Actual source code: neldermead.c
petsc-3.8.4 2018-03-24
1: #include <../src/tao/unconstrained/impls/neldermead/neldermead.h>
2: #include <petscvec.h>
5: /*------------------------------------------------------------*/
6: static PetscErrorCode NelderMeadSort(TAO_NelderMead *nm)
7: {
8: PetscReal *values = nm->f_values;
9: PetscInt *indices = nm->indices;
10: PetscInt dim = nm->N+1;
11: PetscInt i,j,index;
12: PetscReal val;
15: for (i=1;i<dim;i++) {
16: index = indices[i];
17: val = values[index];
18: for (j=i-1; j>=0 && values[indices[j]] > val; j--) {
19: indices[j+1] = indices[j];
20: }
21: indices[j+1] = index;
22: }
23: return(0);
24: }
27: /*------------------------------------------------------------*/
28: static PetscErrorCode NelderMeadReplace(TAO_NelderMead *nm, PetscInt index, Vec Xmu, PetscReal f)
29: {
33: /* Add new vector's fraction of average */
34: VecAXPY(nm->Xbar,nm->oneOverN,Xmu);
35: VecCopy(Xmu,nm->simplex[index]);
36: nm->f_values[index] = f;
38: NelderMeadSort(nm);
40: /* Subtract last vector from average */
41: VecAXPY(nm->Xbar,-nm->oneOverN,nm->simplex[nm->indices[nm->N]]);
42: return(0);
43: }
45: /* ---------------------------------------------------------- */
46: static PetscErrorCode TaoSetUp_NM(Tao tao)
47: {
49: TAO_NelderMead *nm = (TAO_NelderMead *)tao->data;
50: PetscInt n;
53: VecGetSize(tao->solution,&n);
54: nm->N = n;
55: nm->oneOverN = 1.0/n;
56: VecDuplicateVecs(tao->solution,nm->N+1,&nm->simplex);
57: PetscMalloc1(nm->N+1,&nm->f_values);
58: PetscMalloc1(nm->N+1,&nm->indices);
59: VecDuplicate(tao->solution,&nm->Xbar);
60: VecDuplicate(tao->solution,&nm->Xmur);
61: VecDuplicate(tao->solution,&nm->Xmue);
62: VecDuplicate(tao->solution,&nm->Xmuc);
64: tao->gradient=0;
65: tao->step=0;
66: return(0);
67: }
69: /* ---------------------------------------------------------- */
70: static PetscErrorCode TaoDestroy_NM(Tao tao)
71: {
72: TAO_NelderMead *nm = (TAO_NelderMead*)tao->data;
76: if (tao->setupcalled) {
77: VecDestroyVecs(nm->N+1,&nm->simplex);
78: VecDestroy(&nm->Xmuc);
79: VecDestroy(&nm->Xmue);
80: VecDestroy(&nm->Xmur);
81: VecDestroy(&nm->Xbar);
82: }
83: PetscFree(nm->indices);
84: PetscFree(nm->f_values);
85: PetscFree(tao->data);
86: tao->data = 0;
87: return(0);
88: }
90: /*------------------------------------------------------------*/
91: static PetscErrorCode TaoSetFromOptions_NM(PetscOptionItems *PetscOptionsObject,Tao tao)
92: {
93: TAO_NelderMead *nm = (TAO_NelderMead*)tao->data;
97: PetscOptionsHead(PetscOptionsObject,"Nelder-Mead options");
98: PetscOptionsReal("-tao_nm_lamda","initial step length","",nm->lamda,&nm->lamda,NULL);
99: PetscOptionsReal("-tao_nm_mu","mu","",nm->mu_oc,&nm->mu_oc,NULL);
100: nm->mu_ic = -nm->mu_oc;
101: nm->mu_r = nm->mu_oc*2.0;
102: nm->mu_e = nm->mu_oc*4.0;
103: PetscOptionsTail();
104: return(0);
105: }
107: /*------------------------------------------------------------*/
108: static PetscErrorCode TaoView_NM(Tao tao,PetscViewer viewer)
109: {
110: TAO_NelderMead *nm = (TAO_NelderMead*)tao->data;
111: PetscBool isascii;
115: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
116: if (isascii) {
117: PetscViewerASCIIPushTab(viewer);
118: PetscViewerASCIIPrintf(viewer,"expansions: %D\n",nm->nexpand);
119: PetscViewerASCIIPrintf(viewer,"reflections: %D\n",nm->nreflect);
120: PetscViewerASCIIPrintf(viewer,"inside contractions: %D\n",nm->nincontract);
121: PetscViewerASCIIPrintf(viewer,"outside contractionss: %D\n",nm->noutcontract);
122: PetscViewerASCIIPrintf(viewer,"Shrink steps: %D\n",nm->nshrink);
123: PetscViewerASCIIPopTab(viewer);
124: }
125: return(0);
126: }
128: /*------------------------------------------------------------*/
129: static PetscErrorCode TaoSolve_NM(Tao tao)
130: {
131: PetscErrorCode ierr;
132: TAO_NelderMead *nm = (TAO_NelderMead*)tao->data;
133: TaoConvergedReason reason;
134: PetscReal *x;
135: PetscInt i;
136: Vec Xmur=nm->Xmur, Xmue=nm->Xmue, Xmuc=nm->Xmuc, Xbar=nm->Xbar;
137: PetscReal fr,fe,fc;
138: PetscInt shrink;
139: PetscInt low,high;
142: nm->nshrink = 0;
143: nm->nreflect = 0;
144: nm->nincontract = 0;
145: nm->noutcontract = 0;
146: nm->nexpand = 0;
148: if (tao->XL || tao->XU || tao->ops->computebounds) {
149: PetscPrintf(((PetscObject)tao)->comm,"WARNING: Variable bounds have been set but will be ignored by NelderMead algorithm\n");
150: }
152: VecCopy(tao->solution,nm->simplex[0]);
153: TaoComputeObjective(tao,nm->simplex[0],&nm->f_values[0]);
154: nm->indices[0]=0;
155: for (i=1;i<nm->N+1;i++){
156: VecCopy(tao->solution,nm->simplex[i]);
157: VecGetOwnershipRange(nm->simplex[i],&low,&high);
158: if (i-1 >= low && i-1 < high) {
159: VecGetArray(nm->simplex[i],&x);
160: x[i-1-low] += nm->lamda;
161: VecRestoreArray(nm->simplex[i],&x);
162: }
164: TaoComputeObjective(tao,nm->simplex[i],&nm->f_values[i]);
165: nm->indices[i] = i;
166: }
168: /* Xbar = (Sum of all simplex vectors - worst vector)/N */
169: NelderMeadSort(nm);
170: VecSet(Xbar,0.0);
171: for (i=0;i<nm->N;i++) {
172: VecAXPY(Xbar,1.0,nm->simplex[nm->indices[i]]);
173: }
174: VecScale(Xbar,nm->oneOverN);
175: reason = TAO_CONTINUE_ITERATING;
176: while (1) {
177: shrink = 0;
178: VecCopy(nm->simplex[nm->indices[0]],tao->solution);
179: TaoMonitor(tao,tao->niter++,nm->f_values[nm->indices[0]],nm->f_values[nm->indices[nm->N]]-nm->f_values[nm->indices[0]],0.0,1.0,&reason);
180: if (reason != TAO_CONTINUE_ITERATING) break;
182: /* x(mu) = (1 + mu)Xbar - mu*X_N+1 */
183: VecAXPBYPCZ(Xmur,1+nm->mu_r,-nm->mu_r,0,Xbar,nm->simplex[nm->indices[nm->N]]);
184: TaoComputeObjective(tao,Xmur,&fr);
186: if (nm->f_values[nm->indices[0]] <= fr && fr < nm->f_values[nm->indices[nm->N-1]]) {
187: /* reflect */
188: nm->nreflect++;
189: PetscInfo(0,"Reflect\n");
190: NelderMeadReplace(nm,nm->indices[nm->N],Xmur,fr);
191: } else if (fr < nm->f_values[nm->indices[0]]) {
192: /* expand */
193: nm->nexpand++;
194: PetscInfo(0,"Expand\n");
195: VecAXPBYPCZ(Xmue,1+nm->mu_e,-nm->mu_e,0,Xbar,nm->simplex[nm->indices[nm->N]]);
196: TaoComputeObjective(tao,Xmue,&fe);
197: if (fe < fr) {
198: NelderMeadReplace(nm,nm->indices[nm->N],Xmue,fe);
199: } else {
200: NelderMeadReplace(nm,nm->indices[nm->N],Xmur,fr);
201: }
202: } else if (nm->f_values[nm->indices[nm->N-1]] <= fr && fr < nm->f_values[nm->indices[nm->N]]) {
203: /* outside contraction */
204: nm->noutcontract++;
205: PetscInfo(0,"Outside Contraction\n");
206: VecAXPBYPCZ(Xmuc,1+nm->mu_oc,-nm->mu_oc,0,Xbar,nm->simplex[nm->indices[nm->N]]);
208: TaoComputeObjective(tao,Xmuc,&fc);
209: if (fc <= fr) {
210: NelderMeadReplace(nm,nm->indices[nm->N],Xmuc,fc);
211: } else shrink=1;
212: } else {
213: /* inside contraction */
214: nm->nincontract++;
215: PetscInfo(0,"Inside Contraction\n");
216: VecAXPBYPCZ(Xmuc,1+nm->mu_ic,-nm->mu_ic,0,Xbar,nm->simplex[nm->indices[nm->N]]);
217: TaoComputeObjective(tao,Xmuc,&fc);
218: if (fc < nm->f_values[nm->indices[nm->N]]) {
219: NelderMeadReplace(nm,nm->indices[nm->N],Xmuc,fc);
220: } else shrink = 1;
221: }
223: if (shrink) {
224: nm->nshrink++;
225: PetscInfo(0,"Shrink\n");
227: for (i=1;i<nm->N+1;i++) {
228: VecAXPBY(nm->simplex[nm->indices[i]],1.5,-0.5,nm->simplex[nm->indices[0]]);
229: TaoComputeObjective(tao,nm->simplex[nm->indices[i]], &nm->f_values[nm->indices[i]]);
230: }
231: VecAXPBY(Xbar,1.5*nm->oneOverN,-0.5,nm->simplex[nm->indices[0]]);
233: /* Add last vector's fraction of average */
234: VecAXPY(Xbar,nm->oneOverN,nm->simplex[nm->indices[nm->N]]);
235: NelderMeadSort(nm);
236: /* Subtract new last vector from average */
237: VecAXPY(Xbar,-nm->oneOverN,nm->simplex[nm->indices[nm->N]]);
238: }
239: }
240: return(0);
241: }
243: /* ---------------------------------------------------------- */
244: /*MC
245: TAONM - Nelder-Mead solver for derivative free, unconstrained minimization
247: Options Database Keys:
248: + -tao_nm_lamda - initial step length
249: . -tao_nm_mu - expansion/contraction factor
251: Level: beginner
252: M*/
254: PETSC_EXTERN PetscErrorCode TaoCreate_NM(Tao tao)
255: {
256: TAO_NelderMead *nm;
260: PetscNewLog(tao,&nm);
261: tao->data = (void*)nm;
263: tao->ops->setup = TaoSetUp_NM;
264: tao->ops->solve = TaoSolve_NM;
265: tao->ops->view = TaoView_NM;
266: tao->ops->setfromoptions = TaoSetFromOptions_NM;
267: tao->ops->destroy = TaoDestroy_NM;
269: /* Override default settings (unless already changed) */
270: if (!tao->max_it_changed) tao->max_it = 2000;
271: if (!tao->max_funcs_changed) tao->max_funcs = 4000;
273: nm->simplex = 0;
274: nm->lamda = 1;
276: nm->mu_ic = -0.5;
277: nm->mu_oc = 0.5;
278: nm->mu_r = 1.0;
279: nm->mu_e = 2.0;
281: return(0);
282: }