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backend/src/optimizer.py
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206
backend/src/optimizer.py
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from scipy.optimize import linprog
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import numpy as np
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from scipy.linalg import block_diag
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# Defines the landmark class (aka some place there is to visit)
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class landmark :
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def __init__(self, name: str, attractiveness: int, loc: tuple):
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self.name = name
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self.attractiveness = attractiveness
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self.loc = loc
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# Convert the result (edges from j to k like d_25 = edge between vertex 2 and vertex 5) into the list of indices corresponding to the landmarks
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def untangle(res: list) :
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N = len(res) # length of res
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L = int(np.sqrt(N)) # number of landmarks. CAST INTO INT but should not be a problem because N = L**2 by def.
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n_landmarks = res.sum() # number of visited landmarks
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visit_order = []
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cnt = 0
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if n_landmarks % 2 == 1 : # if odd number of visited checkpoints
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for i in range(L) :
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for j in range(L) :
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if res[i*L + j] == 1 : # if index is 1
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cnt += 1 # increment counter
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if cnt % 2 == 1 : # if counter odd
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visit_order.append(i)
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visit_order.append(j)
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else : # if even number of ones
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for i in range(L) :
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for j in range(L) :
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if res[i*L + j] == 1 : # if index is one
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cnt += 1 # increment counter
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if j % (L-1) == 0 : # if last node
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visit_order.append(j) # append only the last index
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return visit_order # return
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if cnt % 2 == 1 :
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visit_order.append(i)
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visit_order.append(j)
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return visit_order
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# Just to print the result
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def print_res(res: list, P) :
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X = abs(res.x)
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order = untangle(X)
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# print("Optimal value:", -res.fun) # Minimization, so we negate to get the maximum
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# print("Optimal point:", res.x)
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# N = int(np.sqrt(len(X)))
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# for i in range(N):
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# print(X[i*N:i*N+N])
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# print(order)
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if (X.sum()+1)**2 == len(X) :
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print('\nAll landmarks can be visited within max_steps, the following order is most likely not the fastest')
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else :
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print('Could not visit all the landmarks, the following order could be the fastest but not sure')
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print("Order of visit :")
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for i, elem in enumerate(landmarks) :
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if i in order : print('- ' + elem.name)
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steps = path_length(P, abs(res.x))
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print("\nSteps walked : " + str(steps))
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# Constraint to use only the upper triangular indices for travel
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def break_sym(landmarks, A_eq, b_eq):
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L = len(landmarks)
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l = [0]*L*L
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for i in range(L) :
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for j in range(L) :
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if i >= j :
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l[j+i*L] = 1
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A_eq = np.vstack((A_eq,l))
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b_eq.append(0)
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return A_eq, b_eq
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# Constraint to respect max number of travels
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def respect_number(landmarks, A_ub, b_ub):
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h = []
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for i in range(len(landmarks)) : h.append([1]*len(landmarks))
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T = block_diag(*h)
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return np.vstack((A_ub, T)), b_ub + [1]*len(landmarks)
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# Constraint to tie the problem together and have a connected path
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def respect_order(landmarks: list, A_eq, b_eq):
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N = len(landmarks)
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for i in range(N-1) : # Prevent stacked ones
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if i == 0 :
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continue
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else :
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l = [0]*N
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l[i] = -1
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l = l*N
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for j in range(N) :
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l[i*N + j] = 1
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A_eq = np.vstack((A_eq,l))
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b_eq.append(0)
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return A_eq, b_eq
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# Compute manhattan distance between 2 locations
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def manhattan_distance(loc1: tuple, loc2: tuple):
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x1, y1 = loc1
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x2, y2 = loc2
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return abs(x1 - x2) + abs(y1 - y2)
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# Constraint to not stay in position
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def init_eq_not_stay(landmarks):
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L = len(landmarks)
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l = [0]*L*L
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for i in range(L) :
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for j in range(L) :
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if j == i :
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l[j + i*L] = 1
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#A_eq = np.array([np.array(xi) for xi in A_eq]) # Must convert A_eq into an np array
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l = np.array(np.array(l))
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return [l], [0]
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# Initialize A and c. Compute the distances from all landmarks to each other and store attractiveness
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# We want to maximize the sightseeing : max(c) st. A*x < b and A_eq*x = b_eq
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def init_ub_dist(landmarks: list, max_steps: int):
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# Objective function coefficients. a*x1 + b*x2 + c*x3 + ...
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c = []
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# Coefficients of inequality constraints (left-hand side)
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A = []
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for i, spot1 in enumerate(landmarks) :
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dist_table = [0]*len(landmarks)
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c.append(-spot1.attractiveness)
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for j, spot2 in enumerate(landmarks) :
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dist_table[j] = manhattan_distance(spot1.loc, spot2.loc)
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A.append(dist_table)
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c = c*len(landmarks)
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A_ub = []
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for line in A :
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A_ub += line
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return c, A_ub, [max_steps]
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# Go through the landmarks and force the optimizer to use landmarks where attractiveness is set to -1
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def respect_user_mustsee(landmarks: list, A_eq: list, b_eq: list) :
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L = len(landmarks)
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for i, elem in enumerate(landmarks) :
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if elem.attractiveness == -1 :
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l = [0]*L*L
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if elem.name != "arrivée" :
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for j in range(L) :
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l[j +i*L] = 1
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else : # This ensures we go to goal
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for k in range(L-1) :
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l[k*L+L-1] = 1
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A_eq = np.vstack((A_eq,l))
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b_eq.append(1)
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return A_eq, b_eq
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# Computes the path length given path matrix (dist_table) and a result
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def path_length(P: list, resx: list) :
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return np.dot(P, resx)
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# Initialize all landmarks (+ start and goal). Order matters here
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landmarks = []
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landmarks.append(landmark("départ", -1, (0, 0)))
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landmarks.append(landmark("concorde", -1, (5,5)))
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landmarks.append(landmark("tour eiffel", 99, (1,1))) # PUT IN JSON
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landmarks.append(landmark("arc de triomphe", 99, (2,3)))
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landmarks.append(landmark("louvre", 70, (4,2)))
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landmarks.append(landmark("montmartre", 20, (0,2)))
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landmarks.append(landmark("arrivée", -1, (0, 0)))
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# CONSTRAINT TO RESPECT MAX NUMBER OF STEPS
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max_steps = 25
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# SET CONSTRAINTS FOR INEQUALITY
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c, A_ub, b_ub = init_ub_dist(landmarks, max_steps) # Add the distances from each landmark to the other
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P = A_ub # store the paths for later. Needed to compute path length
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A_ub, b_ub = respect_number(landmarks, A_ub, b_ub) # Respect max number of visits.
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# SET CONSTRAINTS FOR EQUALITY
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A_eq, b_eq = init_eq_not_stay(landmarks) # Force solution not to stay in same place
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A_eq, b_eq = respect_user_mustsee(landmarks, A_eq, b_eq) # Check if there are user_defined must_see. Also takes care of start/goal
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A_eq, b_eq = break_sym(landmarks, A_eq, b_eq) # break the symmetry. Only use the upper diagonal values
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A_eq, b_eq = respect_order(landmarks, A_eq, b_eq) # Respect order of visit (only works when max_steps is limiting factor)
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# Bounds for variables (x can only be 0 or 1)
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x_bounds = [(0, 1)] * len(c)
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# Solve linear programming problem
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res = linprog(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq = b_eq, bounds=x_bounds, method='highs', integrality=3)
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# Raise error if no solution is found
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if not res.success :
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raise ValueError("No solution has been found, please adapt your max steps")
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# Print result
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print_res(res, P)
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