proof of concept knapsack optimizer

model_data/optimiser/Optimiser.py

@@ -0,0 +1,73 @@
+from mip import Model, xsum, maximize, BINARY
+
+# Example parts
+wall = [
+    {"id": 1, "cost": 2000, "gain": 5, "type": "wall"},
+    {"id": 2, "cost": 2300, "gain": 6, "type": "wall"}
+]
+
+floor = [
+    {"id": 1, "cost": 1500, "gain": 3, "type": "floor"},
+    {"id": 2, "cost": 1600, "gain": 3.1, "type": "floor"}
+]
+
+roof = [
+    {"id": 1, "cost": 1000, "gain": 2, "type": "roof"},
+    {"id": 2, "cost": 1100, "gain": 2.3, "type": "roof"}
+]
+
+# To solve this, we are solving a constrained Knapsack problem
+# Maximize sum(gain_g . x_g) for g in groups
+# subject to sum(cost_g . x_g) <= C
+# subject to sum(x_g) <= 1 for g in groups
+# x_g in {0, 1} for g in groups
+#
+# The first sum, which is the objective of the optimisation provlem, ensures that we are maximising the gain
+# for the selected parts
+# The second sum (and the first constraint) ensures that the cost of the selected parts is less than or equal to C
+# The third sum (and the second constraint) ensures that at most one part from each group is selected
+# The last constraint ensures that the decision variables are binary
+
+C = 4000
+
+# group all the parts
+groups = [wall, floor, roof]
+
+# Initialize Model
+m = Model("knapsack")
+
+# Create variables
+vars = [[m.add_var(var_type=BINARY, name=str(component["id"])) for component in group] for group in groups]
+
+# Set objective
+# This objective is the sum
+# gain_ig * x_ig, where gain_ig represents the gain for ith part in group g
+# and x_ig is the binary decision variable for the ith part in group g
+m.objective = maximize(
+    xsum(
+        component['gain'] * var for group, group_vars in zip(groups, vars) for component, var in zip(group, group_vars)
+    )
+)
+
+# Add constraints
+# This constrain ensures that sum of cost_ig * x_ig <= C, where cost_ig represents the cost for the ith component
+# in group g, and x_ig is the binary decision variable for the ith component in group g
+m += xsum(item['cost'] * var for group, group_vars in zip(groups, vars) for item, var in zip(group, group_vars)) <= C
+
+# At most one item from each group
+# This constraint ensures that at most one item from each group is selected
+# This is expressed by summing up the decision variables for each group and ensuring that the sum is <= 1
+for group_vars in vars:
+    m += xsum(var for var in group_vars) <= 1
+
+# Solve the problem
+m.optimize()
+
+# Get the selected items
+selected_items = [
+    item for group, group_vars in zip(groups, vars) for item, var in zip(group, group_vars) if var.x >= 0.99
+]
+
+total_gain = m.objective.x
+actual_cost = sum([component['cost'] for component in selected_items])
+print("Selected items:", selected_items)

model_data/requirements.txt

@@ -12,4 +12,5 @@ python-Levenshtein
 dbfread
 pyproj
 pint
-geopandas
+geopandas
+mip