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jupytext:
  text_representation:
    extension: .md
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  language: python
  name: python3
---

Solve with multiple adapters and compare the results
======================================================

Since the OMMX Adapter provides a unified API, you can solve the same problem using multiple solvers and compare the results. Let's consider a simple knapsack problem as an example:

$$
\begin{aligned}
\mathrm{maximize} \quad & \sum_{i=0}^{N-1} v_i x_i \\
\mathrm{s.t.} \quad & \sum_{i=0}^{n-1} w_i x_i - W \leq 0, \\
& x_{i} \in \{ 0, 1\} 
\end{aligned}
$$

```{code-cell} ipython3
from ommx.v1 import Instance, DecisionVariable

v = [10, 13, 18, 31, 7, 15]
w = [11, 25, 20, 35, 10, 33]
W = 47
N = len(v)

x = [
    DecisionVariable.binary(
        id=i,
        name="x",
        subscripts=[i],
    )
    for i in range(N)
]
instance = Instance.from_components(
    decision_variables=x,
    objective=sum(v[i] * x[i] for i in range(N)),
    constraints={0: sum(w[i] * x[i] for i in range(N)) - W <= 0},
    sense=Instance.MAXIMIZE,
)
```

## Solve with multiple adapters

Here, we will use OSS adapters developed as a part of OMMX Python SDK.
For non-OSS solvers, adapters are also available and can be used with the same interface.
A complete list of supported adapters for each solver can be found in [Supported Adapters](../user_guide/supported_ommx_adapters.md).

Here, let's solve the knapsack problem with OSS solvers, Highs, SCIP.

```{code-cell} ipython3
from ommx_highs_adapter import OMMXHighsAdapter
from ommx_pyscipopt_adapter import OMMXPySCIPOptAdapter


# List of adapters to use
adapters = {
    "highs": OMMXHighsAdapter,
    "scip": OMMXPySCIPOptAdapter,
}

# Solve the problem using each adapter
solutions = {
    name: adapter.solve(instance) for name, adapter in adapters.items()
}
```

## Compare the results

Since this knapsack problem is simple, all solvers will find the optimal solution.

```{code-cell} ipython3
from matplotlib import pyplot as plt

marks = {
    "highs": "o",
    "scip": "+",
}

for name, solution in solutions.items():
    x = solution.extract_decision_variables("x")
    subscripts = [key[0] for key in x.keys()]
    plt.plot(subscripts, x.values(), marks[name], label=name)

plt.legend()
```

It would be convenient to concatenate the `pandas.DataFrame` obtained with `decision_variables_df` when analyzing the results of multiple solvers.

```{code-cell} ipython3
import pandas

decision_variables = pandas.concat([
    solution.decision_variables_df.assign(solver=solver)
    for solver, solution in solutions.items()
])
decision_variables
```