*NormConstraints*- normalised constraints
*Objective*- Objective function: min(CostExpr) or max(CostExpr)
*ListOfOptions*- List of solver options
*Handle*- handle to solver state

Create a new solver state for the set of constraints NormConstraints (see normalise_cstrs/3 for how to obtain a set of normalised constraints). Apart from the explicitly listed constraints, the variable's ranges will be taken into account as the variable bounds for the simplex algorithm. Undeclared variables are implicitly declared as reals.

However, when variables have been declared integers by other solvers (e.g.
integers/1 of the ic library) that is not taken into account by the
solver by default. This means that the solver will only work on the
*relaxed problem* (ie. ignoring the integrality constraints),
unless specified otherwise in the options.

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

Options is a list of options (see below). Unless explicitly specified otherwise, each option should occur no more than once.

A solver-handle Handle is returned which is used to refer to the solver subsequently.

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).

The solver Options are:

`integers(+ListOfVars)`- Consider the specified variables to be integers (whether or not
they have been declared such).
This option will instruct the external solver to use its own MIP solver
(ie. branch-and-bound search happens within the external solver).
`reals(+ListOfVars)`- Consider the specified variables to be problem variables, but does
not otherwise constrain the variables. This option allows variables to
be added to the problem without requiring them to occur in other
constraints.
`method(+Method)`- Use the specified method (
`default, auto, primal, dual, net, barrier, sifting, concurrent, concurrent_det`) (representing Primal Simplex, Dual Simplex, Network Simplex, Barrier, Sifting etc) 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 an auxiliary method at all.Note that not every method is available on every external solver. The default method would use the solver's default method, or any selections done via solver-specific optimizer_param(_) settings.

`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`. `mipstart(+Option)`- Use the previous solution values as a warm-start heuristics for
the MIP search. This only has an effect for certain solvers (e.g.
Gurobi), if there are integrality constraints, and if there is a
previous solution available. Possible values are
`none`(no mipstart values, the default),`all`(use previous solution for all variables), or`integers`(use previous solution for all variables that are now constrained to be integral). `cache_iis(YesNo)`- Specify if an IIS should be computed immediately for an infeasible problem
(if supported by the external solver), and store it so that it can bee retrieved by
eplex_get_iis/4 or lp_get_iis/5 (called from within a user-defined infeasible
handler). This will be done before the problem can be modified and make the computing
of the IIS impossible. The IIS will only be available before the problem is solved
again, and also before the infeasible solve is backtracked. This option has no effect
if the external solver does not support the computation of an IIS. Note that if this
option is set, eplex will always ask for an IIS to computed for an infeasible problem,
even if it is immediately backtracked by the infeasible handler failing, and that the
option is only needed if the problem instance in the external solver is modified
before eplex_get_iis/4 or lp_get_iis/5 is called.
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. `integers(+ListOfVars)`- Consider the specified variables to be integers (whether or not
they have been declared such).
This option will instruct the external solver to use its own MIP solver
(ie. branch-and-bound search happens within the external solver).
`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. This can occur multiple times, for different sets of variables.`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. This can occur multiple times, for different sets of variables.`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. If the external solver supports per-problem optimizer_params, their global defaults will be used for presolve(yes). `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 settings, 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_unbounded`event. `infeasible_handler(+Goal)`- Specifies a user defined goal Goal to handle the case when the
external solver found that the problem is infeasible. Goal would be run
in place of raising the default
`eplex_infeasible`event. Note that the default and logically correct behaviour is to fail, this handler is provided to allow the user to analyse the cause of the infeasibility. It is recommended that the handler should also fail after performing the analysis. `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 when it is first passed to the external solver, a default name determined by the solver 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`. `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. `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`.