*Objective*- Objective function: min(CostExpr) or max(CostExpr)
*Cost*- Variable bounded by the optimal solution
*ListOfOptions*- List of solver options
*TriggerModes*- List of conditions for re-triggering solver

Setup a new external solver state for the eplex instance EplexInstance.
The solver state will be associated with EplexInstance;
EplexInstance must not already have a solver state associated with it.
This predicate allow various options to be specified when setting up the
solver state. `ListOfOptions` allows a list of solver options to
be specified, and `TriggerModes` allows the
solver state to be set up as a demon so that the external solver is
automatically invoked when the conditions for re-triggering specified in
`TriggerModes` are met. The external solver can also be invoked
explicitly via eplex_solve/1.

Declaratively, this can be seen as a compound constraint representing all
the individual linear constraints that have been set so far and are going
to be set up later for `EplexInstance`. Operationally, when the
external solver is invoked, the delayed constraints posted to
`EplexInstance` are collected and taken into account.

`CostExpr` is a linear cost expression (or quadratic, if supported
by the external solver).

The external solver's best objective bound will be exported as a bound
for `Cost`: For a minimisation problem, each solution's best bound
becomes a lower bound, for maximisation an upper bound on Cost. This
technique allows for repeated re-solving with reduced bounds or added
constraints. Note that Cost is not automatically made a problem variable
(it can be a problem variable if there are constraints that involve it),
and thus may not have bounds associated with in. In order for the bounds
information not to be lost, some bounds should be given to `Cost`
(e.g. making it a problem variable (but this might introduce unnecessary
self-waking on bounds change), or via another solver with bounds
(e.g. ic)).

`ListOfOptions` is the same as in the low-level primitive
lp_demon_setup/5, except that EplexInstance is implicitly associated with
the new external solver state, so the `collect_from` option of
lp_demon_setup/5 is not allowed (it is set to `
collect_from(pool(EplexInstance))` by the predicate). See
below for more details.

`TriggerModes` specifies under which conditions the external solver
will be re-triggered. If no condition is specified, then the solver must
be explicitly triggered, usually via eplex_solve/1. The conditions are the
same as in the low-level primitive lp_demon_setup/5 called by this predicate.
See below (after `ListOfOptions` descriptions) for more details.

Note: Some external solvers need to write temporary files when they are solving a problem. These are written to the temporary directory specified in ECLiPSe's tmp_dir setting (get_flag/2, set_flag/2).

ListOfOptions are (such option should occur no more than once):

`initial_solve(+YesNo)`- Specifies if an initial solve (call to the external solver) should
be performed immediately after problem setup.
YesNo is one of the atoms
`yes`or`no`, the default is`yes`if any trigger condition is specified in TriggerModes,`no`if no trigger condition is specified. `method(+Method)`- Use the specified method (
`default, primal, dual, net, barrier, sifting`) (representing Primal Simplex, Dual Simplex, Network Simplex, Barrier, and Sifting respectively) to solve the problem. For MIP problems, this specifies the start algorithm (the one that is used to solve the initial relaxation). See the external solver's manual for a description of these methods.For some of the methods, an additional `auxiliary' method may be specified in brackets. These are:

`net(Simplex)`:- specifies the Simplex method (
`primal`or`dual`) to follow the network optimisation. For LP problems only. `barrier(Crossover)`:- specifies how the crossover to a basic solution from the barrier
solution is performed.
`Crossover`can be`primal`,`dual`, or`none`.`none`means no crossover is performed. `sifting(SubMethod)`:- specifies the method for solving the sifting subproblem.
`SubMethod`can be`primal, dual, net, barrier`.

`default`can also be specified. This is equivalent to not specifying a auxiliary method at all.Note that not all the methods are available on all external solvers. The default method would use the solver's default method to solve the problem. The actual method depends on the external solver. If no method is specified, default is used.

`node_method(+Method)`- For MIP problems only. Use the specified method (
`default, primal, dual, net, barrier, sifting`) to solve the subproblem at each node of the MIP search-tree, except the root node, which is specified by`method`option above. See method option for more description of the methods. Note that there are less choices in the specifications of the auxiliary methods that in the method option, due to limitations in the solvers. If a specified auxiliary method cannot be used, `default' will be used instead. `solution(+YesNo)`- Make the solutions available each time the problem has been (re-)solved
successfully.
YesNo is one of the atoms
`yes`or`no`, the default is`yes`. `dual_solution(+YesNo)`- Make the dual solutions available each time the problem has been
(re-)solved successfully. If the problem is a MIP, then depending on
the external solver, this is either unavailable or are the values for
the optimal LP node.
YesNo is one of the atoms
`yes`or`no`, the default is`no`. `slack(+YesNo)`- Make the constraint slacks available each time the problem has been
(re-)solved successfully.
YesNo is one of the atoms
`yes`or`no`, the default is`no`. `reduced_cost(+YesNo)`- Make the reduced costs available each time the problem has been
(re-)solved successfully. If the problem is a MIP, then depending on
the external solver, this is either unavailable or are the values for
the optimal LP node.
YesNo is one of the atoms
`yes`or`no`, the default is`no`. `keep_basis(+YesNo)`- Store the basis each time the problem has been solved successfully,
and use this basis as a starting point for re-solving next time.
This option only affects performance.
YesNo is one of the atoms
`yes`or`no`, the default is`no`. `demon_tolerance(RealTol, IntTol)`- Specify how far outside a variable's range an lp-solution
can fall before lp_demon_setup/5 re-triggers.
`RealTol`and`IntTol`are floats and default to 0.00001 and 0.5 respectively. `sos1(VarList)``VarList`is a list of variables which the solver should treat as variables of a type 1 special ordered set (SOS), i.e. at most one of the variables in the set can be non-zero.`sos2(VarList)``VarList`is a list of variables which the solver should treat as variables of a type 2 special ordered set (SOS), i.e. at most two of the variables in the set can be non-zero.`presolve(+YesNo)`- Specify if the external solver should perform presolve for this
problem. With presolving, the external solver will transform the
problem before solving it. This can lead to significantly faster times
to find solutions. However, as the problem has been transformed, some
external solvers have restriction on accessing or changing the problem
state. In addition, if the solver is repeatedly called because the
problem is frequently modified, then presolve may not be an advantage.
YesNo is one of the atoms
`yes`or`no`, the default is determined by the global setting of`presolve`, which can be changed via`lp_set/2`. The initial default is`yes`. Note that the presolve setting cannot be changed for a problem once it is set. `timeout(+TimeOut)`- Set the external solver to time-out after
`TimeOut`seconds.`TimeOut`is a positive number. The solver will abort (in either the abort or suboptimal state, depending on if a suboptimal solution was found) if the optimal solution was not found within the time limit. This should be used instead of setting the solver-specific parameter for time-out directly. In cases where the solver expects an integer for the time-out interval, the time given is rounded up to the next integer value. The timeout is set by setting the external solver's timeout setitngs, and the exact behaviour may be solver dependent. `suboptimal_handler(+Goal)`- Specifies a user defined goal Goal to handle the case when the
external solver returned a suboptimal solution (because the problem
was aborted). Goal would be run in place of raising the default
`eplex_suboptimal`event. `unbounded_handler(+Goal)`- Specifies a user defined goal Goal to handle the case when the
problem is unbounded. Goal would be run in place of raising the
default
`eplex_unknown`event. `unknown_handler(+Goal)`- Specifies a user defined goal Goal to handle the case when the
external solver was not able to determine if the problem is unbounded
or infeasible. Goal would be run in place of raising the default
`eplex_unknown`event. `abort_handler(+Goal)`- Specifies a user defined goal Goal to handle the case when the
external solver aborted without finding any solution. Goal would be
run in place of raising the default
`eplex_abort`event. `use_var_names(+YesNo)`- Specify if variable names (set using
`set_var_name/2`of the var_name library) should be passed to the external solver. If a particular variable does not have a name, a solver's default name would be used. Note that for XPRESS-MP, there is a limit on the length of the name, which can be changed between 8 and 64 in steps of 8 with the parameter`mpsnamelength (XPRS_MPSNAMELENGTH)`. Variable names longer than this limit are truncated to the limit. YesNo is one of the atoms`yes`or`no`, the default is`no`. `priority(+Prio)``Prio`is the scheduling priority with which the solver gets woken up. This priority determines whether the solver is run before or after other constraints. By default, if no priority is specified, the default priority (0, mapped to 5 unless changed) is used. Normally, the default priority should be sufficient and this option is not needed, unless there is a specific need to have the external solver invoked with higher or lower priority than some other constraints.`mip_use_copy(+YesNo)`- Some external solvers do not allow a MIP problem to be modified
once the MIP search has been started. Eplex works around this
problem by making a copy of the problem and solving that, so that
the original problem can still be modified. This can be turned off to
avoid the overhead of making this copy, in which case the MIP
problem cannot be modified. This option is used only when solving a
MIP problem, and the external solver does not allow a MIP problem to
be modified; otherwise it is ignored.
YesNo is one of the atoms
`yes`or`no`, the default is`yes`so that the problem can be modified. `write_before_solve(+Format,+File)`- This option is most useful for debugging purposes. If given, Eplex
will ask the external solver to dump the problem each time the problem
is solved. This allows the problem in an
`eplex_probe/2`or`lp_probe/3`to be dumped. As in`lp_write/3`,`Format`is the format of the dumped file and`File`is its name. Note that the problem is dumped each time the external solver is invoked if the problem has cutpool constraints, where there may be multiple invocations of the solver per solver call. The default without this option is that the problem would not be dumped. `post_equality_when_unified(+YesNo)`- This option determines if an equality constraint between two
variables will be posted to the solver when these variables are
unified. Setting
`YesNo`to no means that the constraint will*not*be posted. Note that this can lead to the solver's problem becoming inconsistent with ECLiPSe's. YesNo is one of the atoms`yes`or`no`, the default is`yes`. `sync_bounds(+YesNo)`- This option determines if the bounds of the problems variables are
synchronised with other solvers (i.e. the generic bounds are obtained
with get_var_bounds/3 and then passed to the external solver) before
the external solver is invoked. This was always done for previous
non-standalone version of eplex. For standalone eplex, as the bounds
are communicated directly to the external solver, the synchronisation
of variable bounds is not needed unless the user is using eplex
co-operatively with other solvers (e.g. ic). Even in such cases, it may
be more efficient to communicate these bounds changes by explicitly
programming it, especially if the problem has many variables and bounds
changes happen only to a few of the variables. Setting
`YesNo`to yes should increase compatibility with previous code (but note that previous eplex obtained the bounds from a specific bounds keeper like ic rather than the generic bounds). YesNo is one of the atoms`yes`or`no`, the default is`no`.

`TriggerModes` can be a list of the following specifiers:

`inst`- re-trigger if a problem variable gets instantiated.
`ModuleName:Index`- re-trigger when the suspension list given by ModuleName:Index is woken
for any of the problem variables.
The format for
`ModuleName:Index`is the same as for specifying the suspension list in suspend/3,4. `deviating_inst`- re-trigger if a problem variable gets instantiated to a value that differs from its lp-solution more than a tolerance.
`bounds`- re-trigger each time a variable bound for the solver instance changes.
`deviating_bounds`- re-trigger each time a variable's solver instance bound changes such that its lp-solution gets excluded more than a tolerance.
`new_constraint`- re-trigger each time a new (arithmetic or integral) constraint is added to the solver instance. Note that adding integral constraint on new problem variables, or adding bounds constraint, or adding constraints to the cutpool will *not* re-trigger.
`trigger(Atom)`- re-trigger each time the symbolic trigger Atom is pulled by invoking schedule_suspensions/1
`pre(Goal)`- an additional condition to be used together with other triggers. When
the demon is triggered, it first executes
`PreGoal`. Only if that succeeds, does the appropriate external solver get invoked. This provides a way of reducing the number of (possibly expensive) solver invocations when given preconditions are not met. `post(Goal)`- this is not a trigger condition, but specifies a goal to be executed after solver success, but before the Cost variable gets constrained. It is intended as a hook for exporting solution information, e.g. copying solutions from the solver state into variable attributes (eg. tentative value), or computing weights for labelling heuristics from the solver state.
`suspension(Susp)`- this is not a trigger condition, but instead is used to access the demon used to trigger the solver. Susp is instantiated to the suspension that triggers the solver: by waking Susp, the solver is triggered. Susp is a demon in that it stays around after being woken. Accessing Susp allows the user to specify orbitally conditions for triggering the solver.

If several trigger conditions are specified, then any of them will trigger the solver.

When a solver demon runs frequently on relatively small problems, it can be important for efficiency to switch off the presolve option to reduce overheads.