建議

本研究所應用之混合演算法結合倒傳遞類神經網路架構結合啟發式演算法，未來 建議可針對啟發式演算法做修正，以符合不同品質特性的問題。

在案例中，本研究以「接收訊號強度」做為品質特性，未來根據不同的需求可考 慮以連線品質(link quality)、訊框錯誤率(frame error rate; FER)或傳輸速率(packets per second or throughput)等不同的傳輸品質指標，取代本實驗中的「接收訊號強度」做為 品質特性。另外在評估系統的輸入變數方面，可考慮再加入不同的筆記型電腦或是 PDA、WAP 手機等同時進行預估。利用倒傳遞類神經網路易建立系統模型之能力，

整合所有的傳輸品質之參考指數，可更完整的整合估測系統，為網路規劃者帶來更多 的參考數值，設計出更佳的無線區域網路系統。

參考文獻

一、中文部份

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附 錄

分散式搜尋法之 C 語言程式碼

1. SS_main

#include "ss.h"

double evaluate(SS *prob,double *x) {

double value;

int nvar;

nvar=prob->n_var;

value = 100*pow(x[2]-pow(x[2],2),2)+pow(1-x[1],2)+90*pow(x[4]-pow(x[3],2),2)+

pow(1-x[3],2)+10.1*pow(x[2]-1,2)+10.1*pow(x[4]-1,2)+19.8*(x[2]-1)*(x[4]-1);

return value;

}

void main(void) {

int MaxIter,Iter,i,nvar,b1,b2,PSize,LocalSearch;

double *best,best_value,LowerBound,UpperBound;

SS *prob;

/* Parameters Defined by the User */

MaxIter = 2; /* Number of global iterations */

nvar = 4; /* Number of variables (size of x) */

LowerBound = -10; /* Lower Bound of all variables */

UpperBound = 10; /* Upper Bound of all variables */

b1 = 10; /* Size of reference set 1 (quality) */

b2 = 10; /* Size of reference set 2 (diversity) */

PSize = 100; /* Size of the diversification generator population */

LocalSearch= 1; /* =1 Nelder and Mead Simplex Method activated,=0 OFF */

prob=DataStructures_init(nvar,b1,b2,PSize,LocalSearch);

/* Assign Variable Bounds */

for(i=1;i<=nvar;i++) {

prob->low[i] = LowerBound;

prob->high[i] = UpperBound;

}

/* Build Reference Set */

Initiate_RefSet(prob);

/* Perform Search */

for(Iter=1;Iter<=MaxIter;Iter++) {

if(prob->new_elements) Combine_RefSet(prob);

else {

Update_RefSet2(prob);

Combine_RefSet(prob);

} }

/*** Best Solution ***/

best_value = prob->value1[prob->order1[1]];

best = SSallocate_double_array(nvar);

for(i=1;i<=nvar;i++) best[i]=prob->RefSet1[prob->order1[1]][i];

printf("\n\nBest Solution Found. Value = %f\n\n",best_value);

for(i=1;i<=nvar;i++) printf("solution[%d] = %f\n",i,best[i]);

free(best);

Free_DataStructures(prob);

}

2. simplex

/* Nelder and Mead Simplex Method for Nonlinear unconstrained optimization problems

*/

#include "ss.h"

#define NMAX 5000

#define ALPHA 1.0

#define BETA 0.5

#define GAMMA 2.0

#define GET_PSUM for (j=1;j<=ndim;j++) { for (i=1, sum=0.0;i<=mpts;i++) sum +=

p[i][j]; psum[j]=sum; }

int amoeba(double **p, double *y, int ndim, double ftol, double (*funk)(), int *nfunk, SS

*prob) {

int i, j, ilo, ihi, inhi, mpts=ndim+1;

double ytry, ysave, sum, rtol, *psum;

psum = SSallocate_double_array(ndim+1);

*nfunk = 0;

GET_PSUM for (;;) {

ilo = 1;

ihi = y[1] > y[2] ? (inhi = 2, 1) : (inhi = 1, 2);

for (i = 1; i <= mpts; i++) { if (y[i] < y[ilo]) ilo = i;

if (y[i] > y[ihi]) { inhi = ihi;

ihi = i;

} else if (y[i] > y[inhi]) if (i != ihi) inhi = i;

}

rtol = 2.0*fabs(y[ihi]-y[ilo])/(fabs(y[ihi])+fabs(y[ilo]));

if (rtol < ftol) break;

if (*nfunk >= NMAX) return -1;

ytry = amotry(p, y, psum, ndim, funk, ihi, nfunk, -ALPHA,prob);

if (ytry <= y[ilo])

ytry = amotry(p, y, psum, ndim, funk, ihi, nfunk, GAMMA,prob);

else if (ytry >= y[inhi]) { ysave = y[ihi];

ytry = amotry(p, y, psum, ndim, funk, ihi, nfunk, BETA,prob);

if (ytry >= ysave) {

for (i = 1; i <= mpts; i++) { if (i != ilo) {

for (j = 1; j <= ndim; j++) {

psum[j] = 0.5*(p[i][j]+p[ilo][j]);

p[i][j] = psum[j];

}

y[i] = (*funk)(prob,psum);

} }

*nfunk += ndim;

GET_PSUM }

} }

free(psum);

return 0;

}

double amotry(double **p, double *y, double *psum, int ndim, double (*funk)(), int ihi, int

*nfunk, double fac,SS *prob)

{

int j;

double fac1, fac2, ytry, *ptry;

ptry = SSallocate_double_array(ndim+1);

fac1 = (1.0-fac)/(double)ndim;

fac2 = fac1 - fac;

for (j = 1; j <= ndim; j++) ptry[j] = psum[j]*fac1-p[ihi][j]*fac2;

ytry = (*funk)(prob,ptry);

++(*nfunk);

if (ytry < y[ihi]) { y[ihi] = ytry;

for (j = 1; j <= ndim; j++) {

psum[j] += ptry[j]-p[ihi][j];

p[ihi][j] = ptry[j];

} }

free(ptry);

return ytry;

}

3. SS_Memory

#include "ss.h"

SS *DataStructures_init(int nvar,int b1,int b2,int PSize,int LocalSearch) {

SS *problem;

problem = (SS*) calloc(1,sizeof(SS));

if(!problem) SSabort("Memory allocation problem");

problem->n_var = nvar;

problem->b1 = b1;

problem->b2 = b2;

problem->PSize = PSize;

problem->LS = LocalSearch;

problem->digits = 0;

problem->last_combine = 0;

problem->iter=0;

problem->high = SSallocate_double_array(nvar);

if(!problem->high) SSabort("Memory allocation problem");

problem->low = SSallocate_double_array(nvar);

if(!problem->low) SSabort("Memory allocation problem");

problem->ranges = SSallocate_int_matrix(nvar,5);

if(!problem->ranges) SSabort("Memory allocation problem");

problem->value1 = SSallocate_double_array(b1);

if(!problem->value1) SSabort("Memory allocation problem");

problem->RefSet1 = SSallocate_double_matrix(b1,nvar);

if(!problem->RefSet1) SSabort("Memory allocation problem");

problem->order1 = SSallocate_int_array(b1);

if(!problem->order1) SSabort("Memory allocation problem");

problem->iter1 = SSallocate_int_array(b1);

if(!problem->iter1) SSabort("Memory allocation problem");

problem->value2 = SSallocate_double_array(b2);

if(!problem->value2) SSabort("Memory allocation problem");

problem->RefSet2 = SSallocate_double_matrix(b2,nvar);

if(!problem->RefSet1) SSabort("Memory allocation problem");

problem->order2 = SSallocate_int_array(b2);

if(!problem->order1) SSabort("Memory allocation problem");

problem->iter2 = SSallocate_int_array(b2);

if(!problem->iter2) SSabort("Memory allocation problem");

/* Parameters for random generator */

problem->idum = 13171191;

problem->seed_reset = 1;

problem->iff = 0;

return problem;

}

void Free_DataStructures(SS *prob) {

SSfree_double_matrix(prob->RefSet1,prob->b1);

free(prob->value1);

free(prob->order1);

free(prob->iter1);

SSfree_double_matrix(prob->RefSet2,prob->b2);

free(prob->value2);

free(prob->order2);

free(prob->iter2);

SSfree_int_matrix(prob->ranges,prob->n_var);

free(prob->high);

free(prob->low);

free(prob);

}

int **SSallocate_int_matrix(int rows,int columns) {

int **aux;

int i;

aux=(int**)calloc(rows+1,sizeof(int*));

if(!aux) SSabort("Memory allocation problem");

for(i=1;i<=rows;i++) {

aux[i] = SSallocate_int_array(columns);

if(aux[i]==NULL) SSabort("Memory allocation problem");

}

return aux;

}

double **SSallocate_double_matrix(int rows,int columns) {

double **aux;

int i;

aux=(double**)calloc(rows+1,sizeof(double*));

if(!aux) SSabort("Memory allocation problem");

for(i=0;i<=rows;i++) {

aux[i] = SSallocate_double_array(columns);

if(!aux[i]) SSabort("Memory allocation problem");

}

return aux;

}

double *SSallocate_double_array(int size) {

double *aux;

aux=(double*)calloc(size+1,sizeof(double));

if(!aux) SSabort("Memory allocation problem");

return aux;

}

int *SSallocate_int_array(int size) {

int *aux;

aux=(int*)calloc(size+1,sizeof(int));

if(!aux) SSabort("Memory allocation problem");

return aux;

}

void SSfree_double_matrix(double **matrix,int rows) {

int i;

for(i=0;i<=rows;i++) free(matrix[i]);

free(matrix);

}

void SSfree_int_matrix(int **matrix,int rows)

{

int i;

for(i=1;i<=rows;i++) free(matrix[i]);

free(matrix);

}

4. SS_RefSet

#include "ss.h"

void Initiate_RefSet(SS *prob) {

double *current,*min_dist,*value,**solutions;

int j,i,i1,a,*index,*index2,cont=0;

double d,dmax,current_value;

prob->iter=1;

prob->new_elements = 1;

current = SSallocate_double_array(prob->n_var);

if(!current) SSabort("Memory allocation problem");

min_dist = SSallocate_double_array(prob->PSize);

if(!min_dist) SSabort("Memory allocation problem");

value = SSallocate_double_array(prob->PSize);

if(!min_dist) SSabort("Memory allocation problem");

solutions = SSallocate_double_matrix(prob->PSize,prob->n_var);

if(!solutions) SSabort("Memory allocation problem");

for(i=1;i<=prob->PSize;i++)

{

/* Generate new solution */

for(j=1;j<=prob->n_var;j++)

current[j] = SSGenerate_value(prob,j);

/* Evaluate Solution */

current_value=evaluate(prob,current);

if(prob->LS) SSimprove_solution(prob,current,&current_value);

if(is_new(prob,solutions,i-1,current)) {

/* Store solution in matrix "solutions" */

for(j=1;j<=prob->n_var;j++) solutions[i][j] = current[j];

value[i]=current_value;

} else {

i--;

cont++;

}

if(cont>prob->PSize/2) {

prob->digits++;

cont=0;

} }

index = orden_indices(value,prob->PSize,-1);

/* Add the best b1 to RefSet1 */

for(i=1;i<=prob->b1;i++) {

for(j=1;j<=prob->n_var;j++)

prob->RefSet1[i][j] = solutions[index[i]][j];

prob->value1[i] = value[index[i]];

prob->order1[i] = i;

prob->iter1[i] = 1;

}

/* Compute minimum distances */

for(i=1;i<=prob->PSize;i++)

min_dist[i]=distance_to_RefSet1(prob,solutions[i]);

/*Add the second b2 to RefSet2 */

for(i=1;i<=prob->b2;i++) {

/* Select the solution with maximum min. dist */

dmax = -1;

for(j=1;j<=prob->PSize;j++) if(min_dist[j]>dmax)

{

dmax=min_dist[j];

a=j;

}

for(j=1;j<=prob->n_var;j++)

prob->RefSet2[i][j] = solutions[a][j];

prob->value2[i] = min_dist[a];

/* Update minimum distances */

for(i1=1;i1<=prob->PSize;i1++) {

d=0;

for(j=1;j<=prob->n_var;j++)

d += pow(solutions[i1][j]-solutions[a][j],2);

if(d<min_dist[i1]) min_dist[i1]=d;

} }

/* Update minimum distances in RefSet2 */

for(i=1;i<=prob->b2;i++) {

for(a=1;a<=prob->b2 && a!=i ;a++) {

d=0;

for(j=1;j<=prob->n_var;j++)

d += pow(prob->RefSet2[i][j]-prob->RefSet2[a][j],2);

if(prob->value2[i] > d) prob->value2[i]=d;

} }

index2 = orden_indices(prob->value2,prob->b2,1);

for(i=1;i<=prob->b2;i++) {

prob->order2[i] = index2[i];

prob->iter2[i] = 1;

}

free(index);free(index2);free(current);free(min_dist);

free(value);SSfree_double_matrix(solutions,prob->PSize);

}

void Update_RefSet2(SS *prob) {

double *current,*min_dist,*value,**solutions;

int j,i,i1,a,*index2,cont=0;

double d,dmax;

prob->iter++;

prob->digits++;

current = SSallocate_double_array(prob->n_var);

if(!current) SSabort("Memory allocation problem");

min_dist = SSallocate_double_array(prob->PSize);

if(!min_dist) SSabort("Memory allocation problem");

value = SSallocate_double_array(prob->PSize);

if(!min_dist) SSabort("Memory allocation problem");

solutions = SSallocate_double_matrix(prob->PSize,prob->n_var);

if(!solutions) SSabort("Memory allocation problem");

for(i=1;i<=prob->PSize;i++) {

/* Generate new solution */

for(j=1;j<=prob->n_var;j++)

current[j] = SSGenerate_value(prob,j);

if(is_new(prob,solutions,i-1,current)) {

/* Store solution in matrix "solutions" */

for(j=1;j<=prob->n_var;j++) solutions[i][j] = current[j];

} else

{ i--;

cont++;

}

if(cont>prob->PSize/2) {

prob->digits++;

cont=0;

} }

/* Compute minimum distances */

for(i=1;i<=prob->PSize;i++)

min_dist[i]=distance_to_RefSet1(prob,solutions[i]);

/*Add to RefSet */

for(i=1;i<=prob->b2;i++) {

/* Select the solution with maximum min. dist */

dmax = -1;

for(j=1;j<=prob->PSize;j++) if(min_dist[j]>dmax)

{

dmax=min_dist[j];

a=j;

}

for(j=1;j<=prob->n_var;j++)

prob->RefSet2[i][j] = solutions[a][j];

/* Update minimum distances */

for(i1=1;i1<=prob->PSize;i1++) {

d=0;

for(j=1;j<=prob->n_var;j++)

d += pow(solutions[i1][j]-solutions[a][j],2);

if(d<min_dist[i1]) min_dist[i1]=d;

} }

/* Update minimum distances in RefSet2 */

for(i=1;i<=prob->b2;i++) {

for(a=1;a<=prob->b2 && a!=i ;a++) {

d=0;

for(j=1;j<=prob->n_var;j++)

d += pow(prob->RefSet2[i][j]-prob->RefSet2[a][j],2);

if(min_dist[i] > d) min_dist[i]=d;

}

prob->value2[i] = min_dist[i];

}

index2 = orden_indices(prob->value2,prob->b2,1);

for(i=1;i<=prob->b2;i++) {

prob->order2[i] = index2[i];

prob->iter2[i] = prob->iter;

}

prob->new_elements = 1;

free(index2);

free(current);

free(min_dist);

free(value);

SSfree_double_matrix(solutions,prob->PSize);

}

void Combine_RefSet(SS *prob) {

int i,j,a,s,pull_size,total_size;

double **offsprings,**pull;

prob->new_elements=0;

offsprings = SSallocate_double_matrix(4,prob->n_var);

/* New solutions are temporarily stored in a pull */

pull_size=0;

total_size=(4*prob->b1*prob->b1)/2+(3*prob->b1*prob->b2)+

(2*prob->b2*prob->b2)/2;

pull = SSallocate_double_matrix(total_size,prob->n_var);

/* Combine elements in RefSet1 */

for(i=1;i<prob->b1;i++) for(j=i+1;j<=prob->b1;j++) {

/* Combine solutions not combined in the past */

if(prob->iter1[i]>prob->last_combine ||

prob->iter1[j]>prob->last_combine ) {

SScombine(prob,prob->RefSet1[i],prob->RefSet1[j],offsprings,4);

for(a=1;a<=4;a++) {

pull_size++;

for(s=1;s<=prob->n_var;s++)

pull[pull_size][s]=offsprings[a][s];

} } }

/* Combine RefSet1 with RefSet2*/

for(i=1;i<= prob->b1;i++) for(j=1;j<= prob->b2;j++) {

if(prob->iter1[i]>prob->last_combine ||

prob->iter2[j]>prob->last_combine )

prob->iter2[j]>prob->last_combine )

在文檔中 運用混合演算法於田口動態特性之參數設計最佳化 (頁 51-91)