# How to warm-start a solver

Many solvers permit the possibility of giving a valid (or parcially valid in some cases) solution so the solver can start from that solution. This can lead to performance gains.

## Supported solver APIs

The present solver APIs that work with PuLP warm-start are the following: `CPLEX_CMD`

, `GUROBI_CMD`

, `PULP_CBC_CMD`

, `CBC_CMD`

, `CPLEX_PY`

, `GUROBI`

, `XPRESS`

, `XPRESS_PY`

.

## Example problem

We will use as example the model in A Set Partitioning Problem. At the end is the complete modified code.

## Filling a variable with a value

If a model has been previously solved, each variable has already a value. To check the value of a variable we can do it via the `value`

method of the variable.

In our example, if we solve the problem, we could just do the following afterwards:

```
x[('O', 'P', 'Q', 'R')].value() # 1.0
x[('K', 'N', 'O', 'R')].value() # 0.0
```

If we have not yet solved the model, we can use the `setInitialValue`

method to assign a value to the variable.

In our example, if we want to get those two same values, we would do the following:

```
x[('O', 'P', 'Q', 'R')].setInitialValue(1)
x[('K', 'N', 'O', 'R')].setInitialValue(0)
```

## Activating MIP start

Once we have assigned values to all variables and we want to run a model while reusing those values, we just need to pass the `warmStart=True`

argument to the solver when initiating it.

For example, using the default PuLP solver we would do:

```
seating_model.solve(pulp.PULP_CBC_CMD(msg=True, warmStart=True))
```

I usually turn `msg=True`

so I can see the messages from the solver confirming it loaded the solution correctly.

## Fixing a variable

Assigning values to variables also permits fixing those variables to that value. In order to do that, we use the `fixValue`

method of the variable.

For our example, if we know some variable needs to be 1, we can do:

```
_variable = x[('O', 'P', 'Q', 'R')]
_variable.setInitialValue(1)
_variable.fixValue()
```

This implies setting the lower bound and the upperbound to the value of the variable.

## Whole Example

If you want to see the complete code of the warm start version of the example, `click here`

or see below.

```
"""
A set partitioning model of a wedding seating problem
Adaptation where an initial solution is given to solvers: CPLEX_CMD, GUROBI_CMD, PULP_CBC_CMD
Authors: Stuart Mitchell 2009, Franco Peschiera 2019
"""
import pulp
max_tables = 5
max_table_size = 4
guests = "A B C D E F G I J K L M N O P Q R".split()
def happiness(table):
"""
Find the happiness of the table
- by calculating the maximum distance between the letters
"""
return abs(ord(table[0]) - ord(table[-1]))
# create list of all possible tables
possible_tables = [tuple(c) for c in pulp.allcombinations(guests, max_table_size)]
# create a binary variable to state that a table setting is used
x = pulp.LpVariable.dicts(
"table", possible_tables, lowBound=0, upBound=1, cat=pulp.LpInteger
)
seating_model = pulp.LpProblem("Wedding Seating Model", pulp.LpMinimize)
seating_model += pulp.lpSum([happiness(table) * x[table] for table in possible_tables])
# specify the maximum number of tables
seating_model += (
pulp.lpSum([x[table] for table in possible_tables]) <= max_tables,
"Maximum_number_of_tables",
)
# A guest must seated at one and only one table
for guest in guests:
seating_model += (
pulp.lpSum([x[table] for table in possible_tables if guest in table]) == 1,
f"Must_seat_{guest}",
)
# I've taken the optimal solution from a previous solving. x is the variable dictionary.
solution = {
("M", "N"): 1.0,
("E", "F", "G"): 1.0,
("A", "B", "C", "D"): 1.0,
("I", "J", "K", "L"): 1.0,
("O", "P", "Q", "R"): 1.0,
}
for k, v in solution.items():
x[k].setInitialValue(v)
solver = pulp.PULP_CBC_CMD(msg=True, warmStart=True)
# solver = pulp.CPLEX_CMD(msg=True, warmStart=True)
# solver = pulp.GUROBI_CMD(msg=True, warmStart=True)
# solver = pulp.CPLEX_PY(msg=True, warmStart=True)
# solver = pulp.GUROBI(msg=True, warmStart=True)
seating_model.solve(solver)
print(f"The chosen tables are out of a total of {len(possible_tables)}:")
for table in possible_tables:
if x[table].value() == 1.0:
print(table)
```