How to set MIP start (initial solution) with Gurobi solver from PuLP?
<p>I'm using the <code>PuLP</code> module in Python to formulate a mixed integer program. I am trying to work out how to set a <code>MIP start</code> (i.e. a feasible solution for the program to start from) via the <code>PuLP</code> interface.</p>

<p>Details on how to set <code>MIP start</code> are given <a href="https://www.gurobi.com/documentation/6.5/examples/mip_starts.html" rel="noreferrer">here</a></p>

<p>And the developer of the <code>PuLP</code> package claims that you can access the full Gurobi model via the <code>PuLP</code> interface <a href="https://groups.google.com/forum/#!topic/pulp-or-discuss/-aiL7jQyD-k" rel="noreferrer">here</a></p>

<p>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.</p>

<p>I have attempted to set an initial solution (to the optimal values) in both models, but in the <code>PuLP</code> model it is ignored, but in the <code>gurobipy</code> model it works as expected.</p>

<p>How do you set an initial solution for the Gurobi solve via the PuLP interface?</p>

<pre><code>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 &gt;= 2, "Con1"
prob += -5*x1 + 3*x2 + x3 + 3*x4 &gt;= -2, "Con2"
prob += 5*x1 - x2 + 4*x3 - 2*x4 &gt;= 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)
</code></pre>

<p>Which returns:</p>

<pre><code>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
</code></pre>

<p>Secondly I can implement the same model using the <code>gurobipy</code> module, but in this case the MIP start is actually used:</p>

<pre><code>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] &gt;= 2, "Con1")
m.addConstr(-5*xVars[0] + 3*xVars[1] + xVars[2] + 3*xVars[3] &gt;= -2, "Con2")
m.addConstr(5*xVars[0] - xVars[1] + 4*xVars[2] - 2*xVars[3] &gt;= 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])
</code></pre>

<p>Which returns:</p>

<pre><code>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
</code></pre>