Penalty function method for external points-constraints Optimization

Penalty function method for external points-constraints Optimization

The vertices penalty function (r increase, SUMT. Java) is used to solve the constraints optimization problem. The solution steps are as follows:

Step 1 input the target function and the constraint equation, construct the punishment Function Method of the outer point to solve the equation, and initialize the solution.

Step 2 perform a non-constrained optimization (Powell BWE) on the equation to obtain a new solution.

Step 3: the error between the new solution and the original solution is obtained. If the error meets the accuracy requirement, the solution is output. Otherwise, the factor R is added and Step 2 is executed.

BWE. Java (BWE. Java) is a n-dimensional unrestricted solution. One-dimensional solutions need to be called. One-dimensional solutions use the golden division method (GSM. Java ).

In the code that implements the algorithm, I removed the input processing and manually determined the input to reduce the code length.

I will package the files into my downloads. You are welcome to discuss them together.

(1) Penalty Function SUMT. Java:

Package ODM. method; import Java. util. arrays;/** unrestricted optimization method: penalty function method-External vertex Method */public class SUMT {private int n = 6; // dimension, number of variables private final double EPS = 1e-5; // precision private final double C = 5; // increment coefficient private double r = 0.1; // Penalty Factor, tends to infinite public SUMT () {finit (); algorithmprocess (); answeroutput () ;}// result private double [] Xs; private double ans; private void finit () {xs = new double [N]; arrays. fill (XS, 0); ans =-1; // Xs [0] = Xs [1] = Xs [2] = Xs [4] = 1; xs [3] = 3; Xs [5] = 5;} // main algorithm flow private void algorithmprocess () {int icnt = 0; // number of iterations double [] x = new double [N]; // convert it to a solution for the unrestricted optimization problem while (true) {icnt ++; BWE temp = new BWE (n, R, XS); // use the powell method to find the optimal function solution x = temp. retans (); If (retok (x) <= EPS) {// meets the accuracy requirement for (INT I = 0; I <n; I ++) xs [I] = x [I]; ans = temp. mans (); break;} r = C * r; For (INT I = 0; I <n; I ++) XS [I] = x [I];} system. out. println ("iterations:" + icnt);} // convergence condition (only one, not perfect) Private double retok (double [] X) {double sum = 0; for (INT I = 0; I <n; I ++) {sum + = math. pow (X [I]-xs [I], 2);} return math. SQRT (SUM) ;}// the result output private void answeroutput () {for (INT I = 0; I <n; I ++) system. out. printf ("%. 6f \ t ", xs [I]); system. out. printf ("%. 6f \ n ", ANS);} public static void main (string [] ARGs) {// todo auto-generated method stubnew SUMT ();}}

(2) Bao wilfa BWE. Java:

Package ODM. method; import Java. util. arrays; public class BWE {private double r; // initialization variable private double [] x0; // initial solution set private double [] [] E; // initial direction private int N; final private double EPS = 1e-5; private func F; // initialization: Initial Point, initial vector (N, N * n matrix ), dimension private void Init (int n) {This. x0 = new double [N]; If (r =-1) arrays. fill (this. x0, 0); else {} This. E = new double [N] [N]; for (INT I = 0; I <n; I ++) {for (Int J = 0; j <n; j + +) {If (I! = J) E [I] [J] = 0; else E [I] [J] = 1 ;}} this. n = N; If (R! =-1) F = new func (r); elsef = new func ();} // search point, direction vector private double [] [] X; private double [] [] D; // reschedule the queue, queue operation private void queuedir (double [] X) {// Delete the first direction for (INT I = 0; I <N-1; I ++) {for (Int J = 0; j <n; j ++) {d [I] [J] = d [I + 1] [J] ;}// Insert a new direction to the end of the Team for (INT I = 0; I <N; I ++) d [N-1] [I] = x [I];} private void process () {x = new double [n + 1] [N]; D = new double [N] [N]; for (Int J = 0; j <n; j ++) x [0] [J] = x0 [J]; for (INT I = 0; I <n; I ++) {for (Int J = 0; j <n; j ++) {d [I] [J] = E [I] [J] ;}} int K = 0; // number of iterations while (k <n) {for (INT I = 1; I <= N; I ++) {GSM T = new GSM (f, x [I-1], d [I-1]); X [I] = T. getos () ;}double [] x = new double [N]; for (INT I = 0; I <n; I ++) X [I] = x [N] [I]-X [0] [I]; queuedir (x); GSM T = new GSM (f, x [N], x); X [0] = T. getos (); k ++ ;}// print private void answeroutput () {for (INT I = 0; I <n; I ++) {system. out. printf ("X [% d] = %. 6f \ n ", I + 1, x [0] [I]); // system. out. print (X [0] [I] + "");} system. out. printf ("minimum value: %. 6f \ n ", F. fgetval (X [0]); // system. out. println (":" + F. fgetval (X [0]);} public BWE (int n) {This. R =-1; Init (n); process (); answeroutput ();} public BWE (int n, Double R, double [] X) {This. R = r; Init (n); For (INT I = 0; I <n; I ++) x0 [I] = x [I]; process ();} // return result, solution vector and optimal value public double [] retans () {return X [0];} public double Mans () {return F. fgetval (X [0], 0);}/* Public static void main (string [] ARGs) {// todo auto-generated method stubnew BWE (2 );} */}

(3) Golden division GSM. Java:

Package ODM. method;/** golden Division Method */public class GSM {private int N; // dimension private final double Landa = (math. SQRT (5)-1)/2; // 0.618 private double [] x1; private double [] X2; private double [] OS; private final double EPS = 1e-5; // encryption private extm em; // used to obtain the external push result // The optimal value output public double [] getos () {return OS;} // function, initial point, direction vector public GSM (func sample, double [] X, double [] e) {// For (INT I = 0; I <E. length; I ++) System. Out. print (E [I] + ""); system. out. println (); initial (sample, X, e); process (sample); answerprint (sample) ;}// print the private void answerprint (func sample) Result) {OS = new double [N]; for (INT I = 0; I <n; I ++) OS [I] = 0.5*(x1 [I] + x2 [I]); // system. out. println ("OS =" + OS [0] + "" + OS [1]); // system. out. println ("Ans =" + sample. fgetval (OS);} // vector fan value private double fanzhi (double [] B, double [] A) {double sum = 0; for (I NT I = 0; I <n; I ++) {If (B [I]-A [I]! = 0 & B [I] = 0) return EPS * (1e10); If (B [I] = 0) continue; sum + = math. pow (B [I]-A [I])/B [I], 2);} return math. pow (sum, 0.5);} // algorithm main flow private void process (func sample) {double [] xx1 = new double [N]; subarrayscopy (xx1 ); double YY1 = sample. fgetval (xx1); double [] xx2 = new double [N]; addarrayscopy (xx2); double yy2 = sample. fgetval (xx2); // iteration process while (true) {If (YY1> = yy2) {arrayscopy (xx1, X1); arrayscopy (xx2, xx1); YY1 = yy2; addarrayscopy (xx2); yy2 = sample. fgetval (xx2);} else {arrayscopy (xx2, X2); arrayscopy (xx1, xx2); yy2 = YY1; subarrayscopy (xx1); YY1 = sample. fgetval (xx1);} // system. out. println (fanzhi (X2, X1) + "/" + math. ABS (yy2-YY1)/yy2); If (fanzhi (X2, X1) <EPS & math. ABS (yy2-YY1) <EPS) Break ;}// obtain the external push Method Result: The left and right boundary Private void initial (func sample, double [] X, double [] E) {n = x. length; em = new extm (sample, X, e); X1 = em. getx1 (); x2 = em. getx3 () ;}// Vector Value assignment private void arrayscopy (double [] S, double [] e) {for (INT I = 0; I <n; I ++) E [I] = s [I];} // + landdeskvate void addarrayscopy (double [] ARR) {for (INT I = 0; I <n; I ++) arr [I] = x1 [I] + Landa * (X2 [I]-X1 [I]);} //-land1_vate void subarrayscopy (double [] ARR) {for (INT I = 0; I <n; I ++) arr [I] = x2 [I]-Landa * (X2 [I]-X1 [I]);}/* Public static void main (string [] ARGs) {// todo auto-generated method stubdouble [] C = {0, 0}; double [] d = {1, 0}; new GSM (New func (), c, d );}*/}

The above algorithm file contains the function equation. When golden splitting, one-dimensional search is used to determine the "High and Low" interval.

Function Equation func. Java, the extension method extm. java.

Func. Java:

Package ODM. method; public class func {private int N; // n-dimension private double [] Left; // function left boundary Private double [] Right; // function right boundary Private Double R; public func () {r =-1;} public func (double r) {This. R = r;} // defines the function and function value and returns public double fgetval (double [] X) {If (R! =-1) return fgetval (x, R); // 10*(X1 + x2-5) ^ 2 + (x1-x2) ^ 2 return 10 * Math. pow (X [0] + X [1]-5, 2) + math. pow (X [0]-X [1], 2); //} private double max (double A, double B) {return A> B? A: B;} public double fgetval (double [] X, double r) {double ret = 0; // function F1 // ret = math. pow (X [0]-5, 2) + 4 * Math. pow (X [1]-6, 2) // + R * (// + math. pow (max (64-x [0] * X [0]-X [1] * X [1], 0), 2) // + math. pow (max (X [1]-X [0]-10, 0), 0) // + math. pow (max (X [0]-10, 0), 2 )//); // function F2 // ret = x [0] * X [0] + X [1] * X [1] + R * (3o[ 0]> 0? [0]: 0) * ([0]> 0? 1x2 [0]: 0); // function f3ret = math. pow (X [0]-X [3], 2) + math. pow (X [1]-X [4], 2) + math. pow (X [2]-X [5], 2) + R * (+ math. pow (max (X [0] * X [0] + X [1] * X [1] + X [2] * X [2]-5, 0 ), 2) + math. pow (max (math. pow (X [3]-3, 2) + X [4] * X [4]-1, 0), 2) + math. pow (max (X [5]-8, 0), 2) + math. pow (max (4-X [5], 0), 2); return ret ;}}

Extm. Java:

Package ODM. method;/** determine the "high-low-high" interval using the external push Method */public class extm {private int N; // function dimension private double [] x1; private double [] X2; private double [] X3; private double Y1; private double Y2; private double Y3; private double H; // step size private double [] D; // vector public double [] getx1 () {return x1;} public double [] getx2 () {return X2;} public double [] getx3 () {return X3 ;} public double geth () {return h;} // function, initial point, direction public extm (func sample, double [] X, double [] e) {initial (sample, x, e); process (sample); answerprint () ;}// initialization stage private void initial (func sample, double [] X, double [] E) {n = x. length; X1 = new double [N]; x2 = new double [N]; X3 = new double [N]; H = 0.01; D = new double [N]; arrayscopy (E, 0, d); // For (INT I = 0; I <D. length; I ++) system. out. print (d [I]); system. out. println (); arrayscopy (x, 0, X1); Y1 = sample. fgetval (X1); arrayscopy (x, H, X2); y2 = sample. fgetval (X2) ;}// loop part private void process (func sample) {If (Y2> Y1) {H =-H; arrayscopy (x1, 0, X3 ); y3 = Y1;} else {arrayscopy (X2, H, X3); Y3 = sample. fgetval (X3);} while (Y3 <Y2) {H = 2 * h; // system. out. println ("H =" + H); arrayscopy (X2, 0, X1); Y1 = Y2; arrayscopy (X3, 0, X2); y2 = Y3; arrayscopy (X2, h, X3); Y3 = sample. fgetval (X3); // system. out. println ("X1 =" + X1 [0] + "" + X1 [1] + "Y1 =" + Y1); // system. out. println ("X2 =" + x2 [0] + "" + x2 [1] + "y2 =" + y2); // system. out. println ("X3 =" + X3 [0] + "" + X3 [1] + "Y3 =" + Y3) ;}// print the algorithm result private void answerprint () {// system. out. println ("X1 =" + X1 [0] + "" + X1 [1] + "Y1 =" + Y1); // system. out. println ("X2 =" + x2 [0] + "" + x2 [1] + "y2 =" + y2); // system. out. println ("X3 =" + X3 [0] + "" + X3 [1] + "Y3 =" + Y3 );} // vector transfer private void arrayscopy (double [] S, double C, double [] e) {for (INT I = 0; I <S. length; I ++) E [I] = d [I] * C + s [I];}/* Public static void main (string [] ARGs) {// todo auto-generated method stub // new extm ();}*/}