119 lines
4.8 KiB
Python
119 lines
4.8 KiB
Python
#!/usr/bin/env python3
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# Copyright 2010-2022 Google LLC
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""Maximize the minimum of pairwise distances between n robots in a square space."""
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import math
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from typing import Sequence
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from absl import app
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from absl import flags
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from google.protobuf import text_format
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from ortools.sat.python import cp_model
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_NUM_ROBOTS = flags.DEFINE_integer('num_robots', 8,
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'Number of robots to place.')
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_ROOM_SIZE = flags.DEFINE_integer('room_size', 20,
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'Size of the square room where robots are.')
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_PARAMS = flags.DEFINE_string(
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'params',
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'num_search_workers:16, max_time_in_seconds:20',
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'Sat solver parameters.',
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)
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def spread_robots(num_robots: int, room_size: int, params: str):
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"""Optimize robots placement."""
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model = cp_model.CpModel()
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# Create the list of coordinates (x, y) for each robot.
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x = [model.NewIntVar(1, room_size, f'x_{i}') for i in range(num_robots)]
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y = [model.NewIntVar(1, room_size, f'y_{i}') for i in range(num_robots)]
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# The specification of the problem is to maximize the minimum euclidian
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# distance between any two robots. Unfortunately, the euclidian distance
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# uses the square root operation which is not defined on integer variables.
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# To work around, we will create a min_square_distance variable, then we make
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# sure that its value is less than the square of the euclidian distance
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# between any two robots.
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#
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# This encoding has a low precision. To improve the precision, we will scale
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# the domain of the min_square_distance variable by a constant factor, then
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# multiply the square of the euclidian distance between two robots by the same
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# factor.
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#
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# we create a scaled_min_square_distance variable with a domain of
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# [0..scaling * max euclidian distance**2] such that
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# forall i:
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# scaled_min_square_distance <= scaling * (x_diff_sq[i] + y_diff_sq[i])
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scaling = 1000
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scaled_min_square_distance = model.NewIntVar(0, 2 * scaling * room_size**2,
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'scaled_min_square_distance')
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# Build intermediate variables and get the list of squared distances on
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# each dimension.
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for i in range(num_robots - 1):
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for j in range(i + 1, num_robots):
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# Compute the distance on each dimension between robot i and robot j.
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x_diff = model.NewIntVar(-room_size, room_size, f'x_diff{i}')
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y_diff = model.NewIntVar(-room_size, room_size, f'y_diff{i}')
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model.Add(x_diff == x[i] - x[j])
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model.Add(y_diff == y[i] - y[j])
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# Compute the square of the previous differences.
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x_diff_sq = model.NewIntVar(0, room_size**2, f'x_diff_sq{i}')
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y_diff_sq = model.NewIntVar(0, room_size**2, f'y_diff_sq{i}')
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model.AddMultiplicationEquality(x_diff_sq, x_diff, x_diff)
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model.AddMultiplicationEquality(y_diff_sq, y_diff, y_diff)
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# We just need to be <= to the scaled square distance as we are
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# maximizing the min distance, which is equivalent as maximizing the min
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# square distance.
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model.Add(scaled_min_square_distance <= scaling *
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(x_diff_sq + y_diff_sq))
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# Naive symmetry breaking.
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for i in range(1, num_robots):
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model.Add(x[0] <= x[i])
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model.Add(y[0] <= y[i])
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# Objective
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model.Maximize(scaled_min_square_distance)
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# Creates a solver and solves the model.
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solver = cp_model.CpSolver()
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if params:
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text_format.Parse(params, solver.parameters)
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solver.parameters.log_search_progress = True
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status = solver.Solve(model)
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# Prints the solution.
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if status == cp_model.OPTIMAL or status == cp_model.FEASIBLE:
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print(f'Spread {num_robots} with a min pairwise distance of'
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f' {math.sqrt(solver.ObjectiveValue() / scaling)}')
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for i in range(num_robots):
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print(f'robot {i}: x={solver.Value(x[i])} y={solver.Value(y[i])}')
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else:
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print('No solution found.')
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def main(argv: Sequence[str]) -> None:
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if len(argv) > 1:
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raise app.UsageError('Too many command-line arguments.')
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spread_robots(_NUM_ROBOTS.value, _ROOM_SIZE.value, _PARAMS.value)
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if __name__ == '__main__':
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app.run(main)
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