# 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 in performance gains.

## Supported solver APIs¶

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

, `GUROBI_CMD`

, `PULP_CBC_CMD`

, `CBC_CMD`

. `CPLEX_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 `mip_start=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, mip_start=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 mip 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 += sum([happiness(table) * x[table] for table in possible_tables])
# specify the maximum number of tables
seating_model += sum([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 += sum([x[table] for table in possible_tables
if guest in table]) == 1, "Must_seat_%s" % 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=1, mip_start=1)
# solver = pulp.CPLEX_CMD(msg=1, mip_start=1)
# solver = pulp.GUROBI_CMD(msg=1, mip_start=1)
seating_model.solve(solver)
print("The choosen tables are out of a total of %s:" % len(possible_tables))
for table in possible_tables:
if x[table].value() == 1.0:
print(table)
```