is printed with it's resolved optimum value

for v in prob.variables():

print v.name, "=", v.varValue

# Optimised objective function value is printed to the screen

print "OF = ", value(prob.objective)

Which returns:

`Optimize a model with 3 rows, 4 columns and 12 nonzeros`

Coefficient statistics:

Matrix range [1e+00, 6e+00]

Objective range [3e+00, 9e+00]

Bounds range [0e+00, 0e+00]

RHS range [2e+00, 3e+00]

Found heuristic solution: objective 12

Presolve removed 0 rows and 1 columns

Presolve time: 0.00s

Presolved: 3 rows, 3 columns, 9 nonzeros

Variable types: 0 continuous, 3 integer (0 binary)

Root relaxation: objective 7.400000e+00, 1 iterations, 0.00 seconds

Nodes | Current Node | Objective Bounds | Work

Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time

0 0 7.40000 0 1 12.00000 7.40000 38.3% - 0s

H 0 0 8.0000000 7.40000 7.50% - 0s

Explored 0 nodes (1 simplex iterations) in 0.00 seconds

Thread count was 8 (of 8 available processors)

Optimal solution found (tolerance 1.00e-04)

Best objective 8.000000000000e+00, best bound 8.000000000000e+00, gap 0.0%

('Gurobi status=', 2)

Status: Optimal

x1 = 1.0

x2 = 1.0

x3 = -0.0

x4 = -0.0

OF = 8.0

Secondly I can implement the same model using the

`gurobipy`

`from gurobipy import *`

m = Model("min example")

m.modelSense = GRB.MINIMIZE

objFcnCoeffs = [3, 5, 6, 9]

xVars = []

for i in range(4):

xVars.append(m.addVar(vtype=GRB.INTEGER, obj=objFcnCoeffs[i], name="Open%d" % i))

# Update model to integrate new variables

m.update()

# Constraints

m.addConstr(-2*xVars[0] + 6*xVars[1] -3*xVars[2] + 4*xVars[3] >= 2, "Con1")

m.addConstr(-5*xVars[0] + 3*xVars[1] + xVars[2] + 3*xVars[3] >= -2, "Con2")

m.addConstr(5*xVars[0] - xVars[1] + 4*xVars[2] - 2*xVars[3] >= 3, "Con3")

# Attempt to set an initial feasible solution (in this case to an optimal solution)

startValues = [1, 1, 0, 0]

for i in range(4):

xVars[i].start = startValues[i]

# Solve model

m.optimize()

# Print solution

print('\nTOTAL COSTS: %g' % m.objVal)

for i in range(4):

print('\n xVar[%s] = %g' % i, xVars[i])

Which returns:

`Optimize a model with 3 rows, 4 columns and 12 nonzeros`

Coefficient statistics:

Matrix range [1e+00, 6e+00]

Objective range [3e+00, 9e+00]

Bounds range [0e+00, 0e+00]

RHS range [2e+00, 3e+00]

Found heuristic solution: objective 12

Presolve removed 0 rows and 1 columns

Presolve time: 0.00s

Presolved: 3 rows, 3 columns, 9 nonzeros

Loaded MIP start with objective 8

Variable types: 0 continuous, 3 integer (0 binary)

Root relaxation: infeasible, 0 iterations, 0.00 seconds

Explored 0 nodes (0 simplex iterations) in 0.00 seconds

Thread count was 8 (of 8 available processors)

Optimal solution found (tolerance 1.00e-04)

Best objective 8.000000000000e+00, best bound 8.000000000000e+00, gap 0.0%

TOTAL COSTS: 8

xVar[0] = 1

xVar[1] = 1

xVar[2] = 0

xVar[3] = 0

Answer

You are setting the start values like this

```
prob.solverModel.getVars()[0].start = 1
```

and you are then solving the model with this call

```
prob.solve().
```

The oritinal `prob`

is not changed, if you call

```
prob.solver.callSolver(prob)
```

Gurobi will use the start vector.

Source (Stackoverflow)