Source code for pyomo.repn.plugins.gams_writer

#  ___________________________________________________________________________
#
#  Pyomo: Python Optimization Modeling Objects
#  Copyright 2017 National Technology and Engineering Solutions of Sandia, LLC
#  Under the terms of Contract DE-NA0003525 with National Technology and
#  Engineering Solutions of Sandia, LLC, the U.S. Government retains certain
#  rights in this software.
#  This software is distributed under the 3-clause BSD License.
#  ___________________________________________________________________________

#
# Problem Writer for GAMS Format Files
#

from six import StringIO, string_types, iteritems
from six.moves import xrange

from pyutilib.misc import PauseGC

from pyomo.core.expr import current as EXPR
from pyomo.core.expr.numvalue import (
    is_fixed, value, as_numeric, native_types, native_numeric_types,
    nonpyomo_leaf_types,
)
from pyomo.core.base import (
    SymbolMap, ShortNameLabeler, NumericLabeler, Block, Constraint, Expression,
    Objective, Var, Param, minimize, Suffix, SortComponents)
from pyomo.core.base.component import ActiveComponent
from pyomo.core.kernel.base import ICategorizedObject
from pyomo.opt import ProblemFormat
from pyomo.opt.base import AbstractProblemWriter, WriterFactory
from pyomo.repn.util import valid_expr_ctypes_minlp, \
    valid_active_ctypes_minlp

import logging

logger = logging.getLogger('pyomo.core')

_ftoa_precision_str = '%.17g'
def _ftoa(val):
    if val is None:
        return val
    if type(val) not in native_numeric_types:
        if is_fixed(val):
            val = value(val)
        else:
            raise ValueError("non-fixed bound or weight: " + str(val))

    a = _ftoa_precision_str % val
    i = len(a)
    while i > 1:
        try:
            if float(a[:i-1]) == val:
                i -= 1
            else:
                break
        except:
            break
    if i == len(a):
        logger.warning(
            "converting %s to string resulted in loss of precision" % val)
    #if a.startswith('1.57'):
    #    raise RuntimeError("wtf %s %s, %s" % ( val, a, i))
    return a[:i]

_legal_unary_functions = {
    'ceil','floor','exp','log','log10','sqrt',
    'sin','cos','tan','asin','acos','atan','sinh','cosh','tanh',
}
_arc_functions = {'acos','asin','atan'}
_dnlp_functions = {'ceil','floor','abs'}

#
# A visitor pattern that creates a string for an expression
# that is compatible with the GAMS syntax.
#
class ToGamsVisitor(EXPR.ExpressionValueVisitor):

    def __init__(self, smap, treechecker):
        super(ToGamsVisitor, self).__init__()
        self.smap = smap
        self.treechecker = treechecker
        self.is_discontinuous = False

    def visit(self, node, values):
        """ Visit nodes that have been expanded """
        tmp = []
        for i,val in enumerate(values):
            arg = node._args_[i]

            if arg is None:
                tmp.append('Undefined')                 # TODO: coverage
            else:
                parens = False
                if val and val[0] in '-+':
                    parens = True
                elif arg.__class__ in native_numeric_types:
                    pass
                elif arg.__class__ in nonpyomo_leaf_types:
                    val = "'{0}'".format(val)
                elif arg.is_expression_type():
                    if node._precedence() < arg._precedence():
                        parens = True
                    elif node._precedence() == arg._precedence():
                        if i == 0:
                            parens = node._associativity() != 1
                        elif i == len(node._args_)-1:
                            parens = node._associativity() != -1
                        else:
                            parens = True
                if parens:
                    tmp.append("({0})".format(val))
                else:
                    tmp.append(val)

        if node.__class__ is EXPR.PowExpression:
            # If the exponent is a positive integer, use the power() function.
            # Otherwise, use the ** operator.
            exponent = node.arg(1)
            if (exponent.__class__ in native_numeric_types and
                    exponent == int(exponent)):
                return "power({0}, {1})".format(tmp[0], tmp[1])
            else:
                return "{0} ** {1}".format(tmp[0], tmp[1])
        elif node.__class__ is EXPR.UnaryFunctionExpression:
            if node.name not in _legal_unary_functions:
                raise RuntimeError(
                    "GAMS files cannot represent the unary function %s"
                    % ( node.name, ))
            if node.name in _dnlp_functions:
                self.is_discontinuous = True
            if node.name in _arc_functions:
                return "arc{0}({1})".format(node.name[1:], tmp[0])
            else:
                return node._to_string(tmp, None, self.smap, True)
        elif node.__class__ is EXPR.AbsExpression:
            self.is_discontinuous = True
            return node._to_string(tmp, None, self.smap, True)
        else:
            return node._to_string(tmp, None, self.smap, True)

    def visiting_potential_leaf(self, node):
        """
        Visiting a potential leaf.

        Return True if the node is not expanded.
        """
        if node is None:
            return True, None

        if node.__class__ in native_types:
            return True, _ftoa(node)

        if node.is_expression_type():
            # we will descend into this, so type checking will happen later
            if node.is_component_type():
                self.treechecker(node)
            return False, None

        if node.is_component_type():
            if self.ctype(node) not in valid_expr_ctypes_minlp:
                # Make sure all components in active constraints
                # are basic ctypes we know how to deal with.
                raise RuntimeError(
                    "Unallowable component '%s' of type %s found in an active "
                    "constraint or objective.\nThe GAMS writer cannot export "
                    "expressions with this component type."
                    % (node.name, self.ctype(node).__name__))
            if self.ctype(node) is not Var:
                # For these, make sure it's on the right model. We can check
                # Vars later since they don't disappear from the expressions
                self.treechecker(node)

        if node.is_variable_type():
            if node.fixed:
                return True, _ftoa(value(node))
            else:
                label = self.smap.getSymbol(node)
                return True, label

        return True, _ftoa(value(node))

    def ctype(self, comp):
        if isinstance(comp, ICategorizedObject):
            return comp.ctype
        else:
            return comp.type()


def expression_to_string(expr, treechecker, labeler=None, smap=None):
    if labeler is not None:
        if smap is None:
            smap = SymbolMap()
        smap.default_labeler = labeler
    visitor = ToGamsVisitor(smap, treechecker)
    expr_str = visitor.dfs_postorder_stack(expr)
    return expr_str, visitor.is_discontinuous


class Categorizer(object):
    """Class for representing categorized variables.

    Given a list of variable names and a symbol map, categorizes the variable
    names into the categories: binary, ints, positive and reals.

    """

    def __init__(self, var_list, symbol_map):
        self.binary = []
        self.ints = []
        self.positive = []
        self.reals = []

        # categorize variables
        for var in var_list:
            v = symbol_map.getObject(var)
            if v.is_binary():
                self.binary.append(var)
            elif v.is_integer():
                if (v.has_lb() and (value(v.lb) >= 0)) and \
                   (v.has_ub() and (value(v.ub) <= 1)):
                    self.binary.append(var)
                else:
                    self.ints.append(var)
            elif value(v.lb) == 0:
                self.positive.append(var)
            else:
                self.reals.append(var)

    def __iter__(self):
        """Iterate over all variables.

        Yield a tuple containing the variables category and its name.
        """
        for category in ['binary', 'ints', 'positive', 'reals']:
            var_list = getattr(self, category)
            for var_name in var_list:
                yield category, var_name


class StorageTreeChecker(object):
    def __init__(self, model):
        # blocks are hashable so we can use a normal set
        self.tree = {model}
        self.model = model
        # add everything above the model
        pb = self.parent_block(model)
        while pb is not None:
            self.tree.add(pb)
            pb = self.parent_block(pb)

    def __call__(self, comp, exception_flag=True):
        if comp is self.model:
            return True

        # walk up tree until there are no more parents
        seen = set()
        pb = self.parent_block(comp)
        while pb is not None:
            if pb in self.tree:
                self.tree.update(seen)
                return True
            seen.add(pb)
            pb = self.parent_block(pb)

        if exception_flag:
            self.raise_error(comp)
        else:
            return False

    def parent_block(self, comp):
        if isinstance(comp, ICategorizedObject):
            parent = comp.parent
            while (parent is not None) and \
                  (not parent._is_heterogeneous_container):
                parent = parent.parent
            return parent
        else:
            return comp.parent_block()

    def raise_error(self, comp):
        raise RuntimeError(
            "GAMS writer: found component '%s' not on same model tree.\n"
            "All components must have the same parent model." % comp.name)


def split_long_line(line):
    """
    GAMS has an 80,000 character limit for lines, so split as many
    times as needed so as to not have illegal lines.
    """
    new_lines = ''
    while len(line) > 80000:
        i = 80000
        while line[i] != ' ':
            # Walk backwards to find closest space,
            # where it is safe to split to a new line
            if i < 0:
                raise RuntimeError(
                    "Found an 80,000+ character string with no spaces")
            i -= 1
        new_lines += line[:i] + '\n'
        # the space will be the first character in the next line,
        # so that the line doesn't start with the comment character '*'
        line = line[i:]
    new_lines += line
    return new_lines


[docs]@WriterFactory.register('gams', 'Generate the corresponding GAMS file') class ProblemWriter_gams(AbstractProblemWriter): def __init__(self): AbstractProblemWriter.__init__(self, ProblemFormat.gams)
[docs] def __call__(self, model, output_filename, solver_capability, io_options): """ Write a model in the GAMS modeling language format. Keyword Arguments ----------------- output_filename: str Name of file to write GAMS model to. Optionally pass a file-like stream and the model will be written to that instead. io_options: dict - warmstart=True Warmstart by initializing model's variables to their values. - symbolic_solver_labels=False Use full Pyomo component names rather than shortened symbols (slower, but useful for debugging). - labeler=None Custom labeler. Incompatible with symbolic_solver_labels. - solver=None If None, GAMS will use default solver for model type. - mtype=None Model type. If None, will chose from lp, nlp, mip, and minlp. - add_options=None List of additional lines to write directly into model file before the solve statement. For model attributes, <model name> is GAMS_MODEL. - skip_trivial_constraints=False Skip writing constraints whose body section is fixed. - file_determinism=1 | How much effort do we want to put into ensuring the | GAMS file is written deterministically for a Pyomo model: | 0 : None | 1 : sort keys of indexed components (default) | 2 : sort keys AND sort names (over declaration order) - put_results=None Filename for optionally writing solution values and marginals to (put_results).dat, and solver statuses to (put_results + 'stat').dat. """ # Make sure not to modify the user's dictionary, # they may be reusing it outside of this call io_options = dict(io_options) # Use full Pyomo component names rather than # shortened symbols (slower, but useful for debugging). symbolic_solver_labels = io_options.pop("symbolic_solver_labels", False) # Custom labeler option. Incompatible with symbolic_solver_labels. labeler = io_options.pop("labeler", None) # If None, GAMS will use default solver for model type. solver = io_options.pop("solver", None) # If None, will chose from lp, nlp, mip, and minlp. mtype = io_options.pop("mtype", None) # Lines to add before solve statement. add_options = io_options.pop("add_options", None) # Skip writing constraints whose body section is # fixed (i.e., no variables) skip_trivial_constraints = \ io_options.pop("skip_trivial_constraints", False) # How much effort do we want to put into ensuring the # GAMS file is written deterministically for a Pyomo model: # 0 : None # 1 : sort keys of indexed components (default) # 2 : sort keys AND sort names (over declaration order) file_determinism = io_options.pop("file_determinism", 1) sorter_map = {0:SortComponents.unsorted, 1:SortComponents.deterministic, 2:SortComponents.sortBoth} sort = sorter_map[file_determinism] # Warmstart by initializing model's variables to their values. warmstart = io_options.pop("warmstart", True) # Filename for optionally writing solution values and marginals # Set to True by GAMSSolver put_results = io_options.pop("put_results", None) if len(io_options): raise ValueError( "GAMS writer passed unrecognized io_options:\n\t" + "\n\t".join("%s = %s" % (k,v) for k,v in iteritems(io_options))) if solver is not None and solver.upper() not in valid_solvers: raise ValueError( "GAMS writer passed unrecognized solver: %s" % solver) if mtype is not None: valid_mtypes = set([ 'lp', 'qcp', 'nlp', 'dnlp', 'rmip', 'mip', 'rmiqcp', 'rminlp', 'miqcp', 'minlp', 'rmpec', 'mpec', 'mcp', 'cns', 'emp']) if mtype.lower() not in valid_mtypes: raise ValueError("GAMS writer passed unrecognized " "model type: %s" % mtype) if (solver is not None and mtype.upper() not in valid_solvers[solver.upper()]): raise ValueError("GAMS writer passed solver (%s) " "unsuitable for given model type (%s)" % (solver, mtype)) if output_filename is None: output_filename = model.name + ".gms" if symbolic_solver_labels and (labeler is not None): raise ValueError("GAMS writer: Using both the " "'symbolic_solver_labels' and 'labeler' " "I/O options is forbidden") if symbolic_solver_labels: # Note that the Var and Constraint labelers must use the # same labeler, so that we can correctly detect name # collisions (which can arise when we truncate the labels to # the max allowable length. GAMS requires all identifiers # to start with a letter. We will (randomly) choose "s_" # (for 'shortened') var_labeler = con_labeler = ShortNameLabeler( 63, prefix='s_', suffix='_', caseInsensitive=True, legalRegex='^[a-zA-Z]') elif labeler is None: var_labeler = NumericLabeler('x') con_labeler = NumericLabeler('c') else: var_labeler = con_labeler = labeler var_list = [] def var_recorder(obj): ans = var_labeler(obj) try: if obj.is_variable_type(): var_list.append(ans) except: pass return ans def var_label(obj): #if obj.is_fixed(): # return str(value(obj)) return symbolMap.getSymbol(obj, var_recorder) symbolMap = SymbolMap(var_label) # when sorting, there are a non-trivial number of # temporary objects created. these all yield # non-circular references, so disable GC - the # overhead is non-trivial, and because references # are non-circular, everything will be collected # immediately anyway. with PauseGC() as pgc: try: if isinstance(output_filename, string_types): output_file = open(output_filename, "w") else: # Support passing of stream such as a StringIO # on which to write the model file output_file = output_filename self._write_model( model=model, output_file=output_file, solver_capability=solver_capability, var_list=var_list, var_label=var_label, symbolMap=symbolMap, con_labeler=con_labeler, sort=sort, skip_trivial_constraints=skip_trivial_constraints, warmstart=warmstart, solver=solver, mtype=mtype, add_options=add_options, put_results=put_results ) finally: if isinstance(output_filename, string_types): output_file.close() return output_filename, symbolMap
def _write_model(self, model, output_file, solver_capability, var_list, var_label, symbolMap, con_labeler, sort, skip_trivial_constraints, warmstart, solver, mtype, add_options, put_results): constraint_names = [] ConstraintIO = StringIO() linear = True linear_degree = set([0,1]) dnlp = False # Make sure there are no strange ActiveComponents. The expression # walker will handle strange things in constraints later. model_ctypes = model.collect_ctypes(active=True) invalids = set() for t in (model_ctypes - valid_active_ctypes_minlp): if issubclass(t, ActiveComponent): invalids.add(t) if len(invalids): invalids = [t.__name__ for t in invalids] raise RuntimeError( "Unallowable active component(s) %s.\nThe GAMS writer cannot " "export models with this component type." % ", ".join(invalids)) tc = StorageTreeChecker(model) # Walk through the model and generate the constraint definition # for all active constraints. Any Vars / Expressions that are # encountered will be added to the var_list due to the labeler # defined above. for con in model.component_data_objects(Constraint, active=True, sort=sort): if not con.has_lb() and not con.has_ub(): assert not con.equality continue # non-binding, so skip con_body = as_numeric(con.body) if skip_trivial_constraints and con_body.is_fixed(): continue if linear: if con_body.polynomial_degree() not in linear_degree: linear = False cName = symbolMap.getSymbol(con, con_labeler) con_body_str, con_discontinuous = expression_to_string( con_body, tc, smap=symbolMap) dnlp |= con_discontinuous if con.equality: constraint_names.append('%s' % cName) ConstraintIO.write('%s.. %s =e= %s ;\n' % ( constraint_names[-1], con_body_str, _ftoa(con.upper) )) else: if con.has_lb(): constraint_names.append('%s_lo' % cName) ConstraintIO.write('%s.. %s =l= %s ;\n' % ( constraint_names[-1], _ftoa(con.lower), con_body_str, )) if con.has_ub(): constraint_names.append('%s_hi' % cName) ConstraintIO.write('%s.. %s =l= %s ;\n' % ( constraint_names[-1], con_body_str, _ftoa(con.upper) )) obj = list(model.component_data_objects(Objective, active=True, sort=sort)) if len(obj) != 1: raise RuntimeError( "GAMS writer requires exactly one active objective (found %s)" % (len(obj))) obj = obj[0] if linear: if obj.expr.polynomial_degree() not in linear_degree: linear = False obj_expr_str, obj_discontinuous = expression_to_string( obj.expr, tc, smap=symbolMap) dnlp |= obj_discontinuous oName = symbolMap.getSymbol(obj, con_labeler) constraint_names.append(oName) ConstraintIO.write('%s.. GAMS_OBJECTIVE =e= %s ;\n' % ( oName, obj_expr_str, )) # Categorize the variables that we found categorized_vars = Categorizer(var_list, symbolMap) # Write the GAMS model # $offdigit ignores extra precise digits instead of erroring output_file.write("$offdigit\n\n") output_file.write("EQUATIONS\n\t") output_file.write("\n\t".join(constraint_names)) if categorized_vars.binary: output_file.write(";\n\nBINARY VARIABLES\n\t") output_file.write("\n\t".join(categorized_vars.binary)) if categorized_vars.ints: output_file.write(";\n\nINTEGER VARIABLES") output_file.write("\n\t") output_file.write("\n\t".join(categorized_vars.ints)) if categorized_vars.positive: output_file.write(";\n\nPOSITIVE VARIABLES\n\t") output_file.write("\n\t".join(categorized_vars.positive)) output_file.write(";\n\nVARIABLES\n\tGAMS_OBJECTIVE\n\t") output_file.write("\n\t".join(categorized_vars.reals)) output_file.write(";\n\n") for line in ConstraintIO.getvalue().splitlines(): if len(line) > 80000: line = split_long_line(line) output_file.write(line + "\n") output_file.write("\n") warn_int_bounds = False for category, var_name in categorized_vars: var = symbolMap.getObject(var_name) tc(var) if category == 'positive': if var.has_ub(): output_file.write("%s.up = %s;\n" % (var_name, _ftoa(var.ub))) elif category == 'ints': if not var.has_lb(): warn_int_bounds = True # GAMS doesn't allow -INF lower bound for ints logger.warning("Lower bound for integer variable %s set " "to -1.0E+100." % var.name) output_file.write("%s.lo = -1.0E+100;\n" % (var_name)) elif value(var.lb) != 0: output_file.write("%s.lo = %s;\n" % (var_name, _ftoa(var.lb))) if not var.has_ub(): warn_int_bounds = True # GAMS has an option value called IntVarUp that is the # default upper integer bound, which it applies if the # integer's upper bound is INF. This option maxes out at # 2147483647, so we can go higher by setting the bound. logger.warning("Upper bound for integer variable %s set " "to +1.0E+100." % var.name) output_file.write("%s.up = +1.0E+100;\n" % (var_name)) else: output_file.write("%s.up = %s;\n" % (var_name, _ftoa(var.ub))) elif category == 'binary': if var.has_lb() and value(var.lb) != 0: output_file.write("%s.lo = %s;\n" % (var_name, _ftoa(var.lb))) if var.has_ub() and value(var.ub) != 1: output_file.write("%s.up = %s;\n" % (var_name, _ftoa(var.ub))) elif category == 'reals': if var.has_lb(): output_file.write("%s.lo = %s;\n" % (var_name, _ftoa(var.lb))) if var.has_ub(): output_file.write("%s.up = %s;\n" % (var_name, _ftoa(var.ub))) else: raise KeyError('Category %s not supported' % category) if warmstart and var.value is not None: output_file.write("%s.l = %s;\n" % (var_name, _ftoa(var.value))) if warn_int_bounds: logger.warning( "GAMS requires finite bounds for integer variables. 1.0E100 " "is as extreme as GAMS will define, and should be enough to " "appear unbounded. If the solver cannot handle this bound, " "explicitly set a smaller bound on the pyomo model, or try a " "different GAMS solver.") model_name = "GAMS_MODEL" output_file.write("\nMODEL %s /all/ ;\n" % model_name) if mtype is None: mtype = ('lp','nlp','mip','minlp')[ (0 if linear else 1) + (2 if (categorized_vars.binary or categorized_vars.ints) else 0)] if mtype == 'nlp' and dnlp: mtype = 'dnlp' if solver is not None: if mtype.upper() not in valid_solvers[solver.upper()]: raise ValueError("GAMS writer passed solver (%s) " "unsuitable for model type (%s)" % (solver, mtype)) output_file.write("option %s=%s;\n" % (mtype, solver)) if add_options is not None: output_file.write("\n* START USER ADDITIONAL OPTIONS\n") for line in add_options: output_file.write('\n' + line) output_file.write("\n\n* END USER ADDITIONAL OPTIONS\n\n") output_file.write( "SOLVE %s USING %s %simizing GAMS_OBJECTIVE;\n\n" % ( model_name, mtype, 'min' if obj.sense == minimize else 'max')) # Set variables to store certain statuses and attributes stat_vars = ['MODELSTAT', 'SOLVESTAT', 'OBJEST', 'OBJVAL', 'NUMVAR', 'NUMEQU', 'NUMDVAR', 'NUMNZ', 'ETSOLVE'] output_file.write("Scalars MODELSTAT 'model status', " "SOLVESTAT 'solve status';\n") output_file.write("MODELSTAT = %s.modelstat;\n" % model_name) output_file.write("SOLVESTAT = %s.solvestat;\n\n" % model_name) output_file.write("Scalar OBJEST 'best objective', " "OBJVAL 'objective value';\n") output_file.write("OBJEST = %s.objest;\n" % model_name) output_file.write("OBJVAL = %s.objval;\n\n" % model_name) output_file.write("Scalar NUMVAR 'number of variables';\n") output_file.write("NUMVAR = %s.numvar\n\n" % model_name) output_file.write("Scalar NUMEQU 'number of equations';\n") output_file.write("NUMEQU = %s.numequ\n\n" % model_name) output_file.write("Scalar NUMDVAR 'number of discrete variables';\n") output_file.write("NUMDVAR = %s.numdvar\n\n" % model_name) output_file.write("Scalar NUMNZ 'number of nonzeros';\n") output_file.write("NUMNZ = %s.numnz\n\n" % model_name) output_file.write("Scalar ETSOLVE 'time to execute solve statement';\n") output_file.write("ETSOLVE = %s.etsolve\n\n" % model_name) if put_results is not None: results = put_results + '.dat' output_file.write("\nfile results /'%s'/;" % results) output_file.write("\nresults.nd=15;") output_file.write("\nresults.nw=21;") output_file.write("\nput results;") output_file.write("\nput 'SYMBOL : LEVEL : MARGINAL' /;") for var in var_list: output_file.write("\nput %s %s.l %s.m /;" % (var, var, var)) for con in constraint_names: output_file.write("\nput %s %s.l %s.m /;" % (con, con, con)) output_file.write("\nput GAMS_OBJECTIVE GAMS_OBJECTIVE.l " "GAMS_OBJECTIVE.m;\n") statresults = put_results + 'stat.dat' output_file.write("\nfile statresults /'%s'/;" % statresults) output_file.write("\nstatresults.nd=15;") output_file.write("\nstatresults.nw=21;") output_file.write("\nput statresults;") output_file.write("\nput 'SYMBOL : VALUE' /;") for stat in stat_vars: output_file.write("\nput '%s' %s /;\n" % (stat, stat))
valid_solvers = { 'ALPHAECP': {'MINLP','MIQCP'}, 'AMPL': {'LP','MIP','RMIP','NLP','MCP','MPEC','RMPEC','CNS','DNLP','RMINLP','MINLP'}, 'ANTIGONE': {'NLP','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'BARON': {'LP','MIP','RMIP','NLP','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'BDMLP': {'LP','MIP','RMIP'}, 'BDMLPD': {'LP','RMIP'}, 'BENCH': {'LP','MIP','RMIP','NLP','MCP','MPEC','RMPEC','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'BONMIN': {'MINLP','MIQCP'}, 'BONMINH': {'MINLP','MIQCP'}, 'CBC': {'LP','MIP','RMIP'}, 'COINBONMIN': {'MINLP','MIQCP'}, 'COINCBC': {'LP','MIP','RMIP'}, 'COINCOUENNE': {'NLP','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'COINIPOPT': {'LP','RMIP','NLP','CNS','DNLP','RMINLP','QCP','RMIQCP'}, 'COINOS': {'LP','MIP','RMIP','NLP','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'COINSCIP': {'MIP','NLP','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'CONOPT': {'LP','RMIP','NLP','CNS','DNLP','RMINLP','QCP','RMIQCP'}, 'CONOPT3': {'LP','RMIP','NLP','CNS','DNLP','RMINLP','QCP','RMIQCP'}, 'CONOPT4': {'LP','RMIP','NLP','CNS','DNLP','RMINLP','QCP','RMIQCP'}, 'CONOPTD': {'LP','RMIP','NLP','CNS','DNLP','RMINLP','QCP','RMIQCP'}, 'CONVERT': {'LP','MIP','RMIP','NLP','MCP','MPEC','RMPEC','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'CONVERTD': {'LP','MIP','RMIP','NLP','MCP','MPEC','RMPEC','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP','EMP'}, 'COUENNE': {'NLP','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'CPLEX': {'LP','MIP','RMIP','QCP','MIQCP','RMIQCP'}, 'CPLEXD': {'LP','MIP','RMIP','QCP','MIQCP','RMIQCP'}, 'CPOPTIMIZER': {'MIP','MINLP','MIQCP'}, 'DE': {'EMP'}, 'DECIS': {'EMP'}, 'DECISC': {'LP'}, 'DECISM': {'LP'}, 'DICOPT': {'MINLP','MIQCP'}, 'DICOPTD': {'MINLP','MIQCP'}, 'EXAMINER': {'LP','MIP','RMIP','NLP','MCP','MPEC','RMPEC','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'EXAMINER2': {'LP','MIP','RMIP','NLP','MCP','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'GAMSCHK': {'LP','MIP','RMIP','NLP','MCP','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'GLOMIQO': {'QCP','MIQCP','RMIQCP'}, 'GUROBI': {'LP','MIP','RMIP','QCP','MIQCP','RMIQCP'}, 'GUSS': {'LP', 'MIP', 'NLP', 'MCP', 'CNS', 'DNLP', 'MINLP', 'QCP', 'MIQCP'}, 'IPOPT': {'LP','RMIP','NLP','CNS','DNLP','RMINLP','QCP','RMIQCP'}, 'IPOPTH': {'LP','RMIP','NLP','CNS','DNLP','RMINLP','QCP','RMIQCP'}, 'JAMS': {'EMP'}, 'KESTREL': {'LP','MIP','RMIP','NLP','MCP','MPEC','RMPEC','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP','EMP'}, 'KNITRO': {'LP','RMIP','NLP','MPEC','RMPEC','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'LGO': {'LP','RMIP','NLP','DNLP','RMINLP','QCP','RMIQCP'}, 'LGOD': {'LP','RMIP','NLP','DNLP','RMINLP','QCP','RMIQCP'}, 'LINDO': {'LP','MIP','RMIP','NLP','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP','EMP'}, 'LINDOGLOBAL': {'LP','MIP','RMIP','NLP','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'LINGO': {'LP','MIP','RMIP','NLP','DNLP','RMINLP','MINLP'}, 'LOCALSOLVER': {'MIP','NLP','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'LOGMIP': {'EMP'}, 'LS': {'LP','RMIP'}, 'MILES': {'MCP'}, 'MILESE': {'MCP'}, 'MINOS': {'LP','RMIP','NLP','CNS','DNLP','RMINLP','QCP','RMIQCP'}, 'MINOS5': {'LP','RMIP','NLP','CNS','DNLP','RMINLP','QCP','RMIQCP'}, 'MINOS55': {'LP','RMIP','NLP','CNS','DNLP','RMINLP','QCP','RMIQCP'}, 'MOSEK': {'LP','MIP','RMIP','NLP','DNLP','RMINLP','QCP','MIQCP','RMIQCP'}, 'MPECDUMP': {'LP','MIP','RMIP','NLP','MCP','MPEC','RMPEC','CNS','DNLP','RMINLP','MINLP'}, 'MPSGE': {}, 'MSNLP': {'NLP','DNLP','RMINLP','QCP','RMIQCP'}, 'NLPEC': {'MCP','MPEC','RMPEC'}, 'OQNLP': {'NLP', 'DNLP', 'MINLP', 'QCP', 'MIQCP'}, 'OS': {'LP','MIP','RMIP','NLP','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'OSICPLEX': {'LP','MIP','RMIP'}, 'OSIGUROBI': {'LP','MIP','RMIP'}, 'OSIMOSEK': {'LP','MIP','RMIP'}, 'OSISOPLEX': {'LP','RMIP'}, 'OSIXPRESS': {'LP','MIP','RMIP'}, 'PATH': {'MCP','CNS'}, 'PATHC': {'MCP','CNS'}, 'PATHNLP': {'LP','RMIP','NLP','DNLP','RMINLP','QCP','RMIQCP'}, 'PYOMO': {'LP','MIP','RMIP','NLP','MCP','MPEC','RMPEC','CNS','DNLP','RMINLP','MINLP'}, 'QUADMINOS': {'LP'}, 'SBB': {'MINLP','MIQCP'}, 'SCENSOLVER': {'LP','MIP','RMIP','NLP','MCP','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'SCIP': {'MIP','NLP','CNS','DNLP','RMINLP','MINLP','QCP','MIQCP','RMIQCP'}, 'SNOPT': {'LP','RMIP','NLP','CNS','DNLP','RMINLP','QCP','RMIQCP'}, 'SOPLEX': {'LP','RMIP'}, 'XA': {'LP','MIP','RMIP'}, 'XPRESS': {'LP','MIP','RMIP','QCP','MIQCP','RMIQCP'} }