Merge pull request #418 from zStupan/fix-problem-definitions

Fix problem definitions

niapy/problems/bent_cigar.py

@@ -27,7 +27,7 @@ class BentCigar(Problem):
         evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
 
         **Global minimum:**
-        :math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)`
+        :math:`f(x^*) = 0`, at :math:`x_i^* = 0`
 
     LaTeX formats:
         Inline:

niapy/problems/discus.py

@@ -27,7 +27,7 @@ class Discus(Problem):
         evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
 
         **Global minimum:**
-        :math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)`
+        :math:`f(x^*) = 0`, at :math:`x_i^* = 0`
 
     LaTeX formats:
         Inline:

niapy/problems/elliptic.py

@@ -27,7 +27,7 @@ class Elliptic(Problem):
         evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
 
         **Global minimum:**
-        :math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)`
+        :math:`f(x^*) = 0`, at :math:`x_i^* = 0`
 
     LaTeX formats:
         Inline:
@@ -70,4 +70,4 @@ def latex_code():
 
     def _evaluate(self, x):
         indices = np.arange(self.dimension)
-        return np.sum(1000000.0 ** (indices / (self.dimension - 1)) * x)
+        return np.sum(1000000.0 ** (indices / (self.dimension - 1)) * x ** 2)

niapy/problems/griewank.py

@@ -96,7 +96,7 @@ class ExpandedGriewankPlusRosenbrock(Problem):
         evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
 
         **Global minimum:**
-        :math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)`
+        :math:`f(x^*) = 0`, at :math:`x_i^* = 0`
 
     LaTeX formats:
         Inline:

niapy/problems/hgbat.py

@@ -26,7 +26,7 @@ class HGBat(Problem):
         evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
 
         **Global minimum:**
-        :math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)`
+        :math:`f(x^*) = 0`, at :math:`x_i^* = -1`
 
     LaTeX formats:
         Inline:

niapy/problems/katsuura.py

@@ -2,7 +2,7 @@
 
 """Implementations of Katsuura functions."""
 
-from math import fabs
+import numpy as np
 from niapy.problems.problem import Problem
 
 __all__ = ['Katsuura']
@@ -20,25 +20,25 @@ class Katsuura(Problem):
     Function:
         **Katsuura Function**
 
-        :math:`f(\textbf{x}) = \frac{10}{D^2} \prod_{i=1}^D \left( 1 + i \sum_{j=1}^{32} \frac{\lvert 2^j x_i - round\left(2^j x_i \right) \rvert}{2^j} \right)^\frac{10}{D^{1.2}} - \frac{10}{D^2}`
+        :math:`f(\textbf{x}) = \prod_{i=1}^D \left( 1 + i \sum_{j=1}^{32} \frac{\lvert 2^j x_i - round\left(2^j x_i \right) \rvert}{2^j} \right)`
 
         **Input domain:**
         The function can be defined on any input domain but it is usually
         evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
 
-        **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)`
+        **Global minimum:** :math:`f(x^*) = 1`, at :math:`x_i^* = 0`
 
     LaTeX formats:
         Inline:
-            $f(\textbf{x}) = \frac{10}{D^2} \prod_{i=1}^D \left( 1 + i \sum_{j=1}^{32} \frac{\lvert 2^j x_i - round\left(2^j x_i \right) \rvert}{2^j} \right)^\frac{10}{D^{1.2}} - \frac{10}{D^2}$
+            $f(\textbf{x}) = \prod_{i=1}^D \left( 1 + i \sum_{j=1}^{32} \frac{\lvert 2^j x_i - round\left(2^j x_i \right) \rvert}{2^j} \right)$
         Equation:
-            \begin{equation} f(\textbf{x}) = \frac{10}{D^2} \prod_{i=1}^D \left( 1 + i \sum_{j=1}^{32} \frac{\lvert 2^j x_i - round\left(2^j x_i \right) \rvert}{2^j} \right)^\frac{10}{D^{1.2}} - \frac{10}{D^2} \end{equation}
+            \begin{equation} f(\textbf{x}) = \prod_{i=1}^D \left( 1 + i \sum_{j=1}^{32} \frac{\lvert 2^j x_i - round\left(2^j x_i \right) \rvert}{2^j} \right)\end{equation}
 
         Domain:
             $-100 \leq x_i \leq 100$
 
     Reference:
-        http://www5.zzu.edu.cn/__local/A/69/BC/D3B5DFE94CD2574B38AD7CD1D12_C802DAFE_BC0C0.pdf
+        Adorio, E. P., & Diliman, U. P. MVF - Multivariate Test Functions Library in C for Unconstrained Global Optimization (2005). 
 
     """
 
@@ -64,13 +64,10 @@ def latex_code():
             str: Latex code.
 
         """
-        return r'''$f(\textbf{x}) = \frac{10}{D^2} \prod_{i=1}^D \left( 1 + i \sum_{j=1}^{32} \frac{| 2^j x_i - round\left(2^j x_i \right) |}{2^j} \right)^\frac{10}{D^{1.2}} - \frac{10}{D^2}$'''
+        return r'''$f(\textbf{x}) = \prod_{i=1}^D \left( 1 + i \sum_{j=1}^{32} \frac{| 2^j x_i - round\left(2^j x_i \right) |}{2^j} \right)$'''
 
     def _evaluate(self, x):
-        val = 1.0
-        for i in range(self.dimension):
-            val_t = 1.0
-            for j in range(1, 33):
-                val_t += fabs(2 ** j * x[i] - round(2 ** j * x[i])) / 2 ** j
-            val *= (1 + (i + 1) * val_t) ** (10 / self.dimension ** 1.2) - (10 / self.dimension ** 2)
-        return 10 / self.dimension ** 2 * val
+        k = np.atleast_2d(np.arange(1, 33)).T
+        i = np.arange(1, self.dimension + 1)
+        inner = np.round(2 ** k * x) * (2.0 ** (-k))
+        return np.prod(np.sum(inner, axis=0) * i + 1)

niapy/problems/powell.py

@@ -69,10 +69,10 @@ def latex_code():
         return r'''$f(\textbf{x}) = \sum_{i = 1}^{D / 4} \left( (x_{4 i - 3} + 10 x_{4 i - 2})^2 + 5 (x_{4 i - 1} - x_{4 i})^2 + (x_{4 i - 2} - 2 x_{4 i - 1})^4 + 10 (x_{4 i - 3} - x_{4 i})^4 \right)$'''
 
     def _evaluate(self, x):
-        x1 = x[range(1, self.dimension - 3, 4)]
-        x2 = x[range(2, self.dimension - 2, 4)]
-        x3 = x[range(3, self.dimension - 1, 4)]
-        x4 = x[range(4, self.dimension, 4)]
+        x1 = x[0::4]
+        x2 = x[1::4]
+        x3 = x[2::4]
+        x4 = x[3::4]
 
         term1 = (x1 + 10 * x2) ** 2.0
         term2 = 5 * (x3 - x4) ** 2.0

niapy/problems/quintic.py

@@ -26,7 +26,7 @@ class Quintic(Problem):
         The function can be defined on any input domain but it is usually
         evaluated on the hypercube :math:`x_i ∈ [-10, 10]`, for all :math:`i = 1, 2,..., D`.
 
-        **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = f(-1\; \text{or}\; 2)`
+        **Global minimum:** :math:`f(x^*) = 0`, at :math:`x_i^* = -1`
 
     LaTeX formats:
         Inline:

niapy/problems/salomon.py

@@ -75,5 +75,5 @@ def latex_code():
                 \right)+ 0.1 \sqrt{\sum_{i=1}^D x_i^2}$'''
 
     def _evaluate(self, x):
-        val = np.sum(x ** 2.0)
-        return 1.0 - np.cos(2.0 * np.pi * np.sqrt(val)) + 0.1 * val
+        val = np.sqrt(np.sum(x ** 2.0))
+        return 1.0 - np.cos(2.0 * np.pi * val) + 0.1 * val

niapy/problems/schaffer.py

@@ -23,9 +23,9 @@ class SchafferN2(Problem):
 
     **Input domain:**
     The function can be defined on any input domain but it is usually
-    evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
+    evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2`.
 
-    **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)`
+    **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0, 0)`
 
     LaTeX formats:
         Inline:
@@ -85,9 +85,9 @@ class SchafferN4(Problem):
 
     **Input domain:**
         The function can be defined on any input domain but it is usually
-        evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
+        evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2`.
 
-    **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)`
+    **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0, 0)`
 
     LaTeX formats:
         Inline:
@@ -143,13 +143,18 @@ class ExpandedSchaffer(Problem):
 
     Function:
         **Expanded Schaffer Function**
-        :math:`f(\textbf{x}) = g(x_D, x_1) + \sum_{i=2}^D g(x_{i - 1}, x_i) \\ g(x, y) = 0.5 + \frac{\sin \left(\sqrt{x^2 + y^2} \right)^2 - 0.5}{\left( 1 + 0.001 (x^2 + y^2) \right)}^2`
+
+        .. math::
+
+           f(\textbf{x}) = g(x_D, x_1) + \sum_{i=2}^D g(x_{i - 1}, x_i)
+
+           g(x, y) = 0.5 + \frac{\sin \left(\sqrt{x^2 + y^2} \right)^2 - 0.5}{\left( 1 + 0.001 (x^2 + y^2) \right)}^2`
 
     **Input domain:**
         The function can be defined on any input domain but it is usually
         evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
 
-    **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)`
+    **Global minimum:** :math:`f(x^*) = 0`, at :math:`x_i^* = 0`
 
     LaTeX formats:
         Inline:

niapy/problems/schwefel.py

@@ -68,7 +68,7 @@ def latex_code():
         return r'''$f(\textbf{x}) = 418.9829d - \sum_{i=1}^{D} x_i \sin(\sqrt{\lvert x_i \rvert})$'''
 
     def _evaluate(self, x):
-        return 418.9829 * self.dimension - np.sum(x * np.sin(np.sqrt(np.abs(x))))
+        return 418.982887272433799807913601398 * self.dimension - np.sum(x * np.sin(np.sqrt(np.abs(x))))
 
 
 class Schwefel221(Problem):

niapy/problems/styblinski_tang.py

@@ -26,7 +26,7 @@ class StyblinskiTang(Problem):
         The function can be defined on any input domain but it is usually
         evaluated on the hypercube :math:`x_i ∈ [-5, 5]`, for all :math:`i = 1, 2,..., D`.
 
-        **Global minimum:** :math:`f(x^*) = -78.332`, at :math:`x^* = (-2.903534,...,-2.903534)`
+        **Global minimum:** :math:`f(x^*) = -39.16616570377142d`, at :math:`x_i^* = -2.903534018185960`
 
     LaTeX formats:
         Inline:

niapy/problems/weierstrass.py

@@ -26,7 +26,7 @@ class Weierstrass(Problem):
         evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
         Default value of a = 0.5, b = 3 and k_max = 20.
 
-        **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)`
+        **Global minimum:** :math:`f(x^*) = 0`, at :math:`x_i^* = 0`
 
     LaTeX formats:
         Inline:
@@ -44,7 +44,7 @@ class Weierstrass(Problem):
     """
 
     def __init__(self, dimension=4, lower=-100.0, upper=100.0, a=0.5, b=3, k_max=20, *args, **kwargs):
-        r"""Initialize Bent Cigar problem..
+        r"""Initialize Weierstrass problem..
 
         Args:
             dimension (Optional[int]): Dimension of the problem.
@@ -74,13 +74,8 @@ def latex_code():
         return r'''$f(\textbf{x}) = \sum_{i=1}^D \left( \sum_{k=0}^{k_{max}} a^k \cos\left( 2 \pi b^k ( x_i + 0.5) \right) \right) - D \sum_{k=0}^{k_{max}} a^k \cos \left( 2 \pi b^k \cdot 0.5 \right)$'''
 
     def _evaluate(self, x):
-        val1 = 0.0
-        for i in range(self.dimension):
-            val = 0.0
-            for k in range(self.k_max):
-                val += self.a ** k * np.cos(2.0 * np.pi * self.b ** k * (x[i] + 0.5))
-            val1 += val
-        val2 = 0.0
-        for k in range(self.k_max):
-            val2 += self.a ** k * np.cos(2 * np.pi * self.b ** k * 0.5)
-        return val1 - self.dimension * val2
+        k = np.atleast_2d(np.arange(self.k_max + 1)).T
+        t1 = self.a ** k * np.cos(2 * np.pi * self.b ** k * (x + 0.5))
+        t2 = self.dimension * np.sum(self.a ** k.T * np.cos(np.pi * self.b ** k.T))
+
+        return np.sum(np.sum(t1, axis=0)) - t2