Emil_Shanaty/Internal_Point
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update implementation and format

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This commit is contained in:
Ilya Grigorev
2024-11-02 20:20:33 +05:00
parent 4dce78c370
commit 9fb3634e9b
1 changed files with 83 additions and 105 deletions
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main.py
+83 -105
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@@ -14,15 +14,17 @@ class Result:
objective_function_value: Optional[np.float64]
solution: Optional[np.array]
maximize: bool
def __init__(self,
state: State,
objective_function_value: Optional[np.array] = None,
solution: np.float64 = None, maximize:bool = True):
solution: np.float64 = None, maximize: bool = True):
self.state = state
self.objective_function_value = objective_function_value
self.solution = solution
self.maximize = maximize
#def print_initial_inputs(Vector &C, Matrix &A, Vector &b, double eps, bool maximize)
def print_initial_inputs(
C: np.array, # Vector of objective function coefficients
A: np.array, # Matrix of constraint coefficients
@@ -37,65 +39,59 @@ def print_initial_inputs(
print(f"alpha: {alpha}")
print(f"x_0: {x_0} \n")
if (maximize):
print("Maximize")
else:
print("Minimize")
z_str = "z = "
previousIsZero = True
lastNonZero = False
for i in range(len(C)):
isNegative = False;
isNegative = False
for k in range(len(C)):
if (C[k] == 0):
lastNonZero = True
else:
lastNonZero = False
break
if (not previousIsZero and not lastNonZero):
z_str += " + ";
z_str += " + "
if (C[i] != 0):
if (C[i] != 1):
if (C[i] < 0):
isNegative = True
z_str += "("
z_str += str(C[i]) + " * "
z_str += "x" + str(i + 1)
if (isNegative):
z_str += ")"
previousIsZero = False
else:
previousIsZero = True
print(z_str)
print("\nsubject to the constrains:\n");
print("\nsubject to the constrains:\n")
for i in range(len(b)):
c_str = ""
previousIsZero = True
lastNonZero = False
for j in range(len(A[i])):
#for (int j = 0; j < A.getColumns(); j++)
isNegative = False
for k in range(j, len(A[i])):
#for (int k = j; k < A[i].size(); k++)
if (A[i][k] == 0):
lastNonZero = True
else:
lastNonZero = False
@@ -103,57 +99,51 @@ def print_initial_inputs(
if (not previousIsZero and not lastNonZero):
c_str += " + "
if (A[i][j] != 0):
if (A[i][j] != 0):
if (A[i][j] != 1):
if (A[i][j] < 0):
isNegative = True
c_str += "("
c_str += str(A[i][j]) + " * "
c_str += "x" + str(j + 1)
if (isNegative):
c_str += ")"
previousIsZero = False
else:
previousIsZero = True
c_str += " <= " + str(b[i])
print(c_str)
def print_result(result:Result):
def print_result(result: Result):
if (result.state == State.INAPPLICABLE):
print("The method is not applicable!")
elif (result.state == State.UNSOLVED ):
elif (result.state == State.UNSOLVED):
print("Unsolved problem!")
else:
print("SOLVED!")
decVar_str = ""
decVar_str +="Decision variables: ["
decVar_str += "Decision variables: ["
for i in range(len(result.solution)):
#for (int i = 0; i < result.solution.size(); i++)
decVar_str += str(result.solution[i])
if (i != len(result.solution) - 1):
decVar_str += ", "
decVar_str += "]"
print(decVar_str)
res_str = ""
if (result.maximize):
res_str += "Maximum "
else:
res_str += "Minimum "
res_str += f"objective function value: {result.objective_function_value}"
print(res_str)
return 0
@@ -162,41 +152,34 @@ def print_result(result:Result):
def interior_point(
C: np.array, # Vector of objective function coefficients
A: np.array, # Matrix of constraint coefficients
b: np.array, # Vector of right-hand side values of constraints
x_0: np.array, # Initial point (vector)
b: np.array, # Vector of right-hand side values of constraints
eps: np.float64 = 0.01, # Solution accuracy
alpha: np.float64 = 0.5, # Step coefficient
maximizing: bool = True) -> Result: # Flag for maximization or minimization
# Check if the method is applicable: the initial point must satisfy the constraints
if (not np.all(np.dot(A, x_0) >= b) or np.any(x_0 == 0)):
if (not np.all(np.dot(A, x_0) <= b) or np.any(x_0 == 0)):
print(np.dot(A, x_0), b)
return Result(State.INAPPLICABLE, maximize=maximizing)
# If the problem is a minimization, invert the coefficients of the objective function
if (not maximizing):
C = -C
m = len(A) # Number of constraints
n = len(A[0]) # Number of variables
m = A.shape[0] # Number of constraints
n = A.shape[1] # Number of variables
# Initialize variables for the initial iteration
x = np.ones(n) # Solution vector
s = np.ones(m) # Slack variables vector
x_0 = np.concatenate((x_0, b-np.dot(A, x_0)))
x = x_0 # Solution vector
A = np.concatenate((A, np.eye(m)), axis=1)
C = np.concatenate((C, np.zeros(m)))
iteration = 0 # Iteration counter
while(True):
# Calculate slack variables for each constraint
for i in range(m):
slack = b[i]
for j in range(n):
slack -= A[i][j] * x[j]
s[i] = slack
# Update solution variables
for i in range(min(m, n)):
x[i] = s[i]
while (True):
# Create a diagonal matrix from the slack variables vector
D = np.diag(s)
D = np.diag(x)
# Solve the system of equations to find x*
x_star = np.dot(np.linalg.inv(D), x)
@@ -204,18 +187,21 @@ def interior_point(
C_star = np.dot(D, C)
# Form the projection matrix
I = np.eye(n)
A_star_transpose = np.transpose(A_star)
P = I - np.dot(A_star_transpose, np.linalg.inv(np.dot(A_star, A_star_transpose)))
P = np.dot(P, A_star)
P = np.eye(n+m) - np.dot(np.dot(A_star_transpose, np.linalg.inv(np.dot(A_star, A_star_transpose))), A_star)
# Calculate the gradient of the objective function
C_p = np.dot(P, C_star)
Mu = np.max(np.absolute(C_p))
Mu = np.min(C_p)
if (Mu > 0):
return Result(State.INAPPLICABLE)
# Update the value of x* considering the step size and gradient
x_star = np.ones(n+m) + alpha / np.abs(Mu) * C_p
x_new = np.dot(D, x_star)
# Check the stopping criterion based on accuracy
if Mu < eps:
result = np.dot(C, x)
if np.linalg.norm(x_new - x) <= eps:
result = np.dot(C, x) if (maximizing) else -np.dot(C, x)
return Result(State.SOLVED, objective_function_value=result, solution=x, maximize=maximizing)
iteration += 1
@@ -224,17 +210,13 @@ def interior_point(
if iteration >= 1000:
return Result(State.UNSOLVED, maximize=maximizing)
# Update the value of x* considering the step size and gradient
x_star += (alpha / Mu) * C_p
x = np.dot(D, x_star)
x = x_new
# TODO 5 tests (from assignment 1) and comparison with simplex and alpha = 0.9
def TEST_CASE_GENERAL():
print("----------------------------RUNNING_TEST_GENERAL_CASE----------------------------")
C = np.array([5, 4])
A = np.array([
[6, 4],
@@ -246,10 +228,10 @@ def TEST_CASE_GENERAL():
eps = 0.01
alpha = 0.5
maximize = True
print_initial_inputs(C, A, b, x_0, eps, alpha, maximize);
result = interior_point(C, A, b, x_0, eps, alpha, maximize);
print_initial_inputs(C, A, b, x_0, eps, alpha, maximize)
result = interior_point(C, A, b, x_0, eps, alpha, maximize)
expected_state = State.SOLVED
if result.state == expected_state:
print_result(result)
@@ -263,8 +245,8 @@ def TEST_CASE_GENERAL():
state_name = "SOLVED"
print(f"incorrect state type. expected SOLVED, got {state_name}.")
def TEST_MINIMIZE_CASE():
print("----------------------------RUNNING_TEST_MINIMIZE_CASE----------------------------")
C = np.array([-2, 2, -6])
A = np.array([
@@ -276,11 +258,10 @@ def TEST_MINIMIZE_CASE():
eps = 0.01
alpha = 0.5
maximize = True
print_initial_inputs(C, A, b, x_0, eps, alpha, maximize);
result = interior_point(C, A, b, x_0, eps, alpha, maximize);
print_initial_inputs(C, A, b, x_0, eps, alpha, maximize)
result = interior_point(C, A, b, x_0, eps, alpha, maximize)
expected_state = State.SOLVED
if result.state == expected_state:
print_result(result)
@@ -292,9 +273,8 @@ def TEST_MINIMIZE_CASE():
state_name = "INAPPLICABLE"
elif result.state == State.SOLVED:
state_name = "SOLVED"
print(f"incorrect state type. expected SOLVED, got {state_name}.")
print(f"incorrect state type. expected SOLVED, got {state_name}.")
def TEST_WITH_SLACK_CASE():
print("----------------------------RUNNING_TEST_WITH_SLACK_CASE----------------------------")
@@ -309,11 +289,10 @@ def TEST_WITH_SLACK_CASE():
eps = 0.01
alpha = 0.5
maximize = True
print_initial_inputs(C, A, b, x_0, eps, alpha, maximize);
result = interior_point(C, A, b, x_0, eps, alpha, maximize);
print_initial_inputs(C, A, b, x_0, eps, alpha, maximize)
result = interior_point(C, A, b, x_0, eps, alpha, maximize)
expected_state = State.SOLVED
if result.state == expected_state:
print_result(result)
@@ -326,7 +305,8 @@ def TEST_WITH_SLACK_CASE():
elif result.state == State.SOLVED:
state_name = "SOLVED"
print(f"incorrect state type. expected SOLVED, got {state_name}.")
def TEST_UNBOUNDED_CASE():
print("----------------------------RUNNING_TEST_UNBOUNDED_CASE----------------------------")
@@ -338,12 +318,11 @@ def TEST_UNBOUNDED_CASE():
x_0 = np.array([1, 1])
eps = 0.01
alpha = 0.5
maximize = True
print_initial_inputs(C, A, b, x_0, eps, alpha, maximize);
result = interior_point(C, A, b, x_0, eps, alpha, maximize);
maximize = True
print_initial_inputs(C, A, b, x_0, eps, alpha, maximize)
result = interior_point(C, A, b, x_0, eps, alpha, maximize)
expected_state = State.SOLVED
if result.state == expected_state:
print_result(result)
@@ -356,7 +335,8 @@ def TEST_UNBOUNDED_CASE():
elif result.state == State.SOLVED:
state_name = "SOLVED"
print(f"incorrect state type. expected SOLVED, got {state_name}.")
def TEST_UNSOLVABLE_CASE():
print("----------------------------RUNNING_TEST_UNSOLVABLE_CASE----------------------------")
@@ -371,12 +351,10 @@ def TEST_UNSOLVABLE_CASE():
eps = 0.01
alpha = 0.5
maximize = True
print_initial_inputs(C, A, b, x_0, eps, alpha, maximize);
result = interior_point(C, A, b, x_0, eps, alpha, maximize);
print_initial_inputs(C, A, b, x_0, eps, alpha, maximize)
result = interior_point(C, A, b, x_0, eps, alpha, maximize)
expected_state = State.SOLVED
if result.state == expected_state:
print_result(result)
@@ -388,4 +366,4 @@ def TEST_UNSOLVABLE_CASE():
state_name = "INAPPLICABLE"
elif result.state == State.SOLVED:
state_name = "SOLVED"
print(f"incorrect state type. expected SOLVED, got {state_name}.")
print(f"incorrect state type. expected SOLVED, got {state_name}.")