rewrite the arc flow cutting stock example
This commit is contained in:
Laurent Perron
@@ -51,26 +51,29 @@ POSSIBLE_CAPACITIES = [4000, 5000, 6000, 7000, 8000]
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def regroup_and_count(raw_input):
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"""Regroup all equal capacities in a multiset."""
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grouped = collections.defaultdict(int)
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for i in raw_input:
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grouped[i] += 1
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output = []
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for size, count in grouped.items():
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output.append([size, count])
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output.sort(reverse=True)
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output.sort(reverse=False)
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return output
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def price_capacity(capacity, capacities):
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def price_usage(usage, capacities):
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"""Compute the best price for a given usage and possible capacities."""
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price = max(capacities)
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for c in capacities:
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if c < capacity:
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for capacity in capacities:
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if capacity < usage:
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continue
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price = min(c - capacity, price)
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price = min(capacity - usage, price)
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return price
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def create_state_graph(items, max_capacity):
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"""Create a state graph from a multiset of items, and a maximum capacity."""
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states = []
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state_to_index = {}
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states.append(0)
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@@ -81,11 +84,11 @@ def create_state_graph(items, max_capacity):
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size, count = size_and_count
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num_states = len(states)
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for state_index in range(num_states):
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previous_state = states[state_index]
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previous_state_index = state_index
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current_state = states[state_index]
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current_state_index = state_index
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for _ in range(count):
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new_state = previous_state + size
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for card in range(count):
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new_state = current_state + size * (card + 1)
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if new_state > max_capacity:
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break
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new_state_index = -1
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@@ -96,15 +99,15 @@ def create_state_graph(items, max_capacity):
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states.append(new_state)
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state_to_index[new_state] = new_state_index
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# Add the transition
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transitions.append(
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[previous_state_index, new_state_index, item_index])
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# And update counters
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previous_state_index = new_state_index
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previous_state = new_state
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transitions.append([
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current_state_index, new_state_index, item_index, card + 1
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])
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return states, transitions
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def solve_cutting_stock_with_arc_flow_with_sat(output_proto):
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def solve_cutting_stock_with_arc_flow_and_sat(output_proto):
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"""Solve the cutting stock with arc-flow and the CP-SAT solver."""
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items = regroup_and_count(DESIRED_LENGTHS)
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print('Items:', items)
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num_items = len(DESIRED_LENGTHS)
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@@ -119,19 +122,25 @@ def solve_cutting_stock_with_arc_flow_with_sat(output_proto):
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outgoing_vars = collections.defaultdict(list)
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incoming_sink_vars = []
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item_vars = collections.defaultdict(list)
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item_coeffs = collections.defaultdict(list)
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transition_vars = []
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model = cp_model.CpModel()
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objective_vars = []
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objective_coeffs = []
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for outgoing, incoming, item_index in transitions:
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for outgoing, incoming, item_index, card in transitions:
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count = items[item_index][1]
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max_count = count // card
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count_var = model.NewIntVar(
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0, count, 'i%i_f%i_t%i' % (item_index, incoming, outgoing))
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0, max_count,
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'i%i_f%i_t%i_C%s' % (item_index, incoming, outgoing, card))
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incoming_vars[incoming].append(count_var)
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outgoing_vars[outgoing].append(count_var)
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item_vars[item_index].append(count_var)
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item_coeffs[item_index].append(card)
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transition_vars.append(count_var)
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for state_index, state in enumerate(states):
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if state_index == 0:
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@@ -139,7 +148,7 @@ def solve_cutting_stock_with_arc_flow_with_sat(output_proto):
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exit_var = model.NewIntVar(0, num_items, 'e%i' % state_index)
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outgoing_vars[state_index].append(exit_var)
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incoming_sink_vars.append(exit_var)
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price = price_capacity(state, POSSIBLE_CAPACITIES)
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price = price_usage(state, POSSIBLE_CAPACITIES)
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objective_vars.append(exit_var)
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objective_coeffs.append(price)
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@@ -153,8 +162,10 @@ def solve_cutting_stock_with_arc_flow_with_sat(output_proto):
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# Items must be placed
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for item_index, size_and_count in enumerate(items):
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size, count = size_and_count
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model.Add(sum(item_vars[item_index]) == count)
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num_arcs = len(item_vars[item_index])
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model.Add(
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sum(item_vars[item_index][i] * item_coeffs[item_index][i]
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for i in range(num_arcs)) == size_and_count[1])
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# Objective is the sum of waste
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model.Minimize(
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@@ -175,7 +186,8 @@ def solve_cutting_stock_with_arc_flow_with_sat(output_proto):
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print(solver.ResponseStats())
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def solve_cutting_stock_with_arc_flow_with_mip():
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def solve_cutting_stock_with_arc_flow_and_mip():
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"""Solve the cutting stock with arc-flow and a MIP solver."""
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items = regroup_and_count(DESIRED_LENGTHS)
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print('Items:', items)
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num_items = len(DESIRED_LENGTHS)
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@@ -189,6 +201,7 @@ def solve_cutting_stock_with_arc_flow_with_mip():
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outgoing_vars = collections.defaultdict(list)
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incoming_sink_vars = []
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item_vars = collections.defaultdict(list)
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item_coeffs = collections.defaultdict(list)
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start_time = time.time()
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solver = pywraplp.Solver('Steel',
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@@ -198,15 +211,16 @@ def solve_cutting_stock_with_arc_flow_with_mip():
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objective_coeffs = []
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var_index = 0
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for outgoing, incoming, item_index in transitions:
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for outgoing, incoming, item_index, card in transitions:
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count = items[item_index][1]
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count_var = solver.IntVar(
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0, count,
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'a%i_i%i_f%i_t%i' % (var_index, item_index, incoming, outgoing))
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0, count, 'a%i_i%i_f%i_t%i_c%i' % (var_index, item_index, incoming,
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outgoing, card))
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var_index += 1
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incoming_vars[incoming].append(count_var)
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outgoing_vars[outgoing].append(count_var)
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item_vars[item_index].append(count_var)
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item_coeffs[item_index].append(card)
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for state_index, state in enumerate(states):
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if state_index == 0:
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@@ -214,7 +228,7 @@ def solve_cutting_stock_with_arc_flow_with_mip():
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exit_var = solver.IntVar(0, num_items, 'e%i' % state_index)
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outgoing_vars[state_index].append(exit_var)
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incoming_sink_vars.append(exit_var)
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price = price_capacity(state, POSSIBLE_CAPACITIES)
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price = price_usage(state, POSSIBLE_CAPACITIES)
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objective_vars.append(exit_var)
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objective_coeffs.append(price)
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@@ -228,8 +242,10 @@ def solve_cutting_stock_with_arc_flow_with_mip():
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# Items must be placed
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for item_index, size_and_count in enumerate(items):
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size, count = size_and_count
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solver.Add(sum(item_vars[item_index]) == count)
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num_arcs = len(item_vars[item_index])
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solver.Add(
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sum(item_vars[item_index][i] * item_coeffs[item_index][i]
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for i in range(num_arcs)) == size_and_count[1])
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# Objective is the sum of waste
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solver.Minimize(
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@@ -250,9 +266,9 @@ def solve_cutting_stock_with_arc_flow_with_mip():
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def main(args):
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"""Main function"""
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if args.solver == 'sat':
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solve_cutting_stock_with_arc_flow_with_sat(args.output_proto)
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solve_cutting_stock_with_arc_flow_and_sat(args.output_proto)
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else: # 'mip'
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solve_cutting_stock_with_arc_flow_with_mip()
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solve_cutting_stock_with_arc_flow_and_mip()
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if __name__ == '__main__':
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