Scippy

SCIP

Solving Constraint Integer Programs

type_nlhdlr.h
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4 /* SCIP --- Solving Constraint Integer Programs */
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24 
25 /**@file type_nlhdlr.h
26  * @ingroup TYPEDEFINITIONS
27  * @brief type definitions related to nonlinear handlers of nonlinear constraints
28  * @author Ksenia Bestuzheva
29  * @author Benjamin Mueller
30  * @author Felipe Serrano
31  * @author Stefan Vigerske
32  *
33  * This file defines the interface for nonlinear handlers.
34  *
35  * - \ref NLHDLRS "List of available nonlinear handlers"
36  */
37 
38 /** @defgroup DEFPLUGINS_NLHDLR Default nonlinear handlers
39  * @ingroup DEFPLUGINS
40  * @brief implementation files (.c files) of the default nonlinear handlers of SCIP
41  */
42 
43 #ifndef SCIP_TYPE_NLHDLR_H_
44 #define SCIP_TYPE_NLHDLR_H_
45 
46 #include "scip/type_expr.h"
47 #include "scip/type_cons.h"
48 #include "scip/type_misc.h"
49 
50 #define SCIP_NLHDLR_METHOD_NONE 0x0u /**< no enforcement */
51 #define SCIP_NLHDLR_METHOD_SEPABELOW 0x1u /**< separation for expr <= auxvar, thus might estimate expr from below */
52 #define SCIP_NLHDLR_METHOD_SEPAABOVE 0x2u /**< separation for expr >= auxvar, thus might estimate expr from above */
53 #define SCIP_NLHDLR_METHOD_SEPABOTH (SCIP_NLHDLR_METHOD_SEPABELOW | SCIP_NLHDLR_METHOD_SEPAABOVE) /**< separation for expr == auxvar */
54 #define SCIP_NLHDLR_METHOD_ACTIVITY 0x4u /**< activity computation (interval evaluation) and propagation (reverse propagation) */
55 #define SCIP_NLHDLR_METHOD_ALL (SCIP_NLHDLR_METHOD_SEPABOTH | SCIP_NLHDLR_METHOD_ACTIVITY) /**< all enforcement methods */
56 
57 typedef unsigned int SCIP_NLHDLR_METHOD; /**< nlhdlr methods bitflags */
58 
59 /** nonlinear handler copy callback
60  *
61  * The method includes the nonlinear handler into a nonlinear constraint handler.
62  *
63  * This method is usually called when doing a copy of a nonlinear constraint handler.
64  *
65  * \param[in] targetscip target SCIP main data structure
66  * \param[in] targetconshdlr target nonlinear constraint handler
67  * \param[out] sourceconshdlr nonlinear constraint handler in source SCIP
68  * \param[out] sourcenlhdlr nonlinear handler in source SCIP
69  */
70 #define SCIP_DECL_NLHDLRCOPYHDLR(x) SCIP_RETCODE x (\
71  SCIP* targetscip, \
72  SCIP_CONSHDLR* targetconshdlr, \
73  SCIP_CONSHDLR* sourceconshdlr, \
74  SCIP_NLHDLR* sourcenlhdlr)
75 
76 /** callback to free data of handler
77  *
78  * \param[in] scip SCIP data structure
79  * \param[in] nlhdlr nonlinear handler
80  * \param[in] nlhdlrdata nonlinear handler data to be freed
81  */
82 #define SCIP_DECL_NLHDLRFREEHDLRDATA(x) SCIP_RETCODE x (\
83  SCIP* scip, \
84  SCIP_NLHDLR* nlhdlr, \
85  SCIP_NLHDLRDATA** nlhdlrdata)
86 
87 /** callback to free expression specific data
88  *
89  * \param[in] scip SCIP data structure
90  * \param[in] nlhdlr nonlinear handler
91  * \param[in] expr expression
92  * \param[in] nlhdlrexprdata nonlinear handler expression data to be freed
93  */
94 #define SCIP_DECL_NLHDLRFREEEXPRDATA(x) SCIP_RETCODE x (\
95  SCIP* scip, \
96  SCIP_NLHDLR* nlhdlr, \
97  SCIP_EXPR* expr, \
98  SCIP_NLHDLREXPRDATA** nlhdlrexprdata)
99 
100 /** callback to be called in initialization (called after problem was transformed)
101  *
102  * \param[in] scip SCIP data structure
103  * \param[in] nlhdlr nonlinear handler
104  */
105 #define SCIP_DECL_NLHDLRINIT(x) SCIP_RETCODE x (\
106  SCIP* scip, \
107  SCIP_NLHDLR* nlhdlr)
108 
109 /** callback to be called in deinitialization (called before transformed problem is freed)
110  *
111  * \param[in] scip SCIP data structure
112  * \param[in] nlhdlr nonlinear handler
113  */
114 #define SCIP_DECL_NLHDLREXIT(x) SCIP_RETCODE x (\
115  SCIP* scip, \
116  SCIP_NLHDLR* nlhdlr)
117 
118 /** callback to detect structure in expression
119  *
120  * The nonlinear handler shall analyze the current expression and decide whether it wants to contribute
121  * in enforcing the relation between this expression (`expr`) and its descendants (e.g., children) via
122  * linear under- or overestimation, cut generation, and/or activity computation and propagation.
123  * For linear under- or overestimation and cut generation, an auxiliary variable (`auxvar`) can be assumed to
124  * be associated with `expr` and auxiliary variables may be requested in descendant expressions.
125  *
126  * We distinguish the following enforcement methods:
127  * - \ref SCIP_NLHDLR_METHOD_SEPABELOW : linear underestimation of `expr` or cut generation for the relation `expr` &le; `auxvar` (denoted as "below")
128  * - \ref SCIP_NLHDLR_METHOD_SEPAABOVE : linear overestimation of `expr` or cut generation for the relation `expr` &ge; `auxvar` (denoted as "above")
129  * - \ref SCIP_NLHDLR_METHOD_ACTIVITY : domain propagation (i.e., constant under/overestimation) for the relation `expr` = `auxvar`.
130  *
131  * On input, parameter `enforcing` indicates for any of these methods, whether
132  * - it is not necessary to have such a method, e.g., because no `auxvar` will exist for `expr`, or no one uses or sets activities of this expression,
133  * or because analysis of the expression has shown that a relation like `expr` &ge; `auxvar` is not necessary to be satisfied,
134  * - or there already exists a nonlinear handler that will provide this method in an "enforcement" sense, that is,
135  * it believes that no one else could provide this method in a stronger sense. (This is mainly used by nlhdlr_default to check whether
136  * it should still reach out to the exprhdlr or whether it would be dominated by some nonlinear handler.)
137  *
138  * The DETECT callback shall augment the `enforcing` bitmask by setting the enforcement methods it wants to provide in an "enforcement" sense.
139  *
140  * Additionally, the `participating` bitmask shall be set if the nonlinear handler wants to be called on this expression at all.
141  * Here, it shall set all methods that it wants to provide, which are those set in `enforcing`, but additionally those where it wants
142  * to participate but leave enforcement to another nonlinear handler.
143  * This can be useful for nonlinear handlers that do not implement a complete enforcement, e.g., a handler that only contributes
144  * cutting planes in some situations only.
145  *
146  * A nonlinear handler will be called only for those callbacks that it mentioned in `participating`, which is
147  * - \ref SCIP_DECL_NLHDLRENFO "ENFO" and/or \ref SCIP_DECL_NLHDLRESTIMATE "ESTIMATE" will be called with `overestimate==FALSE` if \ref SCIP_NLHDLR_METHOD_SEPABELOW has been set
148  * - \ref SCIP_DECL_NLHDLRENFO "ENFO" and/or \ref SCIP_DECL_NLHDLRESTIMATE "ESTIMATE" will be called with `overestimate==TRUE` if \ref SCIP_NLHDLR_METHOD_SEPAABOVE has been set
149  * - \ref SCIP_DECL_NLHDLRINTEVAL "INTEVAL" and/or \ref SCIP_DECL_NLHDLRREVERSEPROP "REVERSEPROP" will be called if \ref SCIP_NLHDLR_METHOD_ACTIVITY has been set
150  *
151  * If \ref SCIP_NLHDLR_METHOD_SEPABELOW or \ref SCIP_NLHDLR_METHOD_SEPAABOVE has been set, then at least one of the
152  * callbacks \ref SCIP_DECL_NLHDLRENFO "ENFO" and \ref SCIP_DECL_NLHDLRESTIMATE "ESTIMATE" needs to be implemented.
153  * Also \ref SCIP_DECL_NLHDLREVALAUX "EVALAUX" will be called in this case.
154  * If \ref SCIP_NLHDLR_METHOD_ACTIVITY has been set, then at least one of \ref SCIP_DECL_NLHDLRINTEVAL "INTEVAL" and
155  * \ref SCIP_DECL_NLHDLRREVERSEPROP "REVERSEPROP" needs to be implemented.
156  * If the nonlinear handler chooses not to participate, then it must not set `nlhdlrexprdata` and can leave `participating` at its
157  * initial value (\ref SCIP_NLHDLR_METHOD_NONE).
158  *
159  * Additionally, a nonlinear handler that decides to participate in any of the enforcement methods must call
160  * @ref SCIPregisterExprUsageNonlinear() for every subexpression that it will use and indicate whether
161  * - it will use an auxiliary variable in \ref SCIP_DECL_NLHDLRENFO "ENFO" or \ref SCIP_DECL_NLHDLRESTIMATE "ESTIMATE",
162  * - it will use activity for some subexpressions when computing estimators or cuts, and
163  * - it will use activity for some subexpressions when in \ref SCIP_DECL_NLHDLRINTEVAL "INTEVAL" or \ref SCIP_DECL_NLHDLRREVERSEPROP "REVERSEPROP".
164  *
165  * @note Auxiliary variables do not exist in subexpressions during DETECT and are not created by a call to @ref SCIPregisterExprUsageNonlinear().
166  * They will be available when the \ref SCIP_DECL_NLHDLRINITSEPA "INITSEPA" callback is called.
167  *
168  * \param[in] scip SCIP data structure
169  * \param[in] conshdlr nonlinear constraint handler
170  * \param[in] nlhdlr nonlinear handler
171  * \param[in] expr expression to analyze
172  * \param[in] cons the constraint that expression defines, or NULL when the expr does not define any constraint, that is, when it is not the root of an expression of a constraint
173  * \param[in,out] enforcing enforcement methods that are provided by some nonlinear handler (to be updated by detect callback)
174  * \param[out] participating enforcement methods that this nonlinear handler should be called for (to be set by detect callback), initialized to SCIP_NLHDLR_METHOD_NONE
175  * \param[out] nlhdlrexprdata nlhdlr's expr data to be stored in expr, can only be set to non-NULL if success is set to TRUE
176  */
177 #define SCIP_DECL_NLHDLRDETECT(x) SCIP_RETCODE x (\
178  SCIP* scip, \
179  SCIP_CONSHDLR* conshdlr, \
180  SCIP_NLHDLR* nlhdlr, \
181  SCIP_EXPR* expr, \
182  SCIP_CONS* cons, \
183  SCIP_NLHDLR_METHOD* enforcing, \
184  SCIP_NLHDLR_METHOD* participating, \
185  SCIP_NLHDLREXPRDATA** nlhdlrexprdata)
186 
187 /** auxiliary evaluation callback of nonlinear handler
188  *
189  * Evaluates the expression w.r.t. the auxiliary variables that were introduced by the nonlinear handler (if any).
190  * The method is used to determine the violation of the relation that the nonlinear handler attempts to enforce.
191  * During enforcement, this violation value is used to decide whether estimation/separation callbacks should be called.
192  *
193  * It can be assumed that the expression itself has been evaluated in the given sol.
194  *
195  * \param[in] scip SCIP data structure
196  * \param[in] nlhdlr nonlinear handler
197  * \param[in] expr expression to evaluate
198  * \param[in] nlhdlrexprdata expression specific data of the nonlinear handler
199  * \param[out] auxvalue buffer to store value of expression w.r.t. auxiliary variables
200  * \param[in] sol point to evaluate
201  */
202 #define SCIP_DECL_NLHDLREVALAUX(x) SCIP_RETCODE x (\
203  SCIP* scip, \
204  SCIP_NLHDLR* nlhdlr, \
205  SCIP_EXPR* expr, \
206  SCIP_NLHDLREXPRDATA* nlhdlrexprdata, \
207  SCIP_Real* auxvalue, \
208  SCIP_SOL* sol)
209 
210 /** nonlinear handler interval evaluation (activity computation) callback
211  *
212  * The method computes an interval that contains the image (range) of the expression.
213  *
214  * \param[in] scip SCIP main data structure
215  * \param[in] nlhdlr nonlinear handler
216  * \param[in] expr expression
217  * \param[in] nlhdlrexprdata expression specific data of the nonlinear handler
218  * \param[in,out] interval buffer where to store interval (on input: current interval for expr, on output: computed interval for expr)
219  * \param[in] intevalvar callback to be called when interval evaluating a variable
220  * \param[in] intevalvardata data to be passed to intevalvar callback
221  */
222 #define SCIP_DECL_NLHDLRINTEVAL(x) SCIP_RETCODE x (\
223  SCIP* scip, \
224  SCIP_NLHDLR* nlhdlr, \
225  SCIP_EXPR* expr, \
226  SCIP_NLHDLREXPRDATA* nlhdlrexprdata, \
227  SCIP_INTERVAL* interval, \
228  SCIP_DECL_EXPR_INTEVALVAR((*intevalvar)), \
229  void* intevalvardata)
230 
231 /** nonlinear handler callback for reverse propagation
232  *
233  * The method propagates the given bounds over the arguments of an expression.
234  * The arguments of an expression are other expressions and the tighter intervals should be passed
235  * to the corresponding argument (expression) via SCIPtightenExprIntervalNonlinear().
236  *
237  * \param[in] scip SCIP main data structure
238  * \param[in] conshdlr nonlinear constraint handler
239  * \param[in] nlhdlr nonlinear handler
240  * \param[in] expr expression
241  * \param[in] nlhdlrexprdata expression specific data of the nonlinear handler
242  * \param[in] bounds the bounds on the expression that should be propagated
243  * \param[out] infeasible buffer to store whether an expression's bounds were propagated to an empty interval
244  * \param[out] nreductions buffer to store the number of interval reductions of all children
245  */
246 #define SCIP_DECL_NLHDLRREVERSEPROP(x) SCIP_RETCODE x (\
247  SCIP* scip, \
248  SCIP_CONSHDLR* conshdlr, \
249  SCIP_NLHDLR* nlhdlr, \
250  SCIP_EXPR* expr, \
251  SCIP_NLHDLREXPRDATA* nlhdlrexprdata, \
252  SCIP_INTERVAL bounds, \
253  SCIP_Bool* infeasible, \
254  int* nreductions)
255 
256 /** separation initialization method of a nonlinear handler (called during CONSINITLP)
257  *
258  * The method shall initialize the separation data of the nonlinear handler, if any, and add initial cuts to the LP relaxation.
259  *
260  * \param[in] scip SCIP main data structure
261  * \param[in] conshdlr nonlinear constraint handler
262  * \param[in] cons nonlinear constraint
263  * \param[in] nlhdlr nonlinear handler
264  * \param[in] nlhdlrexprdata exprdata of nonlinear handler
265  * \param[in] expr expression
266  * \param[in] overestimate whether the expression needs to be overestimated
267  * \param[in] underestimate whether the expression needs to be underestimated
268  * \param[out] infeasible buffer to store whether infeasibility was detected while building the LP
269  */
270 #define SCIP_DECL_NLHDLRINITSEPA(x) SCIP_RETCODE x (\
271  SCIP* scip, \
272  SCIP_CONSHDLR* conshdlr, \
273  SCIP_CONS* cons, \
274  SCIP_NLHDLR* nlhdlr, \
275  SCIP_EXPR* expr, \
276  SCIP_NLHDLREXPRDATA* nlhdlrexprdata, \
277  SCIP_Bool overestimate, \
278  SCIP_Bool underestimate, \
279  SCIP_Bool* infeasible)
280 
281 /** separation deinitialization method of a nonlinear handler (called during CONSEXITSOL)
282  *
283  * The method shall deinitialize the separation data of the nonlinear handler, if any.
284  *
285  * \param[in] scip SCIP main data structure
286  * \param[in] nlhdlr nonlinear handler
287  * \param[in] nlhdlrexprdata exprdata of nonlinear handler
288  * \param[in] expr expression
289  */
290 #define SCIP_DECL_NLHDLREXITSEPA(x) SCIP_RETCODE x (\
291  SCIP* scip, \
292  SCIP_NLHDLR* nlhdlr, \
293  SCIP_EXPR* expr, \
294  SCIP_NLHDLREXPRDATA* nlhdlrexprdata)
295 
296 /** nonlinear handler separation and enforcement callback
297  *
298  * The method tries to separate the given solution from the set defined by either
299  * <pre>
300  * expr - auxvar <= 0 (if !overestimate)
301  * </pre>
302  * or
303  * <pre>
304  * expr - auxvar >= 0 (if overestimate),
305  * </pre>
306  * where `auxvar = SCIPgetExprAuxVarNonlinear(expr)`.
307  *
308  * It can do so by
309  * - separation, i.e., finding an affine hyperplane (a cut) that separates the given point,
310  * - bound tightening, i.e., changing bounds on a variable so that the given point is outside the updated domain,
311  * - adding branching scores to potentially split the current problem into 2 subproblems
312  *
313  * If parameter `inenforcement` is FALSE, then only the first option (separation) is allowed.
314  *
315  * If the nonlinear handler always separates by computing a linear under- or overestimator of expr,
316  * then it could be advantageous to implement the \ref SCIP_DECL_NLHDLRESTIMATE "ESTIMATE" callback instead.
317  *
318  * Note, that the nonlinear handler may also choose to separate for a relaxation of the mentioned sets,
319  * e.g., `expr` &le; upperbound(`auxvar`) or `expr` &ge; lowerbound(`auxvar`).
320  * This is especially useful in situations where `expr` is the root expression of a constraint
321  * and it is sufficient to satisfy `lhs` &le; `expr` &le; `rhs`.
322  * cons_nonlinear ensures that `lhs` &le; lowerbound(`auxvar`) and upperbound(`auxvar`) &le; `rhs`.
323  *
324  * cons_nonlinear may call this callback first with `allowweakcuts` = FALSE and repeat later with
325  * `allowweakcuts` = TRUE, if it didn't succeed to enforce a solution without using weak cuts.
326  * If in enforcement and the nonlinear handler cannot enforce by separation or bound tightening, it should register
327  * branching scores for those expressions where branching may help to compute tighter cuts in children.
328  *
329  * The nonlinear handler must set `result` to \ref SCIP_SEPARATED if it added a cut,
330  * to \ref SCIP_REDUCEDDOM if it added a bound change, and
331  * to \ref SCIP_BRANCHED if it added branching scores.
332  * Otherwise, it may set result to \ref SCIP_DIDNOTRUN or \ref SCIP_DIDNOTFIND.
333  *
334  * Parameter `cons` gives the constraint that is currently enforced.
335  * Note that `expr` does not need to be the root of this constraint, i.e., `SCIPgetExprNonlinear(cons)==expr` may not hold.
336  * If an expression appears in several constraints, it is not well defined which constraint is given in `cons`.
337  * The main purpose of `cons` is to provide a constraint source for LP rows that are added in this callback.
338  *
339  * \param[in] scip SCIP main data structure
340  * \param[in] conshdlr nonlinear constraint handler
341  * \param[in] cons nonlinear constraint that is currently enforced
342  * \param[in] nlhdlr nonlinear handler
343  * \param[in] expr expression
344  * \param[in] nlhdlrexprdata expression specific data of the nonlinear handler
345  * \param[in] sol solution to be separated (NULL for the LP solution)
346  * \param[in] auxvalue current value of expression w.r.t. auxiliary variables as obtained from \ref SCIP_DECL_NLHDLREVALAUX "EVALAUX"
347  * \param[in] overestimate whether the expression needs to be over- or underestimated
348  * \param[in] allowweakcuts whether we should only look for "strong" cuts, or anything that separates is fine
349  * \param[in] separated whether another nonlinear handler already added a cut for this expression
350  * \param[in] inenforcement whether we are in enforcement, or only in separation
351  * \param[out] result pointer to store the result
352  */
353 #define SCIP_DECL_NLHDLRENFO(x) SCIP_RETCODE x (\
354  SCIP* scip, \
355  SCIP_CONSHDLR* conshdlr, \
356  SCIP_CONS* cons, \
357  SCIP_NLHDLR* nlhdlr, \
358  SCIP_EXPR* expr, \
359  SCIP_NLHDLREXPRDATA* nlhdlrexprdata, \
360  SCIP_SOL* sol, \
361  SCIP_Real auxvalue, \
362  SCIP_Bool overestimate, \
363  SCIP_Bool allowweakcuts, \
364  SCIP_Bool separated, \
365  SCIP_Bool addbranchscores, \
366  SCIP_RESULT* result)
367 
368 /** nonlinear handler under/overestimation callback
369  *
370  * The method tries to compute linear under- or overestimators of `expr` that are as tight as possible at a given point.
371  * If the value of the estimator in the solution is smaller (larger) than `targetvalue`
372  * when underestimating (overestimating), then no estimator needs to be computed.
373  * Note, that `targetvalue` can be infinite if any estimator will be accepted.
374  * If successful, it shall store the estimators in the given `rowpreps` data structure and set the
375  * `rowprep->local` flag accordingly (SCIProwprepSetLocal()).
376  * The sidetype of a rowprep must be set to \ref SCIP_SIDETYPE_LEFT if overestimating and
377  * \ref SCIP_SIDETYPE_RIGHT if underestimating.
378  *
379  * If the callback is required to indicate for which expression a reduction in the local bounds (usually by branching)
380  * would improve the estimator, it shall do so via calls to SCIPaddExprsViolScoreNonlinear().
381  *
382  * \param[in] scip SCIP main data structure
383  * \param[in] conshdlr constraint handler
384  * \param[in] nlhdlr nonlinear handler
385  * \param[in] expr expression
386  * \param[in] nlhdlrexprdata expression data of nonlinear handler
387  * \param[in] sol solution at which to estimate (NULL for the LP solution)
388  * \param[in] auxvalue current value of expression w.r.t. auxiliary variables as obtained from \ref SCIP_DECL_NLHDLREVALAUX "EVALAUX"
389  * \param[in] overestimate whether the expression needs to be over- or underestimated
390  * \param[in] targetvalue a value the estimator shall exceed, can be +/-infinity
391  * \param[in] addbranchscores indicates whether to register branching scores
392  * \param[out] rowpreps an array where to store the estimators
393  * \param[out] success buffer to indicate whether an estimator could be computed
394  * \param[out] addedbranchscores buffer to store whether the branching score callback was successful
395  */
396 #define SCIP_DECL_NLHDLRESTIMATE(x) SCIP_RETCODE x (\
397  SCIP* scip, \
398  SCIP_CONSHDLR* conshdlr, \
399  SCIP_NLHDLR* nlhdlr, \
400  SCIP_EXPR* expr, \
401  SCIP_NLHDLREXPRDATA* nlhdlrexprdata, \
402  SCIP_SOL* sol, \
403  SCIP_Real auxvalue, \
404  SCIP_Bool overestimate, \
405  SCIP_Real targetvalue, \
406  SCIP_Bool addbranchscores, \
407  SCIP_PTRARRAY* rowpreps, \
408  SCIP_Bool* success, \
409  SCIP_Bool* addedbranchscores)
410 
411 typedef struct SCIP_Nlhdlr SCIP_NLHDLR; /**< nonlinear handler */
412 typedef struct SCIP_NlhdlrData SCIP_NLHDLRDATA; /**< nonlinear handler data */
413 typedef struct SCIP_NlhdlrExprData SCIP_NLHDLREXPRDATA; /**< nonlinear handler data for a specific expression */
414 
415 #endif /* SCIP_TYPE_NLHDLR_H_ */
type_misc.h
type definitions for miscellaneous datastructures
SCIP_Nlhdlr
Definition: struct_nlhdlr.h:43
SCIP_NLHDLR_METHOD
unsigned int SCIP_NLHDLR_METHOD
Definition: type_nlhdlr.h:57
type_expr.h
type and macro definitions related to algebraic expressions
SCIP_NLHDLREXPRDATA
struct SCIP_NlhdlrExprData SCIP_NLHDLREXPRDATA
Definition: type_nlhdlr.h:413
SCIP_NLHDLRDATA
struct SCIP_NlhdlrData SCIP_NLHDLRDATA
Definition: type_nlhdlr.h:412
type_cons.h
type definitions for constraints and constraint handlers