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# library(eplex)

Interface to external Simplex or MIP solvers

## Predicates

> EplexInstance: (?Vars $:: ++Lo..Hi)
>   Constrains list elements to lie between the given bounds.
> EplexInstance:(?X $= ?Y)
>   Constrains X to be equal to Y.
> EplexInstance:(?X $=< ?Y)
>   Constrains X to be less than or equal to Y.
> EplexInstance:(?X $>= ?Y)
>   Constrains X to be greater than or equal to Y.
> EplexInstance: (?Vars :: ++Lo..Hi)
>   Constrains list elements to lie between the given bounds.
> EplexInstance:(?X =:= ?Y)
>   Constrains X to be equal to Y.
> EplexInstance:(?X =< ?Y)
>   Constrains X to be less than or equal to Y.
> EplexInstance:(?X >= ?Y)
>   Constrains X to be greater than or equal to Y.
> EplexInstance: eplex_add_constraints(+Constraints,+Integers)
>   Add new constraints to the eplex instance EplexInstance, possibly triggering it.
> EplexInstance:eplex_cleanup
>   Destroy the external solver associated with EplexInstance.
> EplexInstance:eplex_get(++ParamName, -Value)
>   Retrieve information about solver state and results for eplex instance EplexInstance.
> eplex_instance(++EplexInstance)
>   Initialises the eplex instance EplexInstance.
> EplexInstance:eplex_probe(+Probes, -Cost)
>   Invoke EplexInstance's external solver, probing the problem temporarily modified by the probe specifications.
> EplexInstance:eplex_read(++Format,++File)
>   Read a problem from a file into eplex instance EplexInstance.
> EplexInstance:eplex_set(++ParamName, -Value)
>   Change initial options for solver state associated with EplexInstance
> EplexInstance:eplex_solve(-Cost)
>   Explicitly invoke the external solver associated with EplexInstance.
> EplexInstance:eplex_solver_setup(+Objective)
>   Setup an external solver state for eplex instance EplexInstance
> EplexInstance:eplex_solver_setup(+Objective, ?Cost, ++ListOfOptions, +TriggerModes)
>   Setup an external solver state for eplex instance EplexInstance
> EplexInstance:eplex_var_get(+Var, ++What, -Value)
>   Obtain information for an individual solver problem variable Var.
> EplexInstance: eplex_var_get_bounds(+Var, -Lo, -Hi)
>   Returns the bounds stored in the solver state for Var in eplex instance EplexInstance.
> EplexInstance:eplex_write(++Format,++File)
>   Write the problem in the solver for eplex instance EplexInstance to a file.
> EplexInstance:get_changeable_value(?Var, -Val)
>   Interface predicate to access the changeable value for this variable.
> instantiation_deviates(+Handle)
>   A trigger goal for lp_demon_setup/5.
> EplexInstance:integers(?Vars)
>   Constrains Vars to integers for eplex instance EplexInstance.
> lp_add(+Handle, +NewNormCons, +NewIntegers)
>   Add new constraints to a solver state Handle.
> lp_add_columns(+Handle, +Columns)
>   Add new variables as columns to the external solver's matrix.
> lp_add_constraints(+Handle, +Constraints, ++Integers)
>   Add new constraints to the solver Handle, possibly triggering it.
> lp_add_constraints(+Handle, +Constraints, ++Integers, -Indices)
>   Add new expandable constraints to the demon solver Handle.
> lp_add_cutpool_constraints(+Handle, +Constraints, +Options, -Indices)
>   Add constraints to the cutpool associated with solver state Handle.
> lp_add_vars(+Handle, +Vars)
>   Declare Vars to be problem variables for the solver state Handle
> lp_cleanup(+Handle)
>   Destroy the specified solver Handle and clean up.
> lp_demon_setup(+Objective, ?Cost, ++ListOfOptions, ++TriggerModes, -Handle)
>   Setup the external solver as a simplex demon.
> lp_get(++ParamName, ?Value)
>   Obtain the value of a global parameter.
> lp_get(+Handle, ++ParamName, -Value)
>   Retrieve information about solver state and results for solver state Handle.
> lp_get_changeable_value(+Handle, ?Var, -Val)
>   Interface predicate to access the changeable value for this variable.
> lp_get_license
>   Get a runtime license token for the external solver.
> lp_get_license(+LicStr, +LicNum)
>   Get a runtime license token for the external solver.
> lp_get_license_challenge(-Challenge)
>   Get parameter for computing license key (some external solvers only)
> lp_probe(+Handle, +Probes, -Cost)
>   Invoke external solver, probing the problem temporarily modified by the probe specifications.
> lp_read(+File, ++Format, -Handle)
>   Read a problem from a file and setup a solver for it.
> lp_release_license
>   Release a runtime license token for the external solver.
> lp_set(++ParamName, ++Value)
>   Set a global parameter for the external solver.
> lp_set(+Handle, ++What, +Value)
>   Change initial options for solver state Handle.
> lp_setup(+NormConstraints, +Objective, ++ListOfOptions, -Handle)
>   Create a new external solver state for the constraints NormConstraints.
> lp_solve(+Handle, -Cost)
>   Explicitly invoke the external solver.
> lp_suspend_on_change(+Handle, ?Var, +Susp)
>   Record the given suspension to be scheduled whenever a solution is found for the Eplex handle.
> lp_var_get(+Handle, +Var, ++What, -Value)
>   Obtain information for an individual solver problem variable Var.
> lp_var_get_bounds(+Handle, ?Var, -Lo, -Hi)
>   Returns the bounds stored in the solver state of Handle for Var.
> lp_var_occurrence(?Var, ?Handle, -Index)
>   Returns the column number Index for Var in the external solver represented by Handle
> lp_var_set_bounds(+Handle, ?Var, +Lo, +Hi)
>   Imposes new bounds for Var on the solver state of Handle.
> lp_write(+Handle, ++Format, +File)
>   Write a solver problem to a file.
> normalise_cstrs(+Constraints, -NormConstraints, -NonlinConstraints)
>   Normalise the linear constraints in Constraints.
> EplexInstance:piecewise_linear_hull(?X, ++Points, ?Y)
>   Relates X and Y according to a piecewise linear function.
> EplexInstance:reals(?Vars)
>   Constraints Vars to the real domain for EplexInstance.
> reduced_cost_pruning(+Handle, ?GlobalCost)
>   Prune bounds of all problem variables based on their reduced costs
> solution_out_of_range(+Handle)
>   A trigger goal for lp_demon_setup/5.
> EplexInstance:suspend_on_change(?Var, +Susp)
>   Record the given suspension to be scheduled whenever a solution is found for the EplexInstance.

## Reexports

> reexport eplex_s
>   except add_constraint / 1, lp_eq / 3, lp_ge / 3, lp_le / 3, lp_interval / 3, lp_int_interval / 3, lp_real_interval / 3, reals / 2, integers / 2, lp_var_non_monotonic_set_bounds / 4, eplex_get / 3, eplex_cleanup / 1, eplex_probe / 3, eplex_solve / 2, eplex_var_get / 4, eplex_set / 3, eplex_read / 3, eplex_write / 3

## Description

This library lets you use an external Mathematical Programming solver from within ECLiPSe. This is done either directly to the solver, like CPLEX or XPRESS-MP, or indirectly via COIN-OR project's Open Solver Interface (OSI), which provides a common and open API for several solvers. Specifically, this allow COIN-OR's own open source solvers like CLP and For the commercial solvers, the library provides just the interface, and does not include the solver or any required licence to use them.

The constraints provided are:

X =:= Y
  equality over linear expressions
X >= Y
  inequality over linear expressions
X =< Y
  inequality over linear expressions
X $= Y
  equality over linear expressions
X $>= Y
  inequality over linear expressions
X $=< Y
  inequality over linear expressions
integers(Xs)
  integrality of variables
Vs :: Bound
  Bounds on variables
Vs $:: Bound
  Bounds on variables

Their operational behaviour is as follows:

- When they contain no variables, they simply succeed or fail.
- When they contain exactly one variable, they are translated into a bound update on that variable for the external solver instance. This can lead to immediate failure if the lower bound is greater than the upper.
- Otherwise, the constraint is transferred to the external solver instance immediately.

The following arithmetic expression can be used inside the constraints:

X
  Variables. If X is not yet a problem variable for the external solver instance, it is turned into one via an implicit declaration `X :: -inf..inf`.

123, 3.4
  Integer or floating point constants.

+Expr
  Identity.

-Expr
  Sign change.

E1+E2
  Addition.

sum(ListOfExpr)
  Equivalent to the sum of all list elements.

E1-E2
  Subtraction.

E1*E2
  Multiplication.

ListOfExpr1*ListOfExpr2
  Scalar product: The sum of the products of the corresponding elements in the two lists. The lists must be of equal length.

The external solver can either be explicitly invoked to solve the problem represented by the constraints, or be invoked in response to certain trigger conditions. This mechanism makes it possible to tailor the solving behaviour for a particular application's needs.

## About

- Author: Joachim Schimpf and Kish Shen
- Copyright © Cisco Systems, Inc.
- Date: $Date: 2006/09/23 01:53:26 $

Generated from eplex.eci on Sat Nov 8 06:58:35 2008