this repo has no description
dekker.one
1/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
2/*
3 * Main authors:
4 * Guido Tack <tack@gecode.org>
5 *
6 * Copyright:
7 * Guido Tack, 2009
8 *
9 * This file is part of Gecode, the generic constraint
10 * development environment:
11 * http://www.gecode.org
12 *
13 * Permission is hereby granted, free of charge, to any person obtaining
14 * a copy of this software and associated documentation files (the
15 * "Software"), to deal in the Software without restriction, including
16 * without limitation the rights to use, copy, modify, merge, publish,
17 * distribute, sublicense, and/or sell copies of the Software, and to
18 * permit persons to whom the Software is furnished to do so, subject to
19 * the following conditions:
20 *
21 * The above copyright notice and this permission notice shall be
22 * included in all copies or substantial portions of the Software.
23 *
24 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
25 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
26 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
27 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
28 * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
29 * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
30 * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
31 *
32 */
33
34#include <gecode/driver.hh>
35#include <gecode/int.hh>
36#include <gecode/minimodel.hh>
37
38using namespace Gecode;
39
40namespace {
41 /**
42 * \brief Specification of an open shop instance
43 *
44 */
45 class OpenShopSpec {
46 public:
47 const int m; //< number of machines
48 const int n; //< number of jobs
49 const int* p; //< processing times of the tasks
50 /// Constructor
51 OpenShopSpec(int m0, int n0, const int* p0) : m(m0), n(n0), p(p0) {}
52 };
53
54 extern OpenShopSpec examples[];
55 extern const unsigned int n_examples;
56}
57
58/**
59 * \brief %Example: open-shop scheduling
60 *
61 * \ingroup Example
62 *
63 */
64class OpenShop : public IntMinimizeScript {
65protected:
66 /// The instance specification
67 const OpenShopSpec& spec;
68 /// Precedences
69 BoolVarArray b;
70 /// Makespan
71 IntVar makespan;
72 /// Start times
73 IntVarArray _start;
74
75 /// %Task representation for CROSH heuristic
76 class Task {
77 public:
78 int j; //< Job
79 int m; //< Machine
80 int p; //< Processing time
81 /// Default constructor
82 Task(void) {}
83 /// Constructor
84 Task(int j0, int m0, int p0) : j(j0), m(m0), p(p0) {}
85 };
86
87 /** \brief Use Constructive Randomized Open-Shop Heuristics
88 * to compute lower and upper bounds
89 *
90 * This heuristic is taken from the paper
91 * A. Malapert, H. Cambazard, C. Gueret, N. Jussien, A. Langevin,
92 * L.-M. Rousseau: An Optimal Constraint Programming Approach to the
93 * Open-Shop Problem. Technical report, CIRRELT-2009-25.
94 *
95 */
96 void crosh(Matrix<IntArgs>& dur, int& minmakespan, int& maxmakespan) {
97 Support::RandomGenerator rnd;
98
99 // Compute maximum makespan as the sum of all production times.
100 maxmakespan = 0;
101 for (int i=0; i<spec.m; i++)
102 for (int j=0; j<spec.n; j++)
103 maxmakespan += dur(i,j);
104
105 // Compute minimum makespan as the maximum of individual jobs and machines
106 minmakespan = 0;
107 for (int i=0; i<spec.m; i++) {
108 int ms = 0;
109 for (int j=0; j<spec.n; j++) {
110 ms += dur(i,j);
111 }
112 minmakespan = std::max(minmakespan, ms);
113 }
114 for (int j=0; j<spec.n; j++) {
115 int ms = 0;
116 for (int i=0; i<spec.m; i++) {
117 ms += dur(i,j);
118 }
119 minmakespan = std::max(minmakespan, ms);
120 }
121
122 Region re;
123 int* ct_j = re.alloc<int>(spec.n); // Job completion time
124 int* ct_m = re.alloc<int>(spec.m); // Machine completion time
125 Task* tasks = re.alloc<Task>(spec.n*spec.m); // Tasks
126 int k=0;
127 for (int i=spec.m; i--;)
128 for (int j=spec.n; j--;)
129 new (&tasks[k++]) Task(j,i,dur(i,j));
130 int* t0_tasks = re.alloc<int>(spec.n*spec.m); // Earliest possible tasks
131
132 bool stopCROSH = false;
133
134 int maxIterations;
135 switch (spec.n) {
136 case 3: maxIterations = 5; break;
137 case 4: maxIterations = 25; break;
138 case 5: maxIterations = 50; break;
139 case 6: maxIterations = 1000; break;
140 case 7: maxIterations = 10000; break;
141 case 8: maxIterations = 10000; break;
142 case 9: maxIterations = 10000; break;
143 default: maxIterations = 25000; break;
144 }
145 int iteration = 0;
146 while (!stopCROSH && maxmakespan > minmakespan) {
147 for (int i=spec.n; i--;) ct_j[i] = 0;
148 for (int i=spec.m; i--;) ct_m[i] = 0;
149 int cmax = 0; // Current makespan
150 int u = spec.n*spec.m; // Consider all tasks
151 while (u > 0) {
152 int u_t0 = 0; // Set of selectable tasks
153 int t0 = maxmakespan; // Minimal head of unscheduled tasks
154 for (int i=0; i<u; i++) {
155 const Task& t = tasks[i];
156 int est = std::max(ct_j[t.j], ct_m[t.m]); // Head of T_jm
157 if (est < t0) {
158 t0 = est;
159 t0_tasks[0] = i;
160 u_t0 = 1;
161 } else if (est == t0) {
162 t0_tasks[u_t0++] = i;
163 }
164 }
165 int t_j0m0;
166 if (iteration == 0) {
167 // In the first iteration, select tasks with longest processing time
168 t_j0m0 = 0;
169 for (int i=1; i<u_t0; i++)
170 if (tasks[t0_tasks[i]].p > tasks[t0_tasks[t_j0m0]].p)
171 t_j0m0 = i;
172 } else {
173 t_j0m0 = rnd(u_t0); // Select random task
174 }
175 const Task& t = tasks[t0_tasks[t_j0m0]];
176 int ect = t0 + t.p;
177 ct_j[t.j] = ect;
178 ct_m[t.m] = ect;
179 std::swap(tasks[--u],tasks[t0_tasks[t_j0m0]]); // Remove task from u
180 cmax = std::max(cmax, ect);
181 if (cmax > maxmakespan)
182 break;
183 }
184
185 maxmakespan = std::min(maxmakespan,cmax);
186 if (iteration++ > maxIterations)
187 stopCROSH = true; // Iterate a couple of times
188 }
189 }
190public:
191 /// The actual problem
192 OpenShop(const SizeOptions& opt)
193 : IntMinimizeScript(opt),
194 spec(examples[opt.size()]),
195 b(*this, (spec.n+spec.m-2)*spec.n*spec.m/2, 0,1),
196 makespan(*this, 0, Int::Limits::max),
197 _start(*this, spec.m*spec.n, 0, Int::Limits::max) {
198
199 Matrix<IntVarArray> start(_start, spec.m, spec.n);
200 IntArgs _dur(spec.m*spec.n, spec.p);
201 Matrix<IntArgs> dur(_dur, spec.m, spec.n);
202
203 int minmakespan;
204 int maxmakespan;
205 crosh(dur, minmakespan, maxmakespan);
206 rel(*this, makespan <= maxmakespan);
207 rel(*this, makespan >= minmakespan);
208
209 int k=0;
210 for (int m=0; m<spec.m; m++)
211 for (int j0=0; j0<spec.n-1; j0++)
212 for (int j1=j0+1; j1<spec.n; j1++) {
213 // The tasks on machine m of jobs j0 and j1 must be disjoint
214 rel(*this,
215 b[k] == (start(m,j0) + dur(m,j0) <= start(m,j1)));
216 rel(*this,
217 b[k++] == (start(m,j1) + dur(m,j1) > start(m,j0)));
218 }
219
220 for (int j=0; j<spec.n; j++)
221 for (int m0=0; m0<spec.m-1; m0++)
222 for (int m1=m0+1; m1<spec.m; m1++) {
223 // The tasks in job j on machine m0 and m1 must be disjoint
224 rel(*this,
225 b[k] == (start(m0,j) + dur(m0,j) <= start(m1,j)));
226 rel(*this,
227 b[k++] == (start(m1,j) + dur(m1,j) > start(m0,j)));
228 }
229
230 // The makespan is greater than the end time of the latest job
231 for (int m=0; m<spec.m; m++) {
232 for (int j=0; j<spec.n; j++) {
233 rel(*this, start(m,j) + dur(m,j) <= makespan);
234 }
235 }
236
237 // First branch over the precedences
238 branch(*this, b, BOOL_VAR_AFC_MAX(opt.decay()), BOOL_VAL_MAX());
239 // When the precedences are fixed, simply assign the start times
240 assign(*this, _start, INT_ASSIGN_MIN());
241 // When the start times are fixed, use the tightest makespan
242 assign(*this, makespan, INT_ASSIGN_MIN());
243 }
244
245 /// Constructor for cloning \a s
246 OpenShop(OpenShop& s) : IntMinimizeScript(s), spec(s.spec) {
247 b.update(*this, s.b);
248 makespan.update(*this, s.makespan);
249 _start.update(*this, s._start);
250 }
251
252 /// Perform copying during cloning
253 virtual Space*
254 copy(void) {
255 return new OpenShop(*this);
256 }
257
258 /// Minimize the makespan
259 virtual IntVar
260 cost(void) const {
261 return makespan;
262 }
263
264 /// Helper class for representing tasks when printing a solution
265 class PrintTask {
266 public:
267 int start; //< Start time
268 int job; //< Job number
269 int p; //< Processing time
270 /// Comparison of tasks based on start time, used for sorting
271 bool operator()(const PrintTask& t1, const PrintTask& t2) {
272 return t1.start < t2.start;
273 }
274 };
275
276 /// Print solution
277 virtual void
278 print(std::ostream& os) const {
279 Region re;
280 PrintTask* m = re.alloc<PrintTask>(spec.n);
281 for (int i=0; i<spec.m; i++) {
282 int k=0;
283 for (int j=0; j<spec.n; j++) {
284 m[k].start = _start[i*spec.n+j].val();
285 m[k].job = j;
286 m[k].p = spec.p[i*spec.n+j];
287 k++;
288 }
289 Support::quicksort(m, spec.n, m[0]);
290 os << "Machine " << i << ": ";
291 for (int j=0; j<spec.n; j++)
292 os << "\t" << m[j].job << "("<<m[j].p<<")";
293 os << " = " << m[spec.n-1].start+m[spec.n-1].p << std::endl;
294 }
295 os << "Makespan: " << makespan << std::endl;
296 }
297
298};
299
300/** \brief Main-function
301 * \relates OpenShop
302 */
303int
304main(int argc, char* argv[]) {
305 SizeOptions opt("OpenShop");
306 opt.iterations(500);
307 opt.size(0);
308 opt.solutions(0);
309 opt.parse(argc,argv);
310 if (opt.size() >= n_examples) {
311 std::cerr << "Error: size must be between 0 and "
312 << n_examples-1 << std::endl;
313 return 1;
314 }
315 IntMinimizeScript::run<OpenShop,BAB,SizeOptions>(opt);
316 return 0;
317}
318
319namespace {
320
321 /** \name Open shop specifications
322 *
323 * Each specification gives the processing times of the tasks for each
324 * job, as well as the number of jobs and machines.
325 *
326 * \relates OpenShop
327 */
328 //@{
329
330 const int ex0_p[] = {
331 661,6,333,
332 168,489,343,
333 171,505,324
334 };
335 OpenShopSpec ex0(3,3,ex0_p);
336
337 const int ex1_p[] = {
338 54, 34, 61, 2,
339 9, 15, 89, 70,
340 38, 19, 28, 87,
341 95, 34, 7, 29
342 };
343 OpenShopSpec ex1(4,4,ex1_p);
344
345 const int ex2_p[] = {
346 5, 70, 45, 83,
347 24, 80, 58, 45,
348 29, 56, 29, 61,
349 43, 64, 45, 74
350 };
351 OpenShopSpec ex2(4,4,ex2_p);
352
353 const int ex3_p[] = {
354 89, 39, 54, 34, 71, 92, 56,
355 19, 13, 81, 46, 91, 73, 27,
356 66, 95, 48, 24, 96, 18, 14,
357 48, 46, 78, 94, 19, 68, 63,
358 60, 28, 91, 75, 52, 9, 7,
359 33, 98, 37, 11, 2, 30, 38,
360 83, 45, 37, 77, 52, 88, 52
361 };
362 OpenShopSpec ex3(7,7,ex3_p);
363
364 const int ex4_p[] = {
365 49, 58, 37, 79, 16, 64, 71, 65, 6, 44, 17, 85, 99, 57, 89, 4, 16, 8, 40, 66,
366 43, 65, 42, 35, 57, 3, 8, 65, 79, 76, 82, 80, 96, 82, 98, 57, 73, 43, 6, 20,
367 82, 49, 7, 18, 94, 76, 41, 17, 43, 15, 53, 10, 83, 24, 79, 62, 53, 77, 23, 70,
368 18, 30, 80, 7, 97, 84, 10, 27, 7, 91, 14, 12, 7, 31, 24, 97, 16, 33, 99, 15,
369 31, 65, 51, 95, 45, 70, 57, 10, 84, 52, 28, 43, 54, 40, 83, 9, 21, 57, 45, 67,
370 70, 45, 48, 39, 10, 37, 22, 53, 48, 50, 76, 48, 57, 6, 43, 13, 45, 93, 42, 11,
371 80, 5, 53, 97, 75, 22, 10, 70, 79, 92, 96, 18, 57, 3, 82, 52, 1, 21, 23, 38,
372 43, 79, 67, 57, 33, 52, 1, 44, 82, 10, 27, 23, 89, 9, 62, 6, 38, 33, 37, 22,
373 68, 20, 5, 25, 16, 80, 13, 73, 35, 36, 13, 53, 97, 50, 17, 54, 35, 86, 24, 56,
374 60, 83, 8, 81, 3, 4, 48, 14, 77, 10, 71, 57, 86, 94, 49, 36, 62, 62, 41, 56,
375 31, 77, 5, 97, 19, 19, 31, 19, 26, 41, 77, 64, 74, 11, 98, 30, 22, 22, 33, 61,
376 7, 89, 46, 13, 33, 55, 84, 16, 21, 45, 15, 71, 57, 42, 82, 13, 62, 98, 36, 45,
377 84, 90, 20, 61, 24, 59, 8, 49, 53, 53, 83, 76, 28, 62, 59, 11, 41, 2, 58, 46,
378 32, 23, 53, 5, 8, 91, 97, 53, 90, 90, 28, 16, 61, 27, 32, 74, 23, 11, 57, 20,
379 62, 85, 79, 96, 62, 85, 43, 53, 12, 36, 95, 37, 2, 48, 46, 81, 97, 54, 5, 77,
380 57, 35, 41, 55, 72, 98, 22, 81, 6, 8, 70, 64, 55, 53, 7, 38, 58, 30, 83, 81,
381 15, 11, 24, 63, 27, 90, 35, 22, 53, 22, 66, 75, 59, 80, 31, 91, 63, 82, 99, 62,
382 4, 18, 99, 6, 65, 21, 28, 93, 16, 26, 1, 16, 46, 59, 45, 90, 69, 76, 25, 53,
383 50, 24, 66, 2, 17, 85, 5, 86, 4, 88, 44, 5, 29, 19, 27, 14, 36, 57, 59, 15,
384 71, 79, 7, 61, 45, 72, 61, 45, 61, 54, 90, 33, 81, 5, 45, 64, 87, 82, 61, 8
385 };
386 OpenShopSpec ex4(20,20,ex4_p);
387
388 /// The instances
389 OpenShopSpec examples[] = { ex0, ex1, ex2, ex3, ex4 };
390 /// The number of instances
391 const unsigned int n_examples = sizeof(examples) / sizeof(OpenShopSpec);
392
393 //@}
394}
395
396// STATISTICS: example-any