1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
|
/* $Id: ClpSimplexPrimal.hpp 1665 2011-01-04 17:55:54Z lou $ */
// Copyright (C) 2002, International Business Machines
// Corporation and others. All Rights Reserved.
// This code is licensed under the terms of the Eclipse Public License (EPL).
/*
Authors
John Forrest
*/
#ifndef ClpSimplexPrimal_H
#define ClpSimplexPrimal_H
#include "ClpSimplex.hpp"
/** This solves LPs using the primal simplex method
It inherits from ClpSimplex. It has no data of its own and
is never created - only cast from a ClpSimplex object at algorithm time.
*/
class ClpSimplexPrimal : public ClpSimplex {
public:
/**@name Description of algorithm */
//@{
/** Primal algorithm
Method
It tries to be a single phase approach with a weight of 1.0 being
given to getting optimal and a weight of infeasibilityCost_ being
given to getting primal feasible. In this version I have tried to
be clever in a stupid way. The idea of fake bounds in dual
seems to work so the primal analogue would be that of getting
bounds on reduced costs (by a presolve approach) and using
these for being above or below feasible region. I decided to waste
memory and keep these explicitly. This allows for non-linear
costs! I have not tested non-linear costs but will be glad
to do something if a reasonable example is provided.
The code is designed to take advantage of sparsity so arrays are
seldom zeroed out from scratch or gone over in their entirety.
The only exception is a full scan to find incoming variable for
Dantzig row choice. For steepest edge we keep an updated list
of dual infeasibilities (actually squares).
On easy problems we don't need full scan - just
pick first reasonable. This method has not been coded.
One problem is how to tackle degeneracy and accuracy. At present
I am using the modification of costs which I put in OSL and which was
extended by Gill et al. I am still not sure whether we will also
need explicit perturbation.
The flow of primal is three while loops as follows:
while (not finished) {
while (not clean solution) {
Factorize and/or clean up solution by changing bounds so
primal feasible. If looks finished check fake primal bounds.
Repeat until status is iterating (-1) or finished (0,1,2)
}
while (status==-1) {
Iterate until no pivot in or out or time to re-factorize.
Flow is:
choose pivot column (incoming variable). if none then
we are primal feasible so looks as if done but we need to
break and check bounds etc.
Get pivot column in tableau
Choose outgoing row. If we don't find one then we look
primal unbounded so break and check bounds etc. (Also the
pivot tolerance is larger after any iterations so that may be
reason)
If we do find outgoing row, we may have to adjust costs to
keep going forwards (anti-degeneracy). Check pivot will be stable
and if unstable throw away iteration and break to re-factorize.
If minor error re-factorize after iteration.
Update everything (this may involve changing bounds on
variables to stay primal feasible.
}
}
TODO's (or maybe not)
At present we never check we are going forwards. I overdid that in
OSL so will try and make a last resort.
Needs partial scan pivot in option.
May need other anti-degeneracy measures, especially if we try and use
loose tolerances as a way to solve in fewer iterations.
I like idea of dynamic scaling. This gives opportunity to decouple
different implications of scaling for accuracy, iteration count and
feasibility tolerance.
for use of exotic parameter startFinishoptions see Clpsimplex.hpp
*/
int primal(int ifValuesPass = 0, int startFinishOptions = 0);
//@}
/**@name For advanced users */
//@{
/// Do not change infeasibility cost and always say optimal
void alwaysOptimal(bool onOff);
bool alwaysOptimal() const;
/** Normally outgoing variables can go out to slightly negative
values (but within tolerance) - this is to help stability and
and degeneracy. This can be switched off
*/
void exactOutgoing(bool onOff);
bool exactOutgoing() const;
//@}
/**@name Functions used in primal */
//@{
/** This has the flow between re-factorizations
Returns a code to say where decision to exit was made
Problem status set to:
-2 re-factorize
-4 Looks optimal/infeasible
-5 Looks unbounded
+3 max iterations
valuesOption has original value of valuesPass
*/
int whileIterating(int valuesOption);
/** Do last half of an iteration. This is split out so people can
force incoming variable. If solveType_ is 2 then this may
re-factorize while normally it would exit to re-factorize.
Return codes
Reasons to come out (normal mode/user mode):
-1 normal
-2 factorize now - good iteration/ NA
-3 slight inaccuracy - refactorize - iteration done/ same but factor done
-4 inaccuracy - refactorize - no iteration/ NA
-5 something flagged - go round again/ pivot not possible
+2 looks unbounded
+3 max iterations (iteration done)
With solveType_ ==2 this should
Pivot in a variable and choose an outgoing one. Assumes primal
feasible - will not go through a bound. Returns step length in theta
Returns ray in ray_
*/
int pivotResult(int ifValuesPass = 0);
/** The primals are updated by the given array.
Returns number of infeasibilities.
After rowArray will have cost changes for use next iteration
*/
int updatePrimalsInPrimal(CoinIndexedVector * rowArray,
double theta,
double & objectiveChange,
int valuesPass);
/**
Row array has pivot column
This chooses pivot row.
Rhs array is used for distance to next bound (for speed)
For speed, we may need to go to a bucket approach when many
variables go through bounds
If valuesPass non-zero then compute dj for direction
*/
void primalRow(CoinIndexedVector * rowArray,
CoinIndexedVector * rhsArray,
CoinIndexedVector * spareArray,
int valuesPass);
/**
Chooses primal pivot column
updateArray has cost updates (also use pivotRow_ from last iteration)
Would be faster with separate region to scan
and will have this (with square of infeasibility) when steepest
For easy problems we can just choose one of the first columns we look at
*/
void primalColumn(CoinIndexedVector * updateArray,
CoinIndexedVector * spareRow1,
CoinIndexedVector * spareRow2,
CoinIndexedVector * spareColumn1,
CoinIndexedVector * spareColumn2);
/** Checks if tentative optimal actually means unbounded in primal
Returns -3 if not, 2 if is unbounded */
int checkUnbounded(CoinIndexedVector * ray, CoinIndexedVector * spare,
double changeCost);
/** Refactorizes if necessary
Checks if finished. Updates status.
lastCleaned refers to iteration at which some objective/feasibility
cleaning too place.
type - 0 initial so set up save arrays etc
- 1 normal -if good update save
- 2 restoring from saved
saveModel is normally NULL but may not be if doing Sprint
*/
void statusOfProblemInPrimal(int & lastCleaned, int type,
ClpSimplexProgress * progress,
bool doFactorization,
int ifValuesPass,
ClpSimplex * saveModel = NULL);
/// Perturbs problem (method depends on perturbation())
void perturb(int type);
/// Take off effect of perturbation and say whether to try dual
bool unPerturb();
/// Unflag all variables and return number unflagged
int unflag();
/** Get next superbasic -1 if none,
Normal type is 1
If type is 3 then initializes sorted list
if 2 uses list.
*/
int nextSuperBasic(int superBasicType, CoinIndexedVector * columnArray);
/// Create primal ray
void primalRay(CoinIndexedVector * rowArray);
/// Clears all bits and clears rowArray[1] etc
void clearAll();
/// Sort of lexicographic resolve
int lexSolve();
//@}
};
#endif
|
