Repository: N-Wouda/ALNS

Issue:
Adaptive threshold acceptance criterion
[Máximo et al. (2021)](https://arxiv.org/abs/2012.11021v1) implements a threshold-based acceptance criterion. They do not give a specific name, but the threshold changes adaptively during the search, which is why I named it "adaptive threshold". 

>This threshold is calculated according to the average quality of the solutions obtained after the local search, which is denoted by $\bar{f}$.

Comments:

Patch:
diff --git a/alns/accept/AdaptiveThreshold.py b/alns/accept/AdaptiveThreshold.py
new file mode 100644
index 0000000..7cf0abe
--- /dev/null
+++ b/alns/accept/AdaptiveThreshold.py
@@ -0,0 +1,82 @@
+import collections
+from statistics import mean
+from typing import Deque, List
+
+
+class AdaptiveThreshold:
+    """
+    The Adaptive Threshold (AT) criterion accepts solutions
+    if the candidate solution has a value lower than an
+    adaptive threshold. The adaptive threshold is computed as:
+
+    ''adaptive_threshold =  best_solution +
+    eta_parameter * (average_solution - best_solution)''
+
+    where
+    ``best_solution`` is the best solution received so far,
+    ``average_solution`` is the average of the last
+    ``gamma_parameter`` solutions received, and
+    ``eta_parameter`` is a parameter between 0 and 1,
+    the greater the value of
+    ``eta_parameter``, the more likely it is that a solution
+    will be accepted.
+
+    Each time a new solution is received,
+    the threshold is updated. The average solution
+    and best solution are taken by the last "gamma_parameter"
+    solutions received. If the number of solutions received
+    is less than"gamma_parameter" then the threshold
+    is updated with the average of all the solutions
+    received so far.
+
+    The implementation is based on the description of AT in [1].
+
+    Parameters
+    ----------
+    eta: float
+        Used to update/tune the threshold,
+        the greater the value of ``eta_parameter``,
+        the more likely it is that a solution will be accepted.
+    gamma: int
+        Used to update the threshold, the number of solutions
+        received to compute the average & best solution.
+
+    References
+    ----------
+    .. [1] Vinícius R. Máximo, Mariá C.V. Nascimento 2021.
+           "A hybrid adaptive iterated local search with
+           diversification control to the capacitated
+           vehicle routing problem."
+           *European Journal of Operational Research*
+           294 (3): 1108 - 1119.
+    """
+
+    def __init__(self, eta: float, gamma: int):
+        if not (0 <= eta <= 1):
+            raise ValueError("eta must be in [0, 1].")
+
+        if gamma <= 0:
+            raise ValueError("gamma must be positive.")
+
+        self._eta = eta
+        self._gamma = gamma
+        self._history: Deque[float] = collections.deque(maxlen=gamma)
+
+    @property
+    def eta(self) -> float:
+        return self._eta
+
+    @property
+    def gamma(self) -> int:
+        return self._gamma
+
+    @property
+    def history(self) -> List[float]:
+        return list(self._history)
+
+    def __call__(self, rnd, best, current, candidate) -> bool:
+        self._history.append(candidate.objective())
+        best_solution = min(self._history)
+        avg_solution = mean(self._history)
+        threshold = best_solution + self._eta * (avg_solution - best_solution)
+        return candidate.objective() <= threshold


Test patch:
diff --git a/alns/accept/tests/test_adaptive_threshold.py b/alns/accept/tests/test_adaptive_threshold.py
new file mode 100644
index 0000000..e22ad39
--- /dev/null
+++ b/alns/accept/tests/test_adaptive_threshold.py
@@ -0,0 +1,122 @@
+import numpy.random as rnd
+from numpy.testing import assert_, assert_equal, assert_raises
+from pytest import mark
+
+from alns.accept.AdaptiveThreshold import AdaptiveThreshold
+from alns.tests.states import One, Two, VarObj, Zero
+
+
+@mark.parametrize(
+    "eta, gamma",
+    [
+        (-1, 3),  # eta cannot be < 0
+        (2, 3),  # eta cannot be > 1
+        (0.5, -2),  # gamma cannot be < 0
+    ],
+)
+def test_raise_invalid_parameters(eta, gamma):
+    with assert_raises(ValueError):
+        AdaptiveThreshold(eta=eta, gamma=gamma)
+
+
+@mark.parametrize("eta, gamma", [(1, 3), (0.4, 4)])
+def test_no_raise_valid_parameters(eta, gamma):
+    AdaptiveThreshold(eta=eta, gamma=gamma)
+
+
+@mark.parametrize("eta", [0, 0.01, 0.5, 0.99, 1])
+def test_eta(eta):
+    adaptive_threshold = AdaptiveThreshold(eta, 3)
+    assert_equal(adaptive_threshold.eta, eta)
+
+
+@mark.parametrize("gamma", range(1, 10))
+def test_gamma(gamma):
+    adaptive_threshold = AdaptiveThreshold(0.5, gamma)
+    assert_equal(adaptive_threshold.gamma, gamma)
+
+
+def test_accepts_below_threshold():
+    adaptive_threshold = AdaptiveThreshold(eta=0.5, gamma=4)
+    adaptive_threshold(rnd.RandomState(), One(), One(), One())
+    adaptive_threshold(rnd.RandomState(), One(), One(), Zero())
+    result = adaptive_threshold(rnd.RandomState(), One(), One(), Zero())
+
+    # The threshold is set at 0 + 0.5 * (0.5 - 0) = 0.25
+    assert_(result)
+
+
+def test_rejects_above_threshold():
+    adaptive_threshold = AdaptiveThreshold(eta=0.5, gamma=4)
+    adaptive_threshold(rnd.RandomState(), One(), One(), Two())
+    adaptive_threshold(rnd.RandomState(), One(), One(), Zero())
+    result = adaptive_threshold(rnd.RandomState(), One(), One(), One())
+
+    # The threshold is set at 0 + 0.5 * (1 - 0) = 0.5
+    assert_(not result)
+
+
+def test_accepts_equal_threshold():
+    adaptive_threshold = AdaptiveThreshold(eta=0.5, gamma=4)
+    adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7100))
+    adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7200))
+    result = adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7120))
+
+    # The threshold is set at 7100 + 0.5 * (7140 - 7100) = 7120
+    assert_(result)
+
+
+def test_accepts_over_gamma_candidates():
+    adaptive_threshold = AdaptiveThreshold(eta=0.2, gamma=3)
+    adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7100))
+    adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7200))
+    adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7200))
+    result = adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7000))
+
+    # The threshold is set at 7000 + 0.2 * (7133.33 - 7000) = 7013.33
+    assert_(result)
+
+
+def test_rejects_over_gamma_candidates():
+    adaptive_threshold = AdaptiveThreshold(eta=0.2, gamma=3)
+    adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7100))
+    adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7200))
+    adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7200))
+    adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7000))
+    result = adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7100))
+
+    # The threshold is set at 7000 + 0.2 * (7100 - 7000) = 7020
+    assert_(not result)
+
+
+def test_evaluate_consecutive_solutions():
+    """
+    Test if AT correctly accepts and rejects consecutive solutions.
+    """
+    adaptive_threshold = AdaptiveThreshold(eta=0.5, gamma=4)
+
+    result = adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7100))
+    # The threshold is set at 7100, hence the solution is accepted
+    assert_(result)
+
+    result = adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7200))
+    # The threshold is set at 7125, hence the solution is accepted
+    assert_(not result)
+
+    result = adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7120))
+    # The threshold is set at 7120, hence the solution is accepted
+    assert_(result)
+
+
+def test_history():
+    """
+    Test if AT correctly stores the history of the thresholds correctly.
+    """
+    adaptive_threshold = AdaptiveThreshold(eta=0.5, gamma=4)
+
+    adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7100))
+    adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7200))
+    adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7120))
+    adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7100))
+    adaptive_threshold(rnd.RandomState(), One(), One(), VarObj(7200))
+    assert_equal(adaptive_threshold.history, [7200, 7120, 7100, 7200])