Interfacing with LocalSolver: Max Weighted Cut Solver

You can see this app running online at: LocalSolver Max Weighted Cut

What this app does:

  • Solves the Max Weighted Cut Problem, in a geographic setting. The Max Weighted Cut Problem is known to be NP-Complete.

This app aims to demonstrate:

Setup Instructions

Before you can run this app, you will need to Install LocalSolver with a free trial.

Next, use the app name 'tropofy_localsolver_max_cut' to quickstart as in Running and Debugging Tropofy Apps

Full Source


Copyright 2015 Tropofy Pty Ltd, all rights reserved.

This source file is part of Tropofy and governed by the Tropofy terms of service
available at:

The LocalSolver example this app is based on can be found at

Used with permission.

This source file is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the license files for details.

Problem Description:

Given a graph G=(V,E), a cut is a partition of V into two subset S and V-S. The size
of a cut is the number of edges with one extremity in S and the other in V-S. The
Max Weighted Cut problem is to maximise the total weight of the edges in the cut.

Furthermore, a MAX WEIGHTED CUT is implemented, if all weights are not == 1.
In this version each edge has a real number, its weight, and the objective is to maximize
not the number of edges but the .

import subprocess

import pkg_resources
from sqlalchemy.types import Text, Float, Boolean, Integer
from sqlalchemy.schema import Column, UniqueConstraint, ForeignKeyConstraint
from sqlalchemy.orm import relationship
from simplekml import Kml, Style, IconStyle, Icon, LineStyle

from import AppWithDataSets, Step, StepGroup
from tropofy.widgets import ExecuteFunction, SimpleGrid, KMLMap, Chart
from tropofy.database.tropofy_orm import DataSetMixin
from tropofy.file_io import read_write_xl

class MaxWCutNode(DataSetMixin):
    name = Column(Text, nullable=False)
    latitude = Column(Float, nullable=False)
    longitude = Column(Float, nullable=False)
    allocated_group_index = Column(Boolean)  # Only 2 possible groups, thus boolean.

    def get_table_args(cls): 
        return (UniqueConstraint('data_set_id', 'name'),)

    def get_ordered_list_of_all_nodes(cls, data_set):
        return data_set.query(cls).order_by(

class MaxWCutArc(DataSetMixin):
    orig_name = Column(Text, nullable=False)
    dest_name = Column(Text, nullable=False)
    weight = Column(Integer, nullable=False)  # Must be int for Localsolver

    # The primaryjoin argument to relationship is only needed when there is ambiguity
    orig_node = relationship(MaxWCutNode, primaryjoin="and_(MaxWCutArc.data_set_id==MaxWCutNode.data_set_id,")
    dest_node = relationship(MaxWCutNode, primaryjoin="and_(MaxWCutArc.data_set_id==MaxWCutNode.data_set_id,")

    def get_table_args(cls):
        return (
            UniqueConstraint('data_set_id', 'orig_name', 'dest_name'),
            ForeignKeyConstraint(['orig_name', 'data_set_id'], ['', 'maxwcutnode.data_set_id'], ondelete='CASCADE', onupdate='CASCADE'),
            ForeignKeyConstraint(['dest_name', 'data_set_id'], ['', 'maxwcutnode.data_set_id'], ondelete='CASCADE', onupdate='CASCADE')

    def in_cut(self):
        if self.orig_node.allocated_group_index is not None and self.dest_node.allocated_group_index is not None:
            return self.orig_node.allocated_group_index != self.dest_node.allocated_group_index

    def html_description(self):
        return """{orig}, {dest}<br>Weight: {weight}""".format(

class MapArcInput(KMLMap):
    def get_kml(self, app_session):
        kml = Kml()

        node_style = Style(iconstyle=IconStyle(scale=0.8, icon=Icon(href='')))
        node_folder = kml.newfolder(name="Nodes")
        for p in [node_folder.newpoint(, coords=[(n.longitude, n.latitude)]) for n in app_session.data_set.query(MaxWCutNode).all()]:
   = node_style

        arc_folder = kml.newfolder(name="Arcs")
        arcs = app_session.data_set.query(MaxWCutArc).all()
        for arc in arcs:
            arc_style = Style(linestyle=LineStyle(color='FFC86602', width=4))
            l = arc_folder.newlinestring(name=arc.html_description, coords=[(arc.orig_node.longitude, arc.orig_node.latitude), (arc.dest_node.longitude, arc.dest_node.latitude)])
   = arc_style

        return kml.kml()

class MapArcOutput(KMLMap):
    def get_kml(self, app_session):
        kml = Kml()

        group_one_node_style = Style(iconstyle=IconStyle(scale=0.8, icon=Icon(href='')))
        group_one_node_folder = kml.newfolder(name="Nodes - Group 1")
        for p in [group_one_node_folder.newpoint(, coords=[(n.longitude, n.latitude)]) for n in app_session.data_set.query(MaxWCutNode).filter_by(allocated_group_index=True).all()]:
   = group_one_node_style

        group_two_node_style = Style(iconstyle=IconStyle(scale=0.4, icon=Icon(href='')))
        group_two_node_folder = kml.newfolder(name="Nodes - Group 2")
        for p in [group_two_node_folder.newpoint(, coords=[(n.longitude, n.latitude)]) for n in app_session.data_set.query(MaxWCutNode).filter_by(allocated_group_index=False).all()]:
   = group_two_node_style

        arc_in_cut_style = Style(linestyle=LineStyle(color='FF0101F9', width=4))
        arc_not_in_cut_style = Style(linestyle=LineStyle(color='FFC86602', width=3))

        arcs_in_cut_folder = kml.newfolder(name="Arcs in Cut")
        arcs_not_in_cut_folder = kml.newfolder(name="Arcs not in Cut")

        arcs = app_session.data_set.query(MaxWCutArc).all()

        for arc in arcs:
            if arc.in_cut:
                l = arcs_in_cut_folder.newlinestring(name=arc.html_description, coords=[(arc.orig_node.longitude, arc.orig_node.latitude), (arc.dest_node.longitude, arc.dest_node.latitude)])
       = arc_in_cut_style
                l = arcs_not_in_cut_folder.newlinestring(name=arc.html_description, coords=[(arc.orig_node.longitude, arc.orig_node.latitude), (arc.dest_node.longitude, arc.dest_node.latitude)])
       = arc_not_in_cut_style
        return kml.kml()

class WeightInCutPieChart(Chart):
    def get_chart_type(self, app_session):
        return Chart.PIECHART

    def get_table_schema(self, app_session):
        return {"item": ("string", "Item"), "weight": ("number", "Weight")}

    def get_table_data(self, app_session):
        arcs = app_session.data_set.query(MaxWCutArc).all()
        arc_weight_total = sum((arc.weight for arc in arcs))
        arc_weight_in_cut = sum((arc.weight for arc in arcs if arc.in_cut))

        items = [
            {"item": "In Cut", "weight": arc_weight_in_cut},
            {"item": "Not In Cut", "weight": arc_weight_total - arc_weight_in_cut},
        return items

    def get_column_ordering(self, app_session):
        return ["item", "weight"]

    def get_order_by_column(self, app_session):
        return "weight"

    def get_chart_options(self, app_session):
        arcs = app_session.data_set.query(MaxWCutArc).all()
        arc_weight_total = sum((arc.weight for arc in arcs))
        arc_weight_in_cut = sum((arc.weight for arc in arcs if arc.in_cut))
        return {'title': 'Weight in Cut: {percent} ({weight} / {max})'.format(
            percent="{0:.0f}%".format(float(arc_weight_in_cut)/arc_weight_total * 100),

class ExecuteLocalSolver(ExecuteFunction):
    def get_button_text(self, app_session):
        return "Solve Max Weighted Cut"

    def execute_function(self, app_session):

class LocalSolverMaxWeightedCut(AppWithDataSets):
    def get_name(self):
        return 'LocalSolver Max Weighted Cut'

    def get_static_content_path(self, app_session):
        return pkg_resources.resource_filename('te_ls_max_cut', 'static')

    def get_gui(self):
        step_group1 = StepGroup(name='Input')
            help_text="Enter arcs connecting locations. Note that the direction of each arc does not matter. Furthermore, to solve Max Cut instead of Max Weighted Cut, enter all weights as 1.",
        step_group1.add_step(Step(name='Review Inputs', widgets=[MapArcInput()]))

        step_group2 = StepGroup(name='Solve')
        step_group2.add_step(Step(name='Solve Max Weighted cut using LocalSolver', widgets=[ExecuteLocalSolver()]))

        step_group3 = StepGroup(name='Output')
        step_group3.add_step(Step(name='Max Cut Solution', widgets=[
            {"widget": MapArcOutput(), "cols": 12},
            {"widget": WeightInCutPieChart(), "cols": 5},
            {"widget": SimpleGrid(MaxWCutNode), "cols": 7},

        return [step_group1, step_group2, step_group3]

    def get_examples(self):
        return {
            "Demo European data": load_euro_data,
            "Demo Brisbane data": load_brisbane_data,

    def get_default_example_data_set_name(self):
        return "Demo European data"

    def get_icon_url(self):
        return "/{}/static/{}/max_cut.png".format(

def call_local_solver(app_session):
    invoke_localsolver_using_lsp_file(app_session, write_localsolver_input_file(app_session))

def write_localsolver_input_file(app_session):
    input_file_name = ''
    input_file_path = app_session.get_file_path_in_local_data_set_dir(input_file_name)
    f = open(input_file_path, 'w')

    nodes = MaxWCutNode.get_ordered_list_of_all_nodes(app_session.data_set)
    node_name_to_index = { i+1 for i, node in enumerate(nodes)}  # This LocalSolver example indexes from 1
    arcs = app_session.data_set.query(MaxWCutArc).all()

    f.write('%s %s\n' % (len(nodes), len(arcs)))
    for arc in arcs:
        f.write('{orig} {dest} {weight}\n'.format(

    return input_file_name

def invoke_localsolver_using_lsp_file(app_session, input_file_name):
    for item in app_session.data_set.query(MaxWCutNode).all():
        item.allocated_group_index = None  # Reset solution

    lsp_file_path = pkg_resources.resource_filename('te_ls_max_cut', 'max_cut.lsp')
    solution_file_name = 'output.txt'
    solution_file_path = app_session.get_file_path_in_local_data_set_dir(solution_file_name)
    open(solution_file_path, 'w').close()  # clear the solution file if it exists
    p = subprocess.Popen(
        ["localsolver", lsp_file_path, "inFileName=%s" % input_file_name, "solFileName=%s" % solution_file_name, "lsTimeLimit=2"],
    out, _ = p.communicate()
    with open(solution_file_path) as f:
        content = f.readlines()
        if content:
            app_session.task_manager.send_progress_message(out.replace("\n", "<br>"))

            nodes = MaxWCutNode.get_ordered_list_of_all_nodes(app_session.data_set)
            for i, node in enumerate(nodes):
                node.allocated_group_index = int(content[i].split(' ')[1].strip('\n'))
                '''The data you have entered exceeds the limits of the trial version of LocalSolver used to run this
                app. LocalSolver's Trial Version does not allow more than 1000 expressions and 100 decisions.'''

def load_brisbane_data(app_session):
    # Post code geocode data sourced from
        pkg_resources.resource_filename('te_ls_max_cut', 'max_cut_brisbane_example_data.xlsx')

def load_euro_data(app_session):
    # Post code geocode data sourced from
        pkg_resources.resource_filename('te_ls_max_cut', 'max_cut_euro_example_data.xlsx')

LocalSolver lsp File

/********** maxcut.lsp **********/

/* Reads instance data */
function input(){
	 usage = "\nUsage: localsolver maxcut.lsp "
    	 + "inFileName=inputFile [lsTimeLimit=timeLimit]\n";

	if (inFileName == nil) error(usage);
	 for [i in 1..m]{
	     origin[i] = readInt(instance);
	     dest[i] = readInt(instance);
	     w[i] = readInt(instance);

/* Declares the optimization model. */
function model(){
	 // x[i] is 1 if vertex i is in the subset S, 0 if it is in V-S
	 x[1..n] <- bool();
	 //an edge is in the cut-set if it has an extremity in each class of the bipartition
	 incut[i in 1..m] <- x[origin[i]] != x[dest[i]] ? 1 : 0;
	 maximize sum[i in 1..m] (w[i]* incut[i]);

/* Parameterizes the solver. */
function param(){
	 if(lsTimeLimit == nil) 

/* Writes the solution in a file following the following format: 
 * each line contains a vertex number and its subset (1 for S, 0 for V-S) */
function output(){
  println("Write solution into file");
  solFile = openWrite(solFileName);
  for [i in 1..n]
    println(solFile, i, " ", getValue(x[i]));