# Implementing a Novel Algorithm

Note

**TL;DR:**
Your function needs to be callable as: ```
func(profits, weights, capacities,
*args)
```

and needs to return `assignments`

in the binary form.

If you want to implement and test a novel solution algorithm for the QMKP, you
simply need to write a Python function that takes `profits`

as first
argument, `weights`

as second, and `capacities`

as third argument.
Beyond that, it can have an arbitrary number of additional arguments.
However, it needs to be possible to pass them positionally.

The return of the function needs to be the assignment matrix in binary form.

The following example is also illustrated in a Jupyter notebook that you can either run locally or using an online service like Binder.

## Example

As an example, we want to implement the following algorithm

Assign the item \(i\) with the smallest weight \(w_i\) to the first knapsack \(k\) where it fits, i.e., where \(c_k \geq w_i\).

Obviously, this algorithm ignores the profits and will not yield very good results. However, it only serves demonstration purposes.

### Algorithm Implementation

The above algorithm could be implemented as follows

```
1def example_algorithm(profits, weights, capacities):
2 assignments = np.zeros((len(weights), len(capacities)))
3 remaining_capacities = np.copy(capacities)
4 items_by_weight = np.argsort(weights)
5 for _item in items_by_weight:
6 _weight = weights[_item]
7 _first_ks = np.argmax(remaining_capacities >= _weight)
8 assignments[_item, _first_ks] = 1
9 remaining_capacities[_first_ks] -= _weight
10 return assignments
```

It should be emphasized that you should **not** modify any of the input arrays,
e.g., `capacities`

inplace, since this could lead to unintended consequences.

### Using the Algorithm

The newly implemented algorithm can then easily be used as follows.

```
1import numpy as np
2from qmkpy import total_profit_qmkp, QMKProblem
3from qmkpy import algorithms
4
5weights = [5, 2, 3, 4] # four items
6capacities = [1, 5, 5, 6, 2] # five knapsacks
7profits = np.array([[3, 1, 0, 2],
8 [1, 1, 1, 4],
9 [0, 1, 2, 2],
10 [2, 4, 2, 3]]) # symmetric profit matrix
11
12qmkp = QMKProblem(profits, weights, capacities)
13qmkp.algorithm = example_algorithm
14assignments, total_profit = qmkp.solve()
15
16print(assignments)
17print(total_profit)
```

## Contributing a New Algorithm to the Package

When you feel that your algorithm should be added to the QMKPy package, please follow the following steps:

Place your code in the

`qmkpy.algorithms`

module, i.e., in the`qmkpy/algorithms.py`

file.Make sure that you added documentation in form of a docstring. This should also include possible references to literature, if the algorithm is taken from any published work.

Make sure that all unit tests pass. In order to do this, add your algorithm to the

`SOLVERS`

list in the test file`tests/test_algorithms.py`

. Additionally, you should create a new test file`tests/test_algorithm_<your_algo>.py`

which includes tests that are specific to your algorithm, e.g., testing different parameter constellations. You can run all tests using the`pytest`

command.