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@ -59,20 +59,25 @@ class Optimizer:
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def init_ub_time(self, prob: pl.LpProblem, x: pl.LpVariable, L: int, landmarks: list[Landmark], max_time: int):
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"""
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Initialize the objective function coefficients and inequality constraints.
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-> Adds 1 row of constraints
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-> Pre-allocates A_ub for the rest of the computations with L + (L*L-L)/2 rows
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Initialize the objective function and inequality constraints for the linear program.
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This function computes the distances between all landmarks and stores
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their attractiveness to maximize sightseeing. The goal is to maximize
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the objective function subject to the constraints A*x < b and A_eq*x = b_eq.
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This function sets up the objective to maximize the attractiveness of visiting landmarks,
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while ensuring that the total time (including travel and visit duration) does not exceed
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the maximum allowed time. It calculates the pairwise travel times between landmarks and
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incorporates visit duration to form the inequality constraints.
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The objective is to maximize sightseeing by selecting the most attractive landmarks within
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the time limit.
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Args:
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landmarks (list[Landmark]): List of landmarks.
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max_time (int): Maximum time of visit allowed.
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prob (pl.LpProblem): The linear programming problem where constraints and the objective will be added.
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x (pl.LpVariable): A decision variable representing whether a landmark is visited.
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L (int): The number of landmarks.
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landmarks (list[Landmark]): List of landmarks to visit.
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max_time (int): Maximum allowable time for sightseeing, including travel and visit duration.
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Returns:
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tuple[list[float], list[float], list[int]]: Objective function coefficients, inequality
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None: Adds the objective function and constraints to the LP problem directly.
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constraint coefficients, and the right-hand side of the inequality constraint.
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"""
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L = len(landmarks)
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@ -117,14 +122,20 @@ class Optimizer:
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def respect_number(self, prob: pl.LpProblem, x: pl.LpVariable, L: int, max_landmarks: int):
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"""
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Generate constraints to ensure each landmark is visited only once and cap the total number of visited landmarks.
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-> Adds L-1 rows of constraints
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Generate constraints to ensure each landmark is visited at most once and cap the total number of visited landmarks.
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This function adds the following constraints to the linear program:
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1. Each landmark is visited at most once by creating L-2 constraints (one for each landmark).
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2. The total number of visited landmarks is capped by the specified maximum number (`max_landmarks`) plus 2.
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Args:
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L (int): Number of landmarks.
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prob (pl.LpProblem): The linear programming problem where constraints will be added.
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x (pl.LpVariable): Decision variable indicating whether a landmark is visited.
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L (int): The total number of landmarks.
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max_landmarks (int): The maximum number of landmarks that can be visited.
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Returns:
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tuple[np.ndarray, list[int]]: Inequality constraint coefficients and the right-hand side of the inequality constraints.
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None: This function directly modifies the `prob` object by adding constraints.
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"""
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# L-2 constraints: each landmark is visited exactly once
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for i in range(1, L-1):
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@ -137,16 +148,20 @@ class Optimizer:
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def break_sym(self, prob: pl.LpProblem, x: pl.LpVariable, L: int):
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"""
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Generate constraints to prevent simultaneous travel between two landmarks
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in both directions. Constraint to not have d14 and d41 simultaneously.
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Does not prevent cyclic paths with more elements
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-> Adds (L*L-L)/2 rows of constraints (some of which might be zero)
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in both directions. This constraint ensures that, for any pair of landmarks,
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travel from landmark i to landmark j (dij) and travel from landmark j to landmark i (dji)
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cannot happen simultaneously.
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This method adds constraints to break symmetry, specifically to prevent
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cyclic paths with only two elements. It does not prevent cyclic paths involving more than two elements.
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Args:
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L (int): Number of landmarks.
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prob (pl.LpProblem): The linear programming problem where constraints will be added.
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x (pl.LpVariable): Decision variable representing travel between landmarks.
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L (int): The total number of landmarks.
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Returns:
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tuple[np.ndarray, list[int]]: Inequality constraint coefficients and
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the right-hand side of the inequality constraints.
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None: This function modifies the `prob` object by adding constraints in-place.
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"""
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upper_ind = np.triu_indices(L, 0, L) # Get the upper triangular indices
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up_ind_x = upper_ind[0]
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@ -161,15 +176,20 @@ class Optimizer:
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def init_eq_not_stay(self, prob: pl.LpProblem, x: pl.LpVariable, L: int):
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"""
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Generate constraints to prevent staying in the same position (e.g., removing d11, d22, d33, etc.).
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-> Adds 1 row of constraints
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-> Pre-allocates A_eq for the rest of the computations with (L+ 2 + dynamic incr) rows
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Generate constraints to prevent staying at the same position during travel.
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Specifically, it removes travel from a landmark to itself (e.g., d11, d22, d33, etc.).
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This function adds one equality constraint to the optimization problem that ensures
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no decision variable corresponding to staying at the same landmark is included
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in the solution. This helps in ensuring that the path does not include self-loops.
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Args:
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L (int): Number of landmarks.
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prob (pl.LpProblem): The linear programming problem where constraints will be added.
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x (pl.LpVariable): Decision variable representing travel between landmarks.
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L (int): The total number of landmarks.
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Returns:
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tuple[list[np.ndarray], list[int]]: Equality constraint coefficients and the right-hand side of the equality constraints.
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None: This function modifies the `prob` object by adding an equality constraint in-place.
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"""
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A_eq = np.zeros((L, L), dtype=np.int8)
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@ -181,18 +201,23 @@ class Optimizer:
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prob += (pl.lpSum([A_eq[j] * x[j] for j in range(L*L)]) == 0)
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# Constraint to ensure start at start and finish at goal
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def respect_start_finish(self, prob: pl.LpProblem, x: pl.LpVariable, L: int):
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"""
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Generate constraints to ensure that the optimization starts at the designated
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Generate constraints to ensure that the optimization starts at the designated
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start landmark and finishes at the goal landmark.
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-> Adds 3 rows of constraints
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Specifically, this function adds three equality constraints:
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1. Ensures that the path starts at the designated start landmark (row 0).
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2. Ensures that the path finishes at the designated goal landmark (row 1).
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3. Prevents any arrivals at the start landmark or departures from the goal landmark (row 2).
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Args:
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L (int): Number of landmarks.
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prob (pl.LpProblem): The linear programming problem where constraints will be added.
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x (pl.LpVariable): Decision variable representing travel between landmarks.
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L (int): The total number of landmarks.
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Returns:
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tuple[np.ndarray, list[int]]: Inequality constraint coefficients and the right-hand side of the inequality constraints.
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None: This function modifies the `prob` object by adding three equality constraints in-place.
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"""
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# Fill-in row 0.
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A_eq = np.zeros((3,L*L), dtype=np.int8)
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@ -211,27 +236,24 @@ class Optimizer:
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for i in range(3) :
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prob += (pl.lpSum([A_eq[i][j] * x[j] for j in range(L*L)]) == b_eq[i])
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def respect_order(self, prob: pl.LpProblem, x: pl.LpVariable, L: int):
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"""
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Generate constraints to tie the optimization problem together and prevent
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stacked ones, although this does not fully prevent circles.
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-> Adds L-2 rows of constraints
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This function adds constraints to the optimization problem that prevent
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simultaneous travel between landmarks in a way that would result in stacked ones.
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However, it does not fully prevent circular paths.
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Args:
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L (int): Number of landmarks.
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prob (pl.LpProblem): The linear programming problem where constraints will be added.
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x (pl.LpVariable): Decision variable representing travel between landmarks.
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L (int): The total number of landmarks.
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Returns:
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tuple[np.ndarray, list[int]]: Inequality constraint coefficients and the right-hand side of the inequality constraints.
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None: This function modifies the `prob` object by adding L-2 equality constraints in-place.
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"""
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# A_eq = np.zeros(L*L, dtype=np.int8)
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# ones = np.ones(L, dtype=np.int8)
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# # Fill-in rows 4 to L+2
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# for i in range(1, L-1) : # Prevent stacked ones
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# for j in range(L) :
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# A_eq[i + j*L] = -1
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# A_eq[i*L:(i+1)*L] = ones
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# prob += (pl.lpSum([A_eq[j] * x[j] for j in range(L*L)]) == 0)
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# FIXME: weird 0 artifact in the coefficients popping up
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# Loop through rows 1 to L-2 to prevent stacked ones
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for i in range(1, L-1):
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@ -243,14 +265,19 @@ class Optimizer:
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def respect_user_must(self, prob: pl.LpProblem, x: pl.LpVariable, L: int, landmarks: list[Landmark]) :
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"""
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Generate constraints to ensure that landmarks marked as 'must_do' are included in the optimization.
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-> Adds a variable number of rows of constraints BUT CAN BE PRE COMPUTED
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This function adds constraints to the optimization problem to ensure that landmarks marked as
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'must_do' are included in the solution. It precomputes the constraints and adds them to the
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problem accordingly.
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Args:
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prob (pl.LpProblem): The linear programming problem where constraints will be added.
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x (pl.LpVariable): Decision variable representing travel between landmarks.
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L (int): The total number of landmarks.
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landmarks (list[Landmark]): List of landmarks, where some are marked as 'must_do'.
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Returns:
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tuple[np.ndarray, list[int]]: Inequality constraint coefficients and the right-hand side of the inequality constraints.
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None: This function modifies the `prob` object by adding equality constraints in-place.
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"""
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ones = np.ones(L, dtype=np.int8)
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A_eq = np.zeros(L*L, dtype=np.int8)
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@ -264,52 +291,22 @@ class Optimizer:
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prob += (pl.lpSum([A_eq[j] * x[j] for j in range(L*L)]) == 2)
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# Prevent the use of a particular solution. TODO probably can be done faster just using resx
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# def prevent_config(self, prob: pl.LpProblem, x: pl.LpVariable, resx):
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# """
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# Prevent the use of a particular solution by adding constraints to the optimization.
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# Args:
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# resx (list[float]): List of edge weights.
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# Returns:
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# tuple[list[int], list[int]]: A tuple containing a new row for A and new value for ub.
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# """
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# for i, elem in enumerate(resx):
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# resx[i] = round(elem)
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# N = len(resx) # Number of edges
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# L = int(np.sqrt(N)) # Number of landmarks
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# nonzeroind = np.nonzero(resx)[0] # the return is a little funky so I use the [0]
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# nonzero_tup = np.unravel_index(nonzeroind, (L,L))
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# ind_a = nonzero_tup[0].tolist()
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# vertices_visited = ind_a
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# vertices_visited.remove(0)
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# ones = np.ones(L, dtype=np.int8)
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# h = np.zeros(L*L, dtype=np.int8)
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# for i in range(L) :
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# if i in vertices_visited :
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# h[i*L:i*L+L] = ones
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# return h, len(vertices_visited)-1
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# Prevents the creation of the same circle (both directions)
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def prevent_circle(self, prob: pl.LpProblem, x: pl.LpVariable, circle_vertices: list, L: int) :
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"""
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Prevent circular paths by by adding constraints to the optimization.
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Prevent circular paths by adding constraints to the optimization.
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This function ensures that circular paths in both directions (i.e., forward and reverse)
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between landmarks are avoided in the optimization problem by adding the corresponding constraints.
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Args:
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circle_vertices (list): List of vertices forming a circle.
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L (int): Number of landmarks.
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prob (pl.LpProblem): The linear programming problem instance to which the constraints will be added.
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x (pl.LpVariable): Decision variable representing the travel between landmarks in the problem.
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circle_vertices (list): List of indices representing the landmarks that form a circular path.
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L (int): The total number of landmarks.
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Returns:
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tuple[np.ndarray, list[int]]: A tuple containing a new row for constraint matrix and new value for upper bound vector.
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None: This function modifies the `prob` object by adding two equality constraints that
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prevent circular paths in both directions for the specified circle vertices.
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"""
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l = np.zeros((2, L*L), dtype=np.int8)
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@ -544,12 +541,8 @@ class Optimizer:
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return prob, x
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def solve_optimization(
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self,
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max_time: int,
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landmarks: list[Landmark],
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max_landmarks: int = None
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) -> list[Landmark]:
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def solve_optimization(self, max_time: int, landmarks: list[Landmark], max_landmarks: int = None) -> list[Landmark]:
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"""
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Main optimization pipeline to solve the landmark visiting problem.
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@ -563,14 +556,12 @@ class Optimizer:
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Returns:
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list[Landmark]: The optimized tour of landmarks with updated travel times, or None if no valid solution is found.
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"""
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# 1. Setup the optimization proplem.
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# Setup the optimization proplem.
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L = len(landmarks)
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prob, x = self.pre_processing(L, landmarks, max_time, max_landmarks)
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# 2. Solve the problem
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# Solve the problem and extract results.
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prob.solve(pl.PULP_CBC_CMD(msg=False, gapRel=0.1))
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# 3. Extract Results
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status = pl.LpStatus[prob.status]
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solution = [pl.value(var) for var in x] # The values of the decision variables (will be 0 or 1)
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@ -588,10 +579,6 @@ class Optimizer:
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timeout = 40
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while circles is not None :
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i += 1
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# print(f"Iteration {i} of fixing circles")
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# l, b = self.prevent_config(solution)
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# prob += (pl.lpSum([l[j] * x[j] for j in range(L*L)]) == b)
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if i == timeout :
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self.logger.error(f'Timeout: No solution found after {timeout} iterations.')
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raise TimeoutError(f"Optimization took too long. No solution found after {timeout} iterations.")
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@ -611,7 +598,6 @@ class Optimizer:
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if circles is None :
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break
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# Sort the landmarks in the order of the solution
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order = self.get_order(solution)
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tour = [landmarks[i] for i in order]
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import yaml
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from shapely import buffer, LineString, Point, Polygon, MultiPoint, concave_hull
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from ..structs.landmark import Landmark
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from .get_time_distance import get_time
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from .take_most_important import take_most_important
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