Python pulp.LpInteger() Examples

def create_model(self):
        def distances(assignment):
            return l2_distance(self.data[assignment[0]], self.centroids[assignment[1]])

        clusters = list(range(self.k))
        assignments = [(i, j)for i in range(self.n) for j in range(self.k)]

        # outflow variables for data nodes
        self.y = pulp.LpVariable.dicts('data-to-cluster assignments',
                                  assignments,
                                  lowBound=0,
                                  upBound=1,
                                  cat=pulp.LpInteger)

        # outflow variables for cluster nodes
        self.b = pulp.LpVariable.dicts('cluster outflows',
                                  clusters,
                                  lowBound=0,
                                  upBound=self.n-self.min_size,
                                  cat=pulp.LpContinuous)

        # create the model
        self.model = pulp.LpProblem("Model for assignment subproblem", pulp.LpMinimize)

        # objective function
        self.model += pulp.lpSum(distances(assignment) * self.y[assignment] for assignment in assignments)

        # flow balance constraints for data nodes
        for i in range(self.n):
            self.model += pulp.lpSum(self.y[(i, j)] for j in range(self.k)) == 1

        # flow balance constraints for cluster nodes
        for j in range(self.k):
            self.model += pulp.lpSum(self.y[(i, j)] for i in range(self.n)) - self.min_size == self.b[j]

        # flow balance constraint for the sink node
        self.model += pulp.lpSum(self.b[j] for j in range(self.k)) == self.n - (self.k * self.min_size) 

def create_model(self):
        def distances(assignment):
            return l2_distance(self.data[assignment[0]], self.centroids[assignment[1]])

        clusters = list(range(self.k))
        assignments = [(i, j)for i in range(self.n) for j in range(self.k)]

        # outflow variables for data nodes
        self.y = pulp.LpVariable.dicts('data-to-cluster assignments',
                                  assignments,
                                  lowBound=0,
                                  upBound=1,
                                  cat=pulp.LpInteger)

        # outflow variables for cluster nodes
        self.b = pulp.LpVariable.dicts('cluster outflows',
                                  clusters,
                                  lowBound=0,
                                  upBound=self.n-self.min_size,
                                  cat=pulp.LpContinuous)

        # create the model
        self.model = pulp.LpProblem("Model for assignment subproblem", pulp.LpMinimize)

        # objective function
        self.model += pulp.lpSum([distances(assignment) * self.y[assignment] for assignment in assignments])

        # flow balance constraints for data nodes
        for i in range(self.n):
            self.model += pulp.lpSum(self.y[(i, j)] for j in range(self.k)) == 1

        # flow balance constraints for cluster nodes
        for j in range(self.k):
            self.model += pulp.lpSum(self.y[(i, j)] for i in range(self.n)) - self.min_size == self.b[j]
            
        # capacity constraint on outflow of cluster nodes
        for j in range(self.k):
            self.model += self.b[j] <= self.max_size - self.min_size 

        # flow balance constraint for the sink node
        self.model += pulp.lpSum(self.b[j] for j in range(self.k)) == self.n - (self.k * self.min_size) 

def create_model(self):
        def distances(assignment):
            return l2_distance(self.data[assignment[0]], self.centroids[assignment[1]])

        assignments = [(i, j) for i in range(self.n) for j in range(self.k)]

        # assignment variables
        self.y = pulp.LpVariable.dicts('data-to-cluster assignments',
                                  assignments,
                                  lowBound=0,
                                  upBound=1,
                                  cat=pulp.LpInteger)

        # create the model
        self.model = pulp.LpProblem("Model for assignment subproblem", pulp.LpMinimize)

        # objective function
        self.model += pulp.lpSum([distances(assignment) * self.weights[assignment[0]] * self.y[assignment] for assignment in assignments]), 'Objective Function - sum weighted squared distances to assigned centroid'
        # this is also weighted, otherwise the weighted centroid computation don't make sense.

        # constraints on the total weights of clusters
        for j in range(self.k):
            self.model += pulp.lpSum([self.weights[i] * self.y[(i, j)] for i in range(self.n)]) >= self.min_weight, "minimum weight for cluster {}".format(j)
            self.model += pulp.lpSum([self.weights[i] * self.y[(i, j)] for i in range(self.n)]) <= self.max_weight, "maximum weight for cluster {}".format(j)

        # make sure each point is assigned at least once, and only once
        for i in range(self.n):
            self.model += pulp.lpSum([self.y[(i, j)] for j in range(self.k)]) == 1, "must assign point {}".format(i) 

def solve_ilp(self, N):
        # build the A matrix: a_ij is 1 if j-th gram appears in the i-th sentence

        A = np.zeros((len(self.sentences_idx), len(self.ref_ngrams_idx)))
        for i in self.sentences_idx:
            sent = self.sentences[i].untokenized_form
            sngrams = list(extract_ngrams2([sent], self.stemmer, self.LANGUAGE, N))
            for j in self.ref_ngrams_idx:
                if self.ref_ngrams[j] in sngrams:
                    A[i][j] = 1

        # Define ILP variable, x_i is 1 if sentence i is selected, z_j is 1 if gram j appears in the created summary
        x = pulp.LpVariable.dicts('sentences', self.sentences_idx, lowBound=0, upBound=1, cat=pulp.LpInteger)
        z = pulp.LpVariable.dicts('grams', self.ref_ngrams_idx, lowBound=0, upBound=1, cat=pulp.LpInteger)

        # Define ILP problem, maximum coverage of grams from the reference summaries
        prob = pulp.LpProblem("ExtractiveUpperBound", pulp.LpMaximize)
        prob += pulp.lpSum(z[j] for j in self.ref_ngrams_idx)

        # Define ILP constraints, length constraint and consistency constraint (impose that z_j is 1 if j
        # appears in the created summary)
        prob += pulp.lpSum(x[i] * self.sentences[i].length for i in self.sentences_idx) <= self.sum_length

        for j in self.ref_ngrams_idx:
            prob += pulp.lpSum(A[i][j] * x[i] for i in self.sentences_idx) >= z[j]

        # Solve ILP problem and post-processing to get the summary
        try:
            print('Solving using CPLEX')
            prob.solve(pulp.CPLEX(msg=0))
        except:
            print('Fall back to GLPK')
            prob.solve(pulp.GLPK(msg=0))
                

        summary_idx = []
        for idx in self.sentences_idx:
            if x[idx].value() == 1.0:
                summary_idx.append(idx)

        return summary_idx 

def make_into_lp_problem(good_for, N, add_noise=False):
    """
    Helper function for solve_with_lp_and_reduce()

    N --- number of isoform sequences
    good_for --- dict of <isoform_index> --> list of matched paths index
    """
    prob = LpProblem("The Whiskas Problem",LpMinimize)

    # each good_for is (isoform_index, [list of matched paths index])
    # ex: (0, [1,2,4])
    # ex: (3, [2,5])
    used_paths = []
    for t_i, p_i_s in good_for:
        used_paths += p_i_s
    used_paths = list(set(used_paths))

    variables = [LpVariable(str(i),0,1,LpInteger) for i in used_paths]
    #variables = [LpVariable(str(i),0,1,LpInteger) for i in xrange(N)]

    # objective is to minimize sum_{Xi}
    prob += sum(v for v in variables)

    already_seen = set()
    # constraints are for each isoform, expressed as c_i * x_i >= 1
    # where c_i = 1 if x_i is matched for the isoform
    # ex: (0, [1,2,4]) becomes t_0 = x_1 + x_2 + x_4 >= 1
    for t_i, p_i_s in good_for:
        #c_i_s = [1 if i in p_i_s else 0 for i in xrange(N)]
        #prob += sum(variables[i]*(1 if i in p_i_s else 0) for i in xrange(N)) >= 1
        p_i_s.sort()
        pattern = ",".join(map(str,p_i_s))
        #print >> sys.stderr, t_i, p_i_s, pattern
        if pattern not in already_seen:
            if add_noise:
                prob += sum(variables[i]*(1+random.random() if p in p_i_s else 0) for i,p in enumerate(used_paths)) >= 1
            else:
                prob += sum(variables[i]*(1 if p in p_i_s else 0) for i,p in enumerate(used_paths)) >= 1
        already_seen.add(pattern)
    prob.writeLP('cogent.lp')
    return prob 

def create_lscp_model(coverage_dict, model_file=None, delineator="$", ):
    """
    Creates a LSCP (Location set covering problem) using the provided coverage and
    parameters. Writes a .lp file which can be solved with Gurobi

    Church, R., & Murray, A. (2009). Coverage Business Site Selection, Location
    Analysis, and GIS (pp. 209-233). Hoboken, New Jersey: Wiley.

    :param coverage_dict: (dictionary) The coverage to use to generate the model
    :param model_file: (string) The model file to output
    :param delineator: (string) The character(s) to use to delineate the layer from the ids
    :return: (Pulp problem) The generated problem to solve
    """
    validate_coverage(coverage_dict, ["coverage"], ["binary"])
    if not isinstance(coverage_dict, dict):
        raise TypeError("coverage_dict is not a dictionary")
    if model_file and not (isinstance(model_file, str)):
        raise TypeError("model_file is not a string")
    if not isinstance(delineator, str):
        raise TypeError("delineator is not a string")
        # create the variables
    demand_vars = {}
    for demand_id in coverage_dict["demand"]:
        demand_vars[demand_id] = pulp.LpVariable("Y{}{}".format(delineator, demand_id), 0, 1, pulp.LpInteger)
    facility_vars = {}
    for facility_type in coverage_dict["facilities"]:
        facility_vars[facility_type] = {}
        for facility_id in coverage_dict["facilities"][facility_type]:
            facility_vars[facility_type][facility_id] = pulp.LpVariable(
                "{}{}{}".format(facility_type, delineator, facility_id), 0, 1, pulp.LpInteger)
    # create the problem
    prob = pulp.LpProblem("LSCP", pulp.LpMinimize)
    # Create objective, minimize number of facilities
    to_sum = []
    for facility_type in coverage_dict["facilities"]:
        for facility_id in coverage_dict["facilities"][facility_type]:
            to_sum.append(facility_vars[facility_type][facility_id])
    prob += pulp.lpSum(to_sum)
    # add coverage constraints
    for demand_id in coverage_dict["demand"]:
        to_sum = []
        for facility_type in coverage_dict["demand"][demand_id]["coverage"]:
            for facility_id in coverage_dict["demand"][demand_id]["coverage"][facility_type]:
                to_sum.append(facility_vars[facility_type][facility_id])
        # Hack to get model to "solve" when infeasible with GLPK.
        # Pulp will automatically add dummy variables when the sum is empty, since these are all the same name,
        # it seems that GLPK doesn't read the lp problem properly and fails
        if not to_sum:
            to_sum = [pulp.LpVariable("__dummy{}{}".format(delineator, demand_id), 0, 0, pulp.LpInteger)]
        prob += pulp.lpSum(to_sum) >= 1, "D{}".format(demand_id)
    if model_file:
        prob.writeLP(model_file)
    return prob