Merge pull request #196 from jpajasmaa/desdeo2

added zdt2 and zdt3 test problems
industrial-optimization-group · Dec 2, 2024 · ebdc2a3 · ebdc2a3
2 parents 0cc656d + 89fb4ff
commit ebdc2a3
Showing 1 changed file with 175 additions and 5 deletions.
diff --git a/desdeo/problem/testproblems.py b/desdeo/problem/testproblems.py
@@ -348,7 +348,7 @@ def simple_test_problem() -> Problem:
 def zdt1(number_of_variables: int) -> Problem:
     r"""Defines the ZDT1 test problem.
 
-    The problem has a variable number of decision variables and two objective functions to be minimized as 
+    The problem has a variable number of decision variables and two objective functions to be minimized as
     follows:
 
     \begin{align*}
@@ -388,13 +388,25 @@ def zdt1(number_of_variables: int) -> Problem:
     ]
 
     objectives = [
-        Objective(name="f_1", symbol=f1_symbol, func=f1_expr, maximize=False, ideal=0, nadir=1),
-        Objective(name="f_2", symbol=f2_symbol, func=f2_expr, maximize=False, ideal=0, nadir=1),
+        Objective(name="f_1", symbol=f1_symbol, func=f1_expr, maximize=False, ideal=0, nadir=1,
+                  is_convex=True,
+                  is_linear=True,
+                  is_twice_differentiable=True),
+        Objective(name="f_2", symbol=f2_symbol, func=f2_expr, maximize=False, ideal=0, nadir=1,
+                  is_convex=True,
+                  is_linear=False,
+                  is_twice_differentiable=True),
     ]
 
     extras = [
-        ExtraFunction(name="g", symbol=g_symbol, func=g_expr),
-        ExtraFunction(name="h", symbol=h_symbol, func=h_expr),
+        ExtraFunction(name="g", symbol=g_symbol, func=g_expr,
+                      is_convex=True,
+                      is_linear=True,
+                      is_twice_differentiable=True),
+        ExtraFunction(name="h", symbol=h_symbol, func=h_expr,
+                      is_convex=True,
+                      is_linear=False,
+                      is_twice_differentiable=True),
     ]
 
     return Problem(
@@ -403,9 +415,167 @@ def zdt1(number_of_variables: int) -> Problem:
         variables=variables,
         objectives=objectives,
         extra_funcs=extras,
+        is_convex=True,
+        is_linear=False,
+        is_twice_differentiable=True
     )
 
 
+def zdt2(n_variables: int) -> Problem:
+    r"""Defines the ZDT2 test problem.
+
+    The problem has a variable number of decision variables and two objective functions to be minimized as
+    follows:
+
+    \begin{align*}
+        \min\quad f_1(\textbf{x}) &= x_1 \\
+        \min\quad f_2(\textbf{x}) &= g(\textbf{x}) \cdot h(f_1(\textbf{x}), g(\textbf{x}))\\
+        g(\textbf{x}) &= 1 + \frac{9}{n-1} \sum_{i=2}^{n} x_i \\
+        h(f_1, g) &= 1 - \left({\frac{f_1}{g}}\right)^2, \\
+    \end{align*}
+
+    where $f_1$ and $f_2$ are objective functions, $x_1,\dots,x_n$ are decision variable, $n$
+    is the number of decision variables,
+    and $g$ and $h$ are auxiliary functions.
+    """
+    n = n_variables
+
+    # function f_1
+    f1_symbol = "f_1"
+    f1_expr = "x_1"
+
+    # function g
+    g_symbol = "g"
+    g_expr_1 = f"1 + (9 / ({n} - 1))"
+    g_expr_2 = "(" + " + ".join([f"x_{i}" for i in range(2, n + 1)]) + ")"
+    g_expr = g_expr_1 + " * " + g_expr_2
+
+    # function h(f, g)
+    h_symbol = "h"
+    h_expr = f"1 - (({f1_expr}) / ({g_expr})) ** 2"
+
+    # function f_2
+    f2_symbol = "f_2"
+    f2_expr = f"{g_symbol} * {h_symbol}"
+
+    variables = [
+        Variable(name=f"x_{i}", symbol=f"x_{i}", variable_type="real", lowerbound=0, upperbound=1, initial_value=0.5)
+        for i in range(1, n + 1)
+    ]
+
+    objectives = [
+        Objective(name="f_1", symbol=f1_symbol, func=f1_expr, maximize=False, ideal=0, nadir=1,
+                  is_convex=True,
+                  is_linear=True,
+                  is_twice_differentiable=True
+                  ),
+        Objective(name="f_2", symbol=f2_symbol, func=f2_expr, maximize=False, ideal=0, nadir=1,
+                  is_convex=False,
+                  is_linear=False,
+                  is_twice_differentiable=True),
+    ]
+
+    extras = [
+        ExtraFunction(name="g", symbol=g_symbol, func=g_expr,
+                      is_convex=True,
+                      is_linear=True,
+                      is_twice_differentiable=True
+                      ),
+        ExtraFunction(name="h", symbol=h_symbol, func=h_expr,
+                      is_convex=False,
+                      is_linear=False,
+                      is_twice_differentiable=True
+                      ),
+    ]
+
+    return Problem(
+        name="zdt2",
+        description="The ZDT2 test problem.",
+        variables=variables,
+        objectives=objectives,
+        extra_funcs=extras,
+        is_convex=False,
+        is_linear=False,
+        is_twice_differentiable=True
+    )
+
+def zdt3(n_variables: int,) -> Problem:
+    r"""Defines the ZDT3 test problem.
+
+    The problem has a variable number of decision variables and two objective functions to be minimized as
+    follows:
+
+    \begin{align*}
+        \min\quad f_1(x) &= x_1 \\
+        \min\quad f_2(x) &= g(\textbf{x}) \cdot h(f_1(\textbf{x}), g(\textbf{x}))\\
+        g(\textbf{x}) &= 1 + \frac{9}{n-1} \sum_{i=2}^{n} x_i \\
+         h(f_1, g) &= 1 - \sqrt{\frac{f_1}{g}} - \frac{f_1}{g} \sin(10\pi f_1)), \\
+    \end{align*}
+
+    where $f_2$ and $f_2$ are objective functions, $x_1,\dots,x_n$ are decision variable, $n$
+    is the number of decision variables,
+    and $g$ and $h$ are auxiliary functions.
+    """
+    n = n_variables
+
+    # function f_1
+    f1_symbol = "f_1"
+    f1_expr = "x_1"
+
+    # function g
+    g_symbol = "g"
+    g_expr_1 = f"1 + (9 / ({n} - 1))"
+    g_expr_2 = "(" + " + ".join([f"x_{i}" for i in range(2, n + 1)]) + ")"
+    g_expr = g_expr_1 + " * " + g_expr_2
+
+    # function h(f, g)
+    h_symbol = "h"
+    h_expr = f"1 - Sqrt(({f1_expr}) / ({g_expr})) - (({f1_expr}) / ({g_expr})) * Sin (10 * {np.pi} * {f1_expr}) "
+
+    # function f_2
+    f2_symbol = "f_2"
+    f2_expr = f"{g_symbol} * {h_symbol}"
+
+    variables = [
+        Variable(name=f"x_{i}", symbol=f"x_{i}", variable_type="real", lowerbound=0, upperbound=1, initial_value=0.5)
+        for i in range(1, n + 1)
+    ]
+
+    objectives = [
+        Objective(name="f_1", symbol=f1_symbol, func=f1_expr, maximize=False, ideal=0, nadir=1,
+                  is_convex=True,
+                  is_linear=True,
+                  is_twice_differentiable=True),
+        Objective(name="f_2", symbol=f2_symbol, func=f2_expr, maximize=False, ideal=-1, nadir=1,
+                  is_convex=False,
+                  is_linear=False,
+                  is_twice_differentiable=True),
+    ]
+
+    extras = [
+        ExtraFunction(name="g", symbol=g_symbol, func=g_expr,
+                      is_convex=True,
+                      is_linear=True,
+                      is_twice_differentiable=True
+                      ),
+        ExtraFunction(name="h", symbol=h_symbol, func=h_expr,
+                      is_convex=False,
+                      is_linear=False,
+                      is_twice_differentiable=True
+                      ),
+    ]
+
+    return Problem(
+        name="zdt3",
+        description="The ZDT3 test problem.",
+        variables=variables,
+        objectives=objectives,
+        extra_funcs=extras,
+        is_convex=False,
+        is_linear=False,
+        is_twice_differentiable=True
+    )
+
 def simple_data_problem() -> Problem:
     """Defines a simple problem with only data-based objective functions."""
     constants = [Constant(name="c", symbol="c", value=1000)]