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"""Example illustrating the use of Apache Beam for solving distributing
optimization tasks.

This example solves an optimization problem which consists of distributing a
number of crops to grow in several greenhouses. The decision where to grow the
crop has an impact on the production parameters associated with the greenhouse,
which affects the total cost of production at the greenhouse. Additionally,
each crop needs to be transported to a customer so the decision where to grow
the crop has an impact on the transportation costs as well.

This type of optimization problems are known as mixed-integer programs as they
exist of discrete parameters (do we produce a crop in greenhouse A, B or C?)
and continuous parameters (the greenhouse production parameters).

Running this example requires NumPy and SciPy. The input consists of a CSV file
with the following columns (Tx representing the transporation cost/unit if the
crop is produced in greenhouse x): Crop name, Quantity, Ta, Tb, Tc, ....

Example input file with 5 crops and 3 greenhouses (a transporation cost of 0
forbids production of the crop in a greenhouse):
OP01,8,12,0,12
OP02,30,14,3,12
OP03,25,7,3,14
OP04,87,7,2,2
OP05,19,1,7,10

The pipeline consists of three phases:
  - Creating a grid of mappings (assignment of each crop to a greenhouse)
  - For each mapping and each greenhouse, optimization of the production
    parameters for cost, addition of the transporation costs, and aggregation
    of the costs for each mapping.
  - Selecting the mapping with the lowest cost.
"""

from __future__ import absolute_import
from __future__ import division

import argparse
import logging
import string
import uuid
from collections import defaultdict

import numpy as np

import apache_beam as beam
from apache_beam import pvalue
from apache_beam.options.pipeline_options import PipelineOptions
from apache_beam.options.pipeline_options import SetupOptions
from scipy.optimize import minimize


class Simulator(object):
  """Greenhouse simulation for the optimization of greenhouse parameters."""

  def __init__(self, quantities):
    self.quantities = np.atleast_1d(quantities)

    self.A = np.array([[3.0, 10, 30],
                       [0.1, 10, 35],
                       [3.0, 10, 30],
                       [0.1, 10, 35]])

    self.P = 1e-4 * np.array([[3689, 1170, 2673],
                              [4699, 4387, 7470],
                              [1091, 8732, 5547],
                              [381, 5743, 8828]])

    a0 = np.array([[1.0, 1.2, 3.0, 3.2]])
    coeff = np.sum(np.cos(np.dot(a0.T, self.quantities[None, :])), axis=1)
    self.alpha = coeff / np.sum(coeff)

  def simulate(self, xc):
    # Map the input parameter to a cost for each crop.
    weighted_distance = np.sum(self.A * np.square(xc - self.P), axis=1)
    f = -np.sum(self.alpha * np.exp(-weighted_distance))
    return np.square(f) * np.log(self.quantities)


class CreateGrid(beam.PTransform):
  """A transform for generating the mapping grid.

  Input: Formatted records of the input file, e.g.,
  {
    'crop': 'OP009',
    'quantity': 102,
    'transport_costs': [('A', None), ('B', 3), ('C', 8)]
  }
  Output: tuple (mapping_identifier, {crop -> greenhouse})
  """

  class PreGenerateMappings(beam.DoFn):
    """ParDo implementation forming based on two elements a small sub grid.

    This facilitates parallellization of the grid generation.
    Emits two PCollections: the subgrid represented as collection of lists of
    two tuples, and a list of remaining records. Both serve as an input to
    GenerateMappings.
    """

    def process(self, element):
      records = list(element[1])
      # Split of 2 crops and pre-generate the subgrid.
      # Select the crop with highest number of possible greenhouses:
      # in case two crops with only a single possible greenhouse were selected
      # the subgrid would consist of only 1 element.
      best_split = np.argsort([-len(r['transport_costs']) for r in records])[:2]
      rec1 = records[best_split[0]]
      rec2 = records[best_split[1]]

      # Generate & emit all combinations
      for a in rec1['transport_costs']:
        if a[1]:
          for b in rec2['transport_costs']:
            if b[1]:
              combination = [(rec1['crop'], a[0]), (rec2['crop'], b[0])]
              yield pvalue.TaggedOutput('splitted', combination)

      # Pass on remaining records
      remaining = [rec for i, rec in enumerate(records) if i not in best_split]
      yield pvalue.TaggedOutput('combine', remaining)

  class GenerateMappings(beam.DoFn):
    """ParDo implementation to generate all possible mappings.

    Input: output of PreGenerateMappings
    Output: tuples of the form (mapping_identifier, {crop -> greenhouse})
    """

    @staticmethod
    def _coordinates_to_greenhouse(coordinates, greenhouses, crops):
      # Map the grid coordinates back to greenhouse labels
      arr = []
      for coord in coordinates:
        arr.append(greenhouses[coord])
      return dict(zip(crops, np.array(arr)))

    def process(self, element, records):
      # Generate available greenhouses and grid coordinates for each crop.
      grid_coordinates = []
      for rec in records:
        # Get indices for available greenhouses (w.r.t crops)
        filtered = [i for i, av in enumerate(rec['transport_costs']) if av[1]]
        grid_coordinates.append(filtered)

      # Generate all mappings
      grid = np.vstack(list(map(np.ravel, np.meshgrid(*grid_coordinates)))).T
      crops = [rec['crop'] for rec in records]
      greenhouses = [rec[0] for rec in records[0]['transport_costs']]
      for point in grid:
        # translate back to greenhouse label
        mapping = self._coordinates_to_greenhouse(point, greenhouses, crops)
        assert all(rec[0] not in mapping for rec in element)
        # include the incomplete mapping of 2 crops
        mapping.update(element)
        # include identifier
        yield (uuid.uuid4().hex, mapping)

  def expand(self, records):
    o = (
        records
        | 'pair one' >> beam.Map(lambda x: (1, x))
        | 'group all records' >> beam.GroupByKey()
        | 'split one of' >> beam.ParDo(self.PreGenerateMappings())
        .with_outputs('splitted', 'combine')
    )

    # Create mappings, and prevent fusion (this limits the parallelization
    # in the optimization step)
    mappings = (
        o.splitted
        | 'create mappings' >> beam.ParDo(self.GenerateMappings(),
                                          pvalue.AsSingleton(o.combine))
        | 'prevent fusion' >> beam.Reshuffle()
    )

    return mappings


class OptimizeGrid(beam.PTransform):
  """A transform for optimizing all greenhouses of the mapping grid."""

  class CreateOptimizationTasks(beam.DoFn):
    """
    Create tasks for optimization.

    Input: (mapping_identifier, {crop -> greenhouse})
    Output: ((mapping_identifier, greenhouse), [(crop, quantity),...])
    """

    def process(self, element, quantities):
      mapping_identifier, mapping = element

      # Create (crop, quantity) lists for each greenhouse
      greenhouses = defaultdict(list)
      for crop, greenhouse in mapping.items():
        quantity = quantities[crop]
        greenhouses[greenhouse].append((crop, quantity))

      # Create input for OptimizeProductParameters
      for greenhouse, crops in greenhouses.items():
        key = (mapping_identifier, greenhouse)
        yield (key, crops)

  class OptimizeProductParameters(beam.DoFn):
    """Solve the optimization task to determine optimal production parameters.
    Input: ((mapping_identifier, greenhouse), [(crop, quantity),...])
    Two outputs:
      - solution: (mapping_identifier, (greenhouse, [production parameters]))
      - costs: (crop, greenhouse, mapping_identifier, cost)
    """

    @staticmethod
    def _optimize_production_parameters(sim):
      # setup initial starting point & bounds
      x0 = 0.5 * np.ones(3)
      bounds = list(zip(np.zeros(3), np.ones(3)))

      # Run L-BFGS-B optimizer
      result = minimize(lambda x: np.sum(sim.simulate(x)), x0, bounds=bounds)
      return result.x.tolist(), sim.simulate(result.x)

    def process(self, element):
      mapping_identifier, greenhouse = element[0]
      crops, quantities = zip(*element[1])
      sim = Simulator(quantities)
      optimum, costs = self._optimize_production_parameters(sim)
      solution = (mapping_identifier, (greenhouse, optimum))
      yield pvalue.TaggedOutput('solution', solution)
      for crop, cost, quantity in zip(crops, costs, quantities):
        costs = (crop, greenhouse, mapping_identifier, cost * quantity)
        yield pvalue.TaggedOutput('costs', costs)

  def expand(self, inputs):
    mappings, quantities = inputs
    opt = (
        mappings
        | 'optimization tasks' >> beam.ParDo(self.CreateOptimizationTasks(),
                                             pvalue.AsDict(quantities))
        | 'optimize' >> beam.ParDo(self.OptimizeProductParameters())
        .with_outputs('costs', 'solution')
    )
    return opt


class CreateTransportData(beam.DoFn):
  """Transform records to pvalues ((crop, greenhouse), transport_cost)"""

  def process(self, record):
    crop = record['crop']
    for greenhouse, transport_cost in record['transport_costs']:
      yield ((crop, greenhouse), transport_cost)


def add_transport_costs(element, transport, quantities):
  """Adds the transport cost for the crop to the production cost.

  elements are of the form (crop, greenhouse, mapping, cost), the cost only
  corresponds to the production cost. Return the same format, but including
  the transport cost.
  """
  crop = element[0]
  cost = element[3]
  # lookup & compute cost
  transport_key = element[:2]
  transport_cost = transport[transport_key] * quantities[crop]
  return element[:3] + (cost + transport_cost,)


def parse_input(line):
  # Process each line of the input file to a dict representing each crop
  # and the transport costs
  columns = line.split(',')

  # Assign each greenhouse a character
  transport_costs = []
  for greenhouse, cost in zip(string.ascii_uppercase, columns[2:]):
    info = (greenhouse, int(cost) if cost else None)
    transport_costs.append(info)

  return {
      'crop': columns[0],
      'quantity': int(columns[1]),
      'transport_costs': transport_costs
  }


def format_output(element):
  """Transforms the datastructure (unpack lists introduced by CoGroupByKey)
  before writing the result to file.
  """
  result = element[1]
  result['cost'] = result['cost'][0]
  result['production'] = dict(result['production'])
  result['mapping'] = result['mapping'][0]
  return result


def run(argv=None, save_main_session=True):
  parser = argparse.ArgumentParser()
  parser.add_argument('--input',
                      dest='input',
                      required=True,
                      help='Input description to process.')
  parser.add_argument('--output',
                      dest='output',
                      required=True,
                      help='Output file to write results to.')
  known_args, pipeline_args = parser.parse_known_args(argv)
  pipeline_options = PipelineOptions(pipeline_args)
  pipeline_options.view_as(SetupOptions).save_main_session = save_main_session

  with beam.Pipeline(options=pipeline_options) as p:
    # Parse input file
    records = (
        p
        | 'read' >> beam.io.ReadFromText(known_args.input)
        | 'process input' >> beam.Map(parse_input)
    )

    # Create two pcollections, used as side inputs
    transport = (
        records
        | 'create transport' >> beam.ParDo(CreateTransportData())
    )

    quantities = (
        records
        | 'create quantities' >> beam.Map(lambda r: (r['crop'], r['quantity']))
    )

    # Generate all mappings and optimize greenhouse production parameters
    mappings = records | CreateGrid()
    opt = (mappings, quantities) | OptimizeGrid()

    # Then add the transport costs and sum costs per crop.
    costs = (
        opt.costs
        | 'include transport' >> beam.Map(add_transport_costs,
                                          pvalue.AsDict(transport),
                                          pvalue.AsDict(quantities))
        | 'drop crop and greenhouse' >> beam.Map(lambda x: (x[2], x[3]))
        | 'aggregate crops' >> beam.CombinePerKey(sum)
    )

    # Join cost, mapping and production settings solution on mapping identifier.
    # Then select best.
    join_operands = {
        'cost': costs,
        'production': opt.solution,
        'mapping': mappings
    }
    best = (
        join_operands
        | 'join' >> beam.CoGroupByKey()
        | 'select best' >> beam.CombineGlobally(min, key=lambda x: x[1]['cost'])
        .without_defaults()
        | 'format output' >> beam.Map(format_output)
    )

    # pylint: disable=expression-not-assigned
    best | 'write optimum' >> beam.io.WriteToText(known_args.output)


if __name__ == '__main__':
  logging.getLogger().setLevel(logging.INFO)
  run()