Add 5th assignment

05-lagrange_assignment/assignment.py

+import numpy
+import gurobipy as gp
+from gurobipy import GRB
+
+# Returns the best possible lower bound for a given GAP instance obtained from applying the Lagrangian relaxation on all uniqueness constraints.
+# See task.md for more details.
+def lagrange_generalized_assignment_problem(instance):
+    #TODO: Find the lower bound here
+
+# Try to find a greedy feasible solution for GAP
+# If successfull, returns a list which assigns jobs to agents
+# Otherwise, throw an exception (ValueError: min() arg is an empty sequence)
+# Note that determining whether an instance of GAP has a feasible solution is NP-complete (use 3-partition for reduction)
+def get_greedy_solution(instance):
+    assignment = [-1] * instance.jobs # For a job j, assignment[j] is the assigned agent
+    process = list(range(instance.jobs)) # Jobs that has not been assigned yet
+    remains = instance.capacity.copy() # Remaining capacity of each agent
+    while process:
+        # From all unassigned jobs j and agents a having sufficient capacity for j, choose (a,j) with minimal weight
+        w,a,j = min((instance.weight[a][j],a,j) for j in process for a in range(instance.agents) if instance.weight[a][j] <= remains[a])
+        assignment[j] = a
+        process.remove(j)
+        remains[a] -= w
+    return assignment
+
+# Solve the knapsack problem: Given weight and price of items and capacity, find
+# a subset of items with weights at the capacity and maximizing their total cost
+# Returns a pair of the total cost and idices of items in an optimal subset
+# Note that items of non-positive items are ignored
+def solve_knapsack(weight, price, capacity):
+    assert len(weight) == len(price)
+
+    # Lists for dynamic programming
+    max_cost = [0] * (capacity+1) # Maximal possible cost reaching every total weight
+    last_index = [-1] * (capacity+1) # Index of the last added item
+
+    for j, w, p in zip(range(len(weight)), weight, price): # Index, weight and price of each item
+        if p > 0: # Ignore items of non-positive items
+            for i in reversed(range(capacity-w+1)): # Try to insert the item j to all total weights
+                if max_cost[i+w] < max_cost[i] + p:
+                    # Adding item i increases the cost
+                    max_cost[i+w] = max_cost[i] + p
+                    last_index[i+w] = j
+
+    solution = []
+    m = numpy.argmax(max_cost) # Total weight with maximal cost
+    objective = max_cost[m]
+
+    # Using last_index reconstruct an optimal solution
+    while last_index[m] >= 0:
+        solution.append(last_index[m])
+        m -= weight[last_index[m]]
+
+    return (objective, solution)
+
+if __name__ == "__main__":
+    # Some unit tests for our knapsack problem
+    assert solve_knapsack([1], [2], 6) == (2, [0])
+    assert solve_knapsack([1], [-2], 6) == (0, [])
+    assert solve_knapsack([4,6], [2,5], 100) == (7, [1,0])
+    assert solve_knapsack([4,6], [2,5], 7) == (5, [1])
+    assert solve_knapsack([4,6], [2,5], 5) == (2, [0])
+    assert solve_knapsack([4,6,10], [2,5,9], 12) == (9, [2])
+    assert solve_knapsack([4,6,10], [2,5,6], 12) == (7, [1,0])
+    assert solve_knapsack([4,6,10], [2,5,6], 15) == (8, [2,0])

05-lagrange_assignment/assignment_tests.py

+import sys
+import copy
+from time import time
+from prettytable import PrettyTable
+from assignment import lagrange_generalized_assignment_problem
+
+# Instance of the General assignment problem (GAP)
+class Instance:
+    def __init__(self, agents, jobs, cost, weight, capacity):
+        self.agents = agents # The number of agents (e.g. central stores)
+        self.jobs = jobs # The number of jobs (e.g. consumers)
+        self.cost = cost # Cost of assigning a job to an agent; the first index is an agent, the second one is a job
+        self.weight = weight # How much resources a job consume from an agent; the first index is an agent, the second one is a job
+        self.capacity = capacity # The capacity of each agent
+
+# Returns the instance of GAP stored in a given file
+# http://people.brunel.ac.uk/~mastjjb/jeb/orlib/gapinfo.html
+def load(filename):
+    content = [ int(y) for x in open(filename, "r") for y in x.split() ]
+    content.reverse()
+    content.pop()
+    agents = content.pop()
+    jobs = content.pop()
+    cost = [ [ content.pop() for j in range(jobs) ] for a in range(agents) ]
+    weight = [ [ content.pop() for j in range(jobs) ] for a in range(agents) ]
+    capacity = [ content.pop() for a in range(agents) ]
+    return Instance(agents, jobs, cost, weight, capacity)
+
+def verify_solution(instance, solution, bound):
+    if abs(solution - bound) > 0.0001:
+        return (False, "Incorrect bound")
+    return (True, "Correct bound")
+
+def run_test(filename, bound):
+    instance = load(filename)
+    solution = lagrange_generalized_assignment_problem(copy.deepcopy(instance))
+    return verify_solution(instance, solution, bound) + (instance,)
+
+def main():
+    tests = {
+            "first": ("gap1.txt", 258.5, 1),
+            "second": ("gap2.txt", 274.3878787878788, 1),
+            "third": ("gap3.txt", 434.99189237716774, 1),
+            "fourth": ("gap4.txt", 417.7556653611704, 2),
+            "fifth": ("gap5.txt", 402.8431003822761, 1),
+            "sixth": ("gap6.txt", 522.2637096268518, 2),
+            "seventh": ("gap7.txt", 643.210566967029, 3),
+            "eigth": ("gap8.txt", 793.0298487147554, 6),
+            "ninth": ("gap9.txt", 480.81566820276504, 2),
+            "tenth": ("gap10.txt", 634.1139438624057, 5),
+    }
+    if len(sys.argv) == 1:
+        results = PrettyTable(["Instance name", "Points", "Filename", "Jobs", "Agents", "Time limit [s]", "Your time [s]", "Evaluation"])
+        for name in tests:
+            print("Running test", name)
+            filename, bound, time_limit = tests[name]
+            start_time = time()
+            status,msg,instance = run_test(filename, bound)
+            running_time = time() - start_time
+            print(msg)
+            print()
+            results.add_row([name, 1, filename, instance.jobs, instance.agents, time_limit, running_time, msg])
+        print(results)
+    else:
+        name = sys.argv[1]
+        if name in tests:
+            filename, optimal_length, time_limit = tests[name]
+            status, msg, instance = run_test(filename, optimal_length)
+            print(msg)
+        else:
+            print("Unknown test", name)
+
+"""
+To run all tests, run the command
+$ python3 assignment_tests.py
+
+To run a test NAME, run the command
+$ python3 assignment_tests.py NAME
+"""
+if __name__ == "__main__":
+    main()

05-lagrange_assignment/gap1.txt

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05-lagrange_assignment/gap2.txt

+ 5
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