/* ABSTRACT: */
/* Simulated annealing is a global optimization method that distinguishes */
/* different local optima. Starting from an initial point, the algorithm */
/* takes a step and the function is evaluated. When minimizing a function,*/
/* any downhill step is accepted and the process repeats from this new */
/* point. An uphill step may be accepted (thus, it can escape from local */
/* optima). This uphill decision is made by the Metropolis criteria. As */
/* the optimization process proceeds, the length of the steps decline and */
/* the algorithm closes in on the global optimum. Since the algorithm */
/* makes very few assumptions regarding the function to be optimized, it */
/* is quite robust with respect to non-quadratic surfaces. The degree of */
/* robustness can be adjusted by the user. In fact, simulated annealing */
/* can be used as a local optimizer for difficult functions. */
/* */
/* The author can be contacted at h2zr1001@vm.cis.smu.edu */
//
/* This file is a translation of a fortran code, which is an example of the*/
/* Corana et al. simulated annealing algorithm for multimodal and robust */
/* optimization as implemented and modified by by Goffe et al. */
/* */
/* Use the sample function from Judge with the following suggestions */
/* to get a feel for how SA works. When you've done this, you should be */
/* ready to use it on most any function with a fair amount of expertise. */
/* 1. Run the program as is to make sure it runs okay. Take a look at */
/* the intermediate output and see how it optimizes as temperature */
/* (T) falls. Notice how the optimal point is reached and how */
/* falling T reduces VM. */
/* 2. Look through the documentation to SA so the following makes a */
/* bit of sense. In line with the paper, it shouldn't be that hard */
/* to figure out. The core of the algorithm is described on pp. 4-6 */
/* and on pp. 28. Also see Corana et al. pp. 264-9. */
/* 3. To see the importance of different temperatures, try starting */
/* with a very low one (say T = 10E-5). You'll see (i) it never */
/* escapes from the local optima (in annealing terminology, it */
/* quenches) & (ii) the step length (VM) will be quite small. This */
/* is a key part of the algorithm: as temperature (T) falls, step */
/* length does too. In a minor point here, note how VM is quickly */
/* reset from its initial value. Thus, the input VM is not very */
/* important. This is all the more reason to examine VM once the */
/* algorithm is underway. */
/* 4. To see the effect of different parameters and their effect on */
/* the speed of the algorithm, try RT = .95 & RT = .1. Notice the */
/* vastly different speed for optimization. Also try NT = 20. Note */
/* that this sample function is quite easy to optimize, so it will */
/* tolerate big changes in these parameters. RT and NT are the */
/* parameters one should adjust to modify the runtime of the */
/* algorithm and its robustness. */
/* 5. Try constraining the algorithm with either LB or UB. */
//
/* Synopsis: */
/* This routine implements the continuous simulated annealing global */
/* optimization algorithm described in Corana et al.'s article */
/* "Minimizing Multimodal Functions of Continuous Variables with the */
/* "Simulated Annealing" Algorithm" in the September 1987 (vol. 13, */
/* no. 3, pp. 262-280) issue of the ACM Transactions on Mathematical */
/* Software. */
//
/* A very quick (perhaps too quick) overview of SA: */
/* SA tries to find the global optimum of an N dimensional function. */
/* It moves both up and downhill and as the optimization process */
/* proceeds, it focuses on the most promising area. */
/* To start, it randomly chooses a trial point within the step length */
/* VM (a vector of length N) of the user selected starting point. The */
/* function is evaluated at this trial point and its value is compared */
/* to its value at the initial point. */
/* In a maximization problem, all uphill moves are accepted and the */
/* algorithm continues from that trial point. Downhill moves may be */
/* accepted; the decision is made by the Metropolis criteria. It uses T */
/* (temperature) and the size of the downhill move in a probabilistic */
/* manner. The smaller T and the size of the downhill move are, the more */
/* likely that move will be accepted. If the trial is accepted, the */
/* algorithm moves on from that point. If it is rejected, another point */
/* is chosen instead for a trial evaluation. */
/* Each element of VM periodically adjusted so that half of all */
/* function evaluations in that direction are accepted. */
/* A fall in T is imposed upon the system with the RT variable by */
/* T(i+1) = RT*T(i) where i is the ith iteration. Thus, as T declines, */
/* downhill moves are less likely to be accepted and the percentage of */
/* rejections rise. Given the scheme for the selection for VM, VM falls. */
/* Thus, as T declines, VM falls and SA focuses upon the most promising */
/* area for optimization. */
//
/* The importance of the parameter T: */
/* The parameter T is crucial in using SA successfully. It influences */
/* VM, the step length over which the algorithm searches for optima. For */
/* a small intial T, the step length may be too small; thus not enough */
/* of the function might be evaluated to find the global optima. The user */
/* should carefully examine VM in the intermediate output (set IPRINT = */
/* 1) to make sure that VM is appropriate. The relationship between the */
/* initial temperature and the resulting step length is function */
/* dependent. */
/* To determine the starting temperature that is consistent with */
/* optimizing a function, it is worthwhile to run a trial run first. Set */
/* RT = 1.5 and T = 1.0. With RT > 1.0, the temperature increases and VM */
/* rises as well. Then select the T that produces a large enough VM. */
//
/* For modifications to the algorithm and many details on its use, */
/* (particularly for econometric applications) see Goffe, Ferrier */
/* and Rogers, "Global Optimization of Statistical Functions with */
/* the Simulated Annealing," Journal of Econometrics (forthcoming) */
/* For a pre-publication copy, contact */
/* Bill Goffe */
/* Department of Economics */
/* Southern Methodist University */
/* Dallas, TX 75275 */
/* h2zr1001 @ smuvm1 (Bitnet) */
/* h2zr1001 @ vm.cis.smu.edu (Internet) */
//
/* As far as possible, the parameters here have the same name as in */
/* the description of the algorithm on pp. 266-8 of Corana et al. */
//
/* Input Parameters: */
/* Note: The suggested values generally come from Corana et al. To */
/* drastically reduce runtime, see Goffe et al., pp. 17-8 for */
/* suggestions on choosing the appropriate RT and NT. */
/* n - Number of variables in the function to be optimized. (INT) */
/* x - The starting values for the variables of the function to be */
/* optimized. (DP(N)) */
/* max - Denotes whether the function should be maximized or */
/* minimized. A true value denotes maximization while a false */
/* value denotes minimization. */
/* RT - The temperature reduction factor. The value suggested by */
/* Corana et al. is .85. See Goffe et al. for more advice. (DP) */
/* EPS - Error tolerance for termination. If the final function */
/* values from the last neps temperatures differ from the */
/* corresponding value at the current temperature by less than */
/* EPS and the final function value at the current temperature */
/* differs from the current optimal function value by less than */
/* EPS, execution terminates and IER = 0 is returned. (EP) */
/* NS - Number of cycles. After NS*N function evaluations, each element */
/* of VM is adjusted so that approximately half of all function */
/* evaluations are accepted. The suggested value is 20. (INT) */
/* nt - Number of iterations before temperature reduction. After */
/* NT*NS*N function evaluations, temperature (T) is changed */
/* by the factor RT. Value suggested by Corana et al. is */
/* MAX(100, 5*N). See Goffe et al. for further advice. (INT) */
/* NEPS - Number of final function values used to decide upon termi- */
/* nation. See EPS. Suggested value is 4. (INT) */
/* maxevl - The maximum number of function evaluations. If it is */
/* exceeded, IER = 1. (INT) */
/* lb - The lower bound for the allowable solution variables. (DP(N)) */
/* ub - The upper bound for the allowable solution variables. (DP(N)) */
/* If the algorithm chooses X(I) .LT. LB(I) or X(I) .GT. UB(I), */
/* I = 1, N, a point is from inside is randomly selected. This */
/* This focuses the algorithm on the region inside UB and LB. */
/* Unless the user wishes to concentrate the search to a par- */
/* ticular region, UB and LB should be set to very large positive */
/* and negative values, respectively. Note that the starting */
/* vector X should be inside this region. Also note that LB and */
/* UB are fixed in position, while VM is centered on the last */
/* accepted trial set of variables that optimizes the function. */
/* c - Vector that controls the step length adjustment. The suggested */
/* value for all elements is 2.0. (DP(N)) */
/* t - On input, the initial temperature. See Goffe et al. for advice. */
/* On output, the final temperature. (DP) */
/* vm - The step length vector. On input it should encompass the */
/* region of interest given the starting value X. For point */
/* X(I), the next trial point is selected is from X(I) - VM(I) */
/* to X(I) + VM(I). Since VM is adjusted so that about half */
/* of all points are accepted, the input value is not very */
/* important (i.e. is the value is off, SA adjusts VM to the */
/* correct value). (DP(N)) */
//
/* Output Parameters: */
/* xopt - The variables that optimize the function. (DP(N)) */
/* fopt - The optimal value of the function. (DP) */
//
/* JMB this has been modified to work with the gadget object structure */
/* This means that the function has been replaced by a call to ecosystem */
/* object, and we can use the vector objects that have been defined */
#include "gadget.h" //All the required standard header files are in here
#include "optinfo.h"
#include "mathfunc.h"
#include "doublevector.h"
#include "intvector.h"
#include "errorhandler.h"
#include "ecosystem.h"
#include "global.h"
#include "seq_optimize_template.h"
#ifdef GADGET_OPENMP
#include <omp.h>
#endif
extern Ecosystem* EcoSystem;
#ifndef NO_OPENMP
extern Ecosystem** EcoSystems;
#endif
/*sequential code replaced at seq_optimize_template.h*/
//void OptInfoSimann::OptimiseLikelihood() {
//
// //set initial values
// int nacc = 0; //The number of accepted function evaluations
// int nrej = 0; //The number of rejected function evaluations
// int naccmet = 0; //The number of metropolis accepted function evaluations
//
// double tmp, p, pp, ratio, nsdiv;
// double fopt, funcval, trialf;
// int a, i, j, k, l, offset, quit;
// int rchange, rcheck, rnumber; //Used to randomise the order of the parameters
//
// handle.logMessage(LOGINFO, "\nStarting Simulated Annealing optimisation algorithm\n");
// int nvars = EcoSystem->numOptVariables();
// DoubleVector x(nvars);
// DoubleVector init(nvars);
// DoubleVector trialx(nvars, 0.0);
// DoubleVector bestx(nvars);
// DoubleVector scalex(nvars);
// DoubleVector lowerb(nvars);
// DoubleVector upperb(nvars);
// DoubleVector fstar(tempcheck);
// DoubleVector vm(nvars, vminit);
// IntVector param(nvars, 0);
// IntVector nacp(nvars, 0);
//
// EcoSystem->resetVariables(); //JMB need to reset variables in case they have been scaled
// if (scale)
// EcoSystem->scaleVariables();
// EcoSystem->getOptScaledValues(x);
// EcoSystem->getOptLowerBounds(lowerb);
// EcoSystem->getOptUpperBounds(upperb);
// EcoSystem->getOptInitialValues(init);
//
// for (i = 0; i < nvars; i++) {
// bestx[i] = x[i];
// param[i] = i;
// }
//
// if (scale) {
// for (i = 0; i < nvars; i++) {
// scalex[i] = x[i];
// // Scaling the bounds, because the parameters are scaled
// lowerb[i] = lowerb[i] / init[i];
// upperb[i] = upperb[i] / init[i];
// if (lowerb[i] > upperb[i]) {
// tmp = lowerb[i];
// lowerb[i] = upperb[i];
// upperb[i] = tmp;
// }
// }
// }
//
// //funcval is the function value at x
// funcval = EcoSystem->SimulateAndUpdate(x);
// if (funcval != funcval) { //check for NaN
// handle.logMessage(LOGINFO, "Error starting Simulated Annealing optimisation with f(x) = infinity");
// converge = -1;
// iters = 1;
// return;
// }
//
// //the function is to be minimised so switch the sign of funcval (and trialf)
// funcval = -funcval;
// offset = EcoSystem->getFuncEval(); //number of function evaluations done before loop
// nacc++;
// cs /= lratio; //JMB save processing time
// nsdiv = 1.0 / ns;
// fopt = funcval;
// for (i = 0; i < tempcheck; i++)
// fstar[i] = funcval;
//
// //Start the main loop. Note that it terminates if
// //(i) the algorithm succesfully optimises the function or
// //(ii) there are too many function evaluations
// while (1) {
// for (a = 0; a < nt; a++) {
// //Randomize the order of the parameters once in a while, to avoid
// //the order having an influence on which changes are accepted
// rchange = 0;
// while (rchange < nvars) {
// rnumber = rand_r(&seedP) % nvars;
// rcheck = 1;
// for (i = 0; i < rchange; i++)
// if (param[i] == rnumber)
// rcheck = 0;
// if (rcheck) {
// param[rchange] = rnumber;
// rchange++;
// }
// }
//
// for (j = 0; j < ns; j++) {
// for (l = 0; l < nvars; l++) {
// //Generate trialx, the trial value of x
// newValue(nvars, l, param, trialx, x, lowerb, upperb, vm);
//// for (i = 0; i < nvars; i++) {
//// if (i == param[l]) {
//// trialx[i] = x[i] + ((randomNumber() * 2.0) - 1.0) * vm[i];
////
//// //If trialx is out of bounds, try again until we find a point that is OK
//// if ((trialx[i] < lowerb[i]) || (trialx[i] > upperb[i])) {
//// //JMB - this used to just select a random point between the bounds
//// k = 0;
//// while ((trialx[i] < lowerb[i]) || (trialx[i] > upperb[i])) {
//// trialx[i] = x[i] + ((randomNumber() * 2.0) - 1.0) * vm[i];
//// k++;
//// if (k > 10) //we've had 10 tries to find a point neatly, so give up
//// trialx[i] = lowerb[i] + (upperb[i] - lowerb[i]) * randomNumber();
//// }
//// }
////
//// } else
//// trialx[i] = x[i];
//// }
//
//// cout << "param:" << param[l] << "-" << trialx[param[l]] << endl;
//
// //Evaluate the function with the trial point trialx and return as -trialf
// trialf = EcoSystem->SimulateAndUpdate(trialx);
// trialf = -trialf;
//
// //If too many function evaluations occur, terminate the algorithm
// iters = EcoSystem->getFuncEval() - offset;
// if (iters > simanniter) {
// handle.logMessage(LOGINFO, "\nStopping Simulated Annealing optimisation algorithm\n");
// handle.logMessage(LOGINFO, "The optimisation stopped after", iters, "function evaluations");
// handle.logMessage(LOGINFO, "The temperature was reduced to", t);
// handle.logMessage(LOGINFO, "The optimisation stopped because the maximum number of function evaluations");
// handle.logMessage(LOGINFO, "was reached and NOT because an optimum was found for this run");
// handle.logMessage(LOGINFO, "Number of directly accepted points", nacc);
// handle.logMessage(LOGINFO, "Number of metropolis accepted points", naccmet);
// handle.logMessage(LOGINFO, "Number of rejected points", nrej);
//
// score = EcoSystem->SimulateAndUpdate(bestx);
// handle.logMessage(LOGINFO, "\nSimulated Annealing finished with a likelihood score of", score);
// return;
// }
//// cout << "f:" << trialf << endl;
// //Accept the new point if the new function value better
//// cout << "mustAccept:" << trialf << "|" << funcval<< endl;
// if ((trialf - funcval) > verysmall) {
// for (i = 0; i < nvars; i++)
// x[i] = trialx[i];
// funcval = trialf;
// nacc++;
// nacp[param[l]]++; //JMB - not sure about this ...
//
// } else {
// //Accept according to metropolis condition
// p = expRep((trialf - funcval) / t);
// pp = randomNumber(&seedM);
// if (pp < p) {
// //Accept point
// for (i = 0; i < nvars; i++)
// x[i] = trialx[i];
// funcval = trialf;
// naccmet++;
// nacp[param[l]]++;
// } else {
// //Reject point
// nrej++;
// }
// }
//// cout << "goog VALUE:" << funcval << endl;
// // JMB added check for really silly values
// if (isZero(trialf)) {
// handle.logMessage(LOGINFO, "Error in Simulated Annealing optimisation after", iters, "function evaluations, f(x) = 0");
// converge = -1;
// return;
// }
//
// //If greater than any other point, record as new optimum
// if ((trialf > fopt) && (trialf == trialf)) {
// for (i = 0; i < nvars; i++)
// bestx[i] = trialx[i];
// fopt = trialf;
//
// if (scale) {
// for (i = 0; i < nvars; i++)
// scalex[i] = bestx[i] * init[i];
// EcoSystem->storeVariables(-fopt, scalex);
// } else
// EcoSystem->storeVariables(-fopt, bestx);
//
// handle.logMessage(LOGINFO, "\nNew optimum found after", iters, "function evaluations");
// handle.logMessage(LOGINFO, "The likelihood score is", -fopt, "at the point");
// EcoSystem->writeBestValues();
// }
// }
// }
//
// //Adjust vm so that approximately half of all evaluations are accepted
// for (i = 0; i < nvars; i++) {
// ratio = nsdiv * nacp[i];
// nacp[i] = 0;
// if (ratio > uratio) {
// vm[i] = vm[i] * (1.0 + cs * (ratio - uratio));
// } else if (ratio < lratio) {
// vm[i] = vm[i] / (1.0 + cs * (lratio - ratio));
// }
//
// if (vm[i] < rathersmall)
// vm[i] = rathersmall;
// if (vm[i] > (upperb[i] - lowerb[i]))
// vm[i] = upperb[i] - lowerb[i];
// }
// }
//
// //Check termination criteria
// for (i = tempcheck - 1; i > 0; i--)
// fstar[i] = fstar[i - 1];
// fstar[0] = funcval;
//
// quit = 0;
// if (fabs(fopt - funcval) < simanneps) {
// quit = 1;
// for (i = 0; i < tempcheck - 1; i++)
// if (fabs(fstar[i + 1] - fstar[i]) > simanneps)
// quit = 0;
// }
//
// handle.logMessage(LOGINFO, "Checking convergence criteria after", iters, "function evaluations ...");
//
// //Terminate SA if appropriate
// if (quit) {
// handle.logMessage(LOGINFO, "\nStopping Simulated Annealing optimisation algorithm\n");
// handle.logMessage(LOGINFO, "The optimisation stopped after", iters, "function evaluations");
// handle.logMessage(LOGINFO, "The temperature was reduced to", t);
// handle.logMessage(LOGINFO, "The optimisation stopped because an optimum was found for this run");
// handle.logMessage(LOGINFO, "Number of directly accepted points", nacc);
// handle.logMessage(LOGINFO, "Number of metropolis accepted points", naccmet);
// handle.logMessage(LOGINFO, "Number of rejected points", nrej);
//
// converge = 1;
// score = EcoSystem->SimulateAndUpdate(bestx);
// handle.logMessage(LOGINFO, "\nSimulated Annealing finished with a likelihood score of", score);
// return;
// }
//
// //If termination criteria is not met, prepare for another loop.
// t *= rt;
// if (t < rathersmall)
// t = rathersmall; //JMB make sure temperature doesnt get too small
//
// handle.logMessage(LOGINFO, "Reducing the temperature to", t);
// funcval = fopt;
// for (i = 0; i < nvars; i++)
// x[i] = bestx[i];
// }
//}
#ifdef GADGET_OPENMP
void OptInfoSimann::OptimiseLikelihoodOMP() {
//set initial values
int nacc = 0; //The number of accepted function evaluations
int nrej = 0; //The number of rejected function evaluations
int naccmet = 0; //The number of metropolis accepted function evaluations
double tmp, p, pp, ratio, nsdiv;
double fopt, funcval, trialf;
int a, i, j, k, l, offset, quit;
int rchange, rcheck, rnumber; //Used to randomise the order of the parameters
struct Storage {
DoubleVector trialx;
double newLikelihood;
};
handle.logMessage(LOGINFO, "\nStarting Simulated Annealing optimisation algorithm\n");
int nvars = EcoSystem->numOptVariables();
DoubleVector x(nvars);
DoubleVector init(nvars);
DoubleVector trialx(nvars, 0.0);
DoubleVector bestx(nvars);
DoubleVector scalex(nvars);
DoubleVector lowerb(nvars);
DoubleVector upperb(nvars);
DoubleVector fstar(tempcheck);
DoubleVector vm(nvars, vminit);
IntVector param(nvars, 0);
IntVector nacp(nvars, 0);
EcoSystem->resetVariables(); //JMB need to reset variables in case they have been scaled
if (scale)
EcoSystem->scaleVariables();
EcoSystem->getOptScaledValues(x);
EcoSystem->getOptLowerBounds(lowerb);
EcoSystem->getOptUpperBounds(upperb);
EcoSystem->getOptInitialValues(init);
for (i = 0; i < nvars; ++i) {
bestx[i] = x[i];
param[i] = i;
}
if (scale) {
for (i = 0; i < nvars; ++i) {
scalex[i] = x[i];
// Scaling the bounds, because the parameters are scaled
lowerb[i] = lowerb[i] / init[i];
upperb[i] = upperb[i] / init[i];
if (lowerb[i] > upperb[i]) {
tmp = lowerb[i];
lowerb[i] = upperb[i];
upperb[i] = tmp;
}
}
}
//funcval is the function value at x
funcval = EcoSystem->SimulateAndUpdate(x);
if (funcval != funcval) { //check for NaN
handle.logMessage(LOGINFO, "Error starting Simulated Annealing optimisation with f(x) = infinity");
converge = -1;
iters = 1;
return;
}
//the function is to be minimised so switch the sign of funcval (and trialf)
funcval = -funcval;
offset = EcoSystem->getFuncEval(); //number of function evaluations done before loop
nacc++;
cs /= lratio; //JMB save processing time
nsdiv = 1.0 / ns;
fopt = funcval;
for (i = 0; i < tempcheck; ++i)
fstar[i] = funcval;
int numThr = omp_get_max_threads ( );
int bestId=0;
int ini=0;
Storage* storage = new Storage[numThr];
for (i=0; i<numThr; ++i)
storage[i].trialx = trialx;
//Start the main loop. Note that it terminates if
//(i) the algorithm succesfully optimises the function or
//(ii) there are too many function evaluations
int aux;
DoubleVector vns(nvars, 0);
int ns_ = ceil(numThr/2.);
double res;
aux=0;
while (1) {
for (a = 0; a < nt; ++a) {
//Randomize the order of the parameters once in a while, to avoid
//the order having an influence on which changes are accepted
rchange = 0;
while (rchange < nvars) {
rnumber = rand_r(&seedP) % nvars;
rcheck = 1;
for (i = 0; i < rchange; ++i)
if (param[i] == rnumber)
rcheck = 0;
if (rcheck) {
param[rchange] = rnumber;
rchange++;
}
}
for (j = 0; j < (ns*ns_); ++j) {
for (l = ini; l < nvars; l+=numThr) {
for (i=0; i<numThr;++i)
{
if ((l+i) < nvars)
newValue(nvars, l+i, param, storage[i].trialx, x, lowerb, upperb, vm);
else {
newValue(nvars, ini, param, storage[i].trialx, x, lowerb, upperb, vm);
ini++;
if (ini >= nvars)
ini=0;
}
}
# pragma omp parallel private(res)
{
//Evaluate the function with the trial point trialx and return as -trialf
int id = omp_get_thread_num ();
res = EcoSystems[id]->SimulateAndUpdate(storage[id].trialx);
storage[id].newLikelihood = -res;
}
//best value from omp
trialf = storage[0].newLikelihood;
bestId=0;
for (i=0;i<numThr;++i)
{
if (storage[i].newLikelihood > trialf)
{
trialf=storage[i].newLikelihood;
bestId=i;
}
k = param[(l+i)%nvars];
if ((storage[i].newLikelihood - funcval) > verysmall)
{
nacp[k]++;
aux++;
vns[k]++;
}
else {
//Accept according to metropolis condition
p = expRep((storage[i].newLikelihood - funcval) / t);
pp = randomNumber(&seedM);
if (pp < p)
aux++;
else {
vns[k]++;
nrej++;
}
}
if (vns[k] >= ns) {
ratio = nsdiv * nacp[k];
nacp[k] = 0;
if (ratio > uratio) {
vm[k] = vm[k] * (1.0 + cs * (ratio - uratio));
} else if (ratio < lratio) {
vm[k] = vm[k] / (1.0 + cs * (lratio - ratio));
}
if (vm[k] < rathersmall){
vm[k] = rathersmall;
}
if (vm[k] > (upperb[k] - lowerb[k]))
{
vm[k] = upperb[k] - lowerb[k];
}
vns[k]=0;
}
}
aux--;
iters = (EcoSystems[bestId]->getFuncEval() * numThr) -aux;
if (iters > simanniter) {
handle.logMessage(LOGINFO, "\nStopping Simulated Annealing optimisation algorithm\n");
handle.logMessage(LOGINFO, "The optimisation stopped after", iters, "function evaluations");
handle.logMessage(LOGINFO, "The temperature was reduced to", t);
handle.logMessage(LOGINFO, "The optimisation stopped because the maximum number of function evaluations");
handle.logMessage(LOGINFO, "was reached and NOT because an optimum was found for this run");
handle.logMessage(LOGINFO, "Number of directly accepted points", nacc);
handle.logMessage(LOGINFO, "Number of metropolis accepted points", naccmet);
handle.logMessage(LOGINFO, "Number of rejected points", nrej);
score = EcoSystem->SimulateAndUpdate(bestx);
handle.logMessage(LOGINFO, "\nSimulated Annealing finished with a likelihood score of", score);
delete[] storage;
return;
}
//Accept the new point if the new function value better
if ((trialf - funcval) > verysmall) {
for (i = 0; i < nvars; ++i)
x[i] = storage[bestId].trialx[i];
funcval = trialf;
nacc++;
} else {
//Accept according to metropolis condition
p = expRep((trialf - funcval) / t);
pp = randomNumber(&seedP);
if (pp < p) {
//Accept point
for (i = 0; i < nvars; ++i)
x[i] = storage[bestId].trialx[i];
funcval = trialf;
naccmet++;
nacp[param[(l+bestId)%nvars]]++;
} else {
//Reject point
nrej++;
}
}
// JMB added check for really silly values
if (isZero(trialf)) {
handle.logMessage(LOGINFO, "Error in Simulated Annealing optimisation after", iters, "function evaluations, f(x) = 0");
converge = -1;
delete[] storage;
return;
}
//If greater than any other point, record as new optimum
if ((trialf > fopt) && (trialf == trialf)) {
for (i = 0; i < nvars; ++i)
bestx[i] = storage[bestId].trialx[i];
fopt = trialf;
if (scale) {
for (i = 0; i < nvars; ++i)
scalex[i] = bestx[i] * init[i];
EcoSystem->storeVariables(-fopt, scalex);
} else
EcoSystem->storeVariables(-fopt, bestx);
handle.logMessage(LOGINFO, "\nNew optimum found after", iters, "function evaluations");
handle.logMessage(LOGINFO, "The likelihood score is", -fopt, "at the point");
EcoSystem->writeBestValues();
}
}
}
}
//Check termination criteria
for (i = tempcheck - 1; i > 0; i--)
fstar[i] = fstar[i - 1];
fstar[0] = funcval;
quit = 0;
if (fabs(fopt - funcval) < simanneps) {
quit = 1;
for (i = 0; i < tempcheck - 1; ++i)
if (fabs(fstar[i + 1] - fstar[i]) > simanneps)
quit = 0;
}
handle.logMessage(LOGINFO, "Checking convergence criteria after", iters, "function evaluations ...");
//Terminate SA if appropriate
if (quit) {
handle.logMessage(LOGINFO, "\nStopping Simulated Annealing optimisation algorithm\n");
handle.logMessage(LOGINFO, "The optimisation stopped after", iters, "function evaluations");
handle.logMessage(LOGINFO, "The temperature was reduced to", t);
handle.logMessage(LOGINFO, "The optimisation stopped because an optimum was found for this run");
handle.logMessage(LOGINFO, "Number of directly accepted points", nacc);
handle.logMessage(LOGINFO, "Number of metropolis accepted points", naccmet);
handle.logMessage(LOGINFO, "Number of rejected points", nrej);
converge = 1;
score = EcoSystem->SimulateAndUpdate(bestx);
handle.logMessage(LOGINFO, "\nSimulated Annealing finished with a likelihood score of", score);
delete[] storage;
return;
}
//If termination criteria is not met, prepare for another loop.
t *= rt;
if (t < rathersmall)
t = rathersmall; //JMB make sure temperature doesnt get too small
handle.logMessage(LOGINFO, "Reducing the temperature to", t);
funcval = fopt;
for (i = 0; i < nvars; ++i)
x[i] = bestx[i];
}
}
#endif
void OptInfoSimann::newValue(int nvars, int l, IntVector& param, DoubleVector& trialx,
DoubleVector& x, DoubleVector& lowerb, DoubleVector& upperb, DoubleVector& vm)
{
int i, k;
// double old = trialx[param[l]];
// cout << "[" << endl;
for (i = 0; i < nvars; ++i) {
if (i == param[l]) {
trialx[i] = x[i] + ((randomNumber(&seed) * 2.0) - 1.0) * vm[i];
//If trialx is out of bounds, try again until we find a point that is OK
if ((trialx[i] < lowerb[i]) || (trialx[i] > upperb[i])) {
//JMB - this used to just select a random point between the bounds
k = 0;
while ((trialx[i] < lowerb[i]) || (trialx[i] > upperb[i])) {
trialx[i] = x[i] + ((randomNumber(&seed) * 2.0) - 1.0) * vm[i];
k++;
if (k > 10) //we've had 10 tries to find a point neatly, so give up
trialx[i] = lowerb[i] + (upperb[i] - lowerb[i]) * randomNumber(&seed);
}
}
} else
trialx[i] = x[i];
// cout <<" " << trialx[i];
}
// cout << endl<< "old[" <<param[l] << "]:" << old <<"-" << trialx[param[l]]<< " - " << vm[param[l]]<<endl;
}
//Generate trialx, the trial value of x
void newValue(int nvars, int l, IntVector& param, DoubleVector& trialx,
DoubleVector& x, DoubleVector& lowerb, DoubleVector& upperb, DoubleVector& vm, unsigned* seed)
{
int i, k;
for (i = 0; i < nvars; ++i) {
if (i == param[l]) {
trialx[i] = x[i] + ((randomNumber(&*seed) * 2.0) - 1.0) * vm[i];
//If trialx is out of bounds, try again until we find a point that is OK
if ((trialx[i] < lowerb[i]) || (trialx[i] > upperb[i])) {
//JMB - this used to just select a random point between the bounds
k = 0;
while ((trialx[i] < lowerb[i]) || (trialx[i] > upperb[i])) {
trialx[i] = x[i] + ((randomNumber(&*seed) * 2.0) - 1.0) * vm[i];
k++;
if (k > 10) //we've had 10 tries to find a point neatly, so give up
trialx[i] = lowerb[i] + (upperb[i] - lowerb[i]) * randomNumber(&*seed);
}
}
} else
trialx[i] = x[i];
}
}
void buildNewParams_f(Siman& seed, DoubleVector& params) {
newValue(seed.getNvars(), seed.getL(), seed.getParam(), params, seed.getX(),
seed.getLowerb(), seed.getUpperb(), seed.getVm(), seed.getSeed());
}
/// Represents the function that computes how good the parameters are
double evaluate_f(const DoubleVector& params) {
double trialf;
#ifndef NO_OPENMP
int id = omp_get_thread_num ();
trialf = EcoSystems[id]->SimulateAndUpdate(params);
#else
trialf = EcoSystem->SimulateAndUpdate(params);
#endif
return -trialf;
}
struct ControlClass {
void adjustVm(Siman& seed) {
//Adjust vm so that approximately half of all evaluations are accepted
int i;
double ratio, nsdiv = seed.getNsdiv();
DoubleVector vm = seed.getVm();
DoubleVector upperb = seed.getUpperb();
DoubleVector lowerb = seed.getLowerb();
double uratio = seed.getUratio();
double lratio = seed.getLratio();
for (i = 0; i < seed.getNvars(); i++) {
ratio = nsdiv * seed.getNacp(i);
seed.setNacp(i,0);
if (ratio > uratio) {
(vm)[i] = (vm)[i] * (1.0 + seed.getCs() * (ratio - seed.getUratio()));
} else if (ratio < lratio) {
(vm)[i] = (vm)[i] / (1.0 + seed.getCs() * (seed.getLratio() - ratio));
}
if ((vm)[i] < rathersmall)
(vm)[i] = rathersmall;
if ((vm)[i] > (upperb[i] - lowerb[i]))
(vm)[i] = upperb[i] - lowerb[i];
}
seed.setVm(vm);
}
void temperature(Siman& seed, DoubleVector& x){
int i;
double t = seed.getT();
t *= seed.getRt();
if (t < rathersmall)
t = rathersmall; //JMB make sure temperature doesnt get too small
handle.logMessage(LOGINFO, "Reducing the temperature to", t);
seed.setT(t);
DoubleVector* bestx = seed.getBestx();
for (i = 0; i < seed.getNvars(); i++)
x[i] = (*bestx)[i];
}
void optimum(double trialf, double &fopt, int iters, DoubleVector trialx,
DoubleVector init, Siman siman){
//If greater than any other point, record as new optimum
int i, nvars = siman.getNvars();
DoubleVector scalex(nvars);
DoubleVector* bestx = siman.getBestx();
if ((trialf > fopt) && (trialf == trialf)) {
for (i = 0; i < nvars; i++)
(*bestx)[i] = trialx[i];
fopt = trialf;
if (siman.getScale()) {
for (i = 0; i < nvars; i++)
scalex[i] = (*bestx)[i] * init[i];
EcoSystem->storeVariables(-fopt, scalex);
} else
EcoSystem->storeVariables(-fopt, (*bestx));
handle.logMessage(LOGINFO, "\nNew optimum found after", iters, "function evaluations");
handle.logMessage(LOGINFO, "The likelihood score is", -fopt, "at the point");
EcoSystem->writeBestValues();
}
}
/**
@brief Decides wheter the current item evaluated must be chosen as new optimum
@param funcval value for old optimum
@param trialf value for current item evaluated
*/
bool mustAccept(double funcval, double trialf, Siman &siman, int iters) {
//Accept the new point if the new function value better
bool ret = true;
int i;
int aux = siman.getParam()[siman.getL()];
if ((trialf - funcval) > verysmall) {
siman.incrementNacp(aux);
siman.incrementNacc();
//JMB - not sure about this ...
} else {
double p, pp;
//Accept according to metropolis condition
p = expRep((trialf - funcval) / siman.getT());
pp = randomNumber(siman.getSeedM());
if (pp < p) {
siman.incrementNacp(aux);
siman.incrementNaccmet();
// //Accept point
} else {
//Reject point
ret = false;
siman.incrementNrej();
}
}
// JMB added check for really silly values
if (isZero(trialf)) {
handle.logMessage(LOGINFO, "Error in Simulated Annealing optimisation after",
iters, "function evaluations, f(x) = 0");
siman.setConverge(-1);
return false;
}
siman.incrementL();
if (siman.getL() == 0)
siman.incrementNS();
if (siman.getNS() >= siman.getNs()){
siman.setNS(0);
siman.incrementNT();
adjustVm(siman);
siman.randomizeParams();
}
return ret;
}
/**
@brief Decides whether the search must stop.
It does not take into account the number of iterations, which is already considered by the template
@param prev old optimum
@param funcval new/current optimum
*/
bool mustTerminate(double prev, double& funcval, Siman &siman, int iters) {
bool quit = false;
if (siman.getNT() >= siman.getNt())
{
int i;
DoubleVector fstar = siman.getFstar();
siman.setNT(0);
for (i = siman.getTempcheck() - 1; i > 0; i--)
fstar[i] = fstar[i - 1];
fstar[0] = funcval;
if (fabs(prev - funcval) < siman.getSimanneps()) {
quit = true;
for (i = 0; i < siman.getTempcheck() - 1; i++)
if (fabs(fstar[i + 1] - fstar[i]) > siman.getSimanneps())
quit = false;
}
handle.logMessage(LOGINFO, "Checking convergence criteria after", iters,
"function evaluations ...");
temperature(siman, siman.getX());
funcval = prev;
}
return quit;
}
void printResult(bool quit, Siman siman, int iters)
{
double * score = siman.getScore();
DoubleVector * bestX = siman.getBestx();
handle.logMessage(LOGINFO, "\nStopping Simulated Annealing optimisation algorithm\n");
handle.logMessage(LOGINFO, "The optimisation stopped after", iters, "function evaluations");
handle.logMessage(LOGINFO, "The temperature was reduced to", siman.getT());
if (quit) {
int* converge = siman.getConverge();
handle.logMessage(LOGINFO, "The optimisation stopped because an optimum was found for this run");
*converge = 1;
}
else {
handle.logMessage(LOGINFO, "The optimisation stopped because the maximum number of function evaluations");
handle.logMessage(LOGINFO, "was reached and NOT because an optimum was found for this run");
}
handle.logMessage(LOGINFO, "Number of directly accepted points", siman.getNacc());
handle.logMessage(LOGINFO, "Number of metropolis accepted points", siman.getNaccmet());
handle.logMessage(LOGINFO, "Number of rejected points", siman.getNrej());
*score = EcoSystem->SimulateAndUpdate(*bestX);
handle.logMessage(LOGINFO, "\nSimulated Annealing finished with a likelihood score of", *score);
}
};
// Required
std::ostream &operator<<(std::ostream &os, const DoubleVector &p)
{
os << "";
return os;
}
void OptInfoSimann::OptimiseLikelihood() {
//set initial values
double tmp, p, pp;
double funcval, trialf;
int a, i, j, k, l, quit;
int rchange, rcheck, rnumber; //Used to randomise the order of the parameters
handle.logMessage(LOGINFO,
"\nStarting Simulated Annealing optimisation algorithm\n");
int nvars = EcoSystem->numOptVariables();
DoubleVector x(nvars);
DoubleVector init(nvars);
DoubleVector trialx(nvars, 0.0);
DoubleVector bestx(nvars);
DoubleVector scalex(nvars);
DoubleVector lowerb(nvars);
DoubleVector upperb(nvars);
DoubleVector fstar(tempcheck);
DoubleVector vm(nvars, vminit);
IntVector param(nvars, 0);
EcoSystem->resetVariables(); //JMB need to reset variables in case they have been scaled
if (scale) {
EcoSystem->scaleVariables();
#ifndef NO_OPENMP
int numThr = omp_get_max_threads ( );
for(i = 0; i < numThr; i++)
EcoSystems[i]->scaleVariables();
#endif
}
EcoSystem->getOptScaledValues(x);
EcoSystem->getOptLowerBounds(lowerb);
EcoSystem->getOptUpperBounds(upperb);
EcoSystem->getOptInitialValues(init);
for (i = 0; i < nvars; i++) {
bestx[i] = x[i];
param[i] = i;
}
if (scale) {
for (i = 0; i < nvars; i++) {
scalex[i] = x[i];
// Scaling the bounds, because the parameters are scaled
lowerb[i] = lowerb[i] / init[i];
upperb[i] = upperb[i] / init[i];
if (lowerb[i] > upperb[i]) {
tmp = lowerb[i];
lowerb[i] = upperb[i];
upperb[i] = tmp;
}
}
}
//funcval is the function value at x
funcval = EcoSystem->SimulateAndUpdate(x);
if (funcval != funcval) { //check for NaN
handle.logMessage(LOGINFO,
"Error starting Simulated Annealing optimisation with f(x) = infinity");
converge = -1;
iters = 1;
return;
}
//the function is to be minimised so switch the sign of funcval (and trialf)
funcval = -funcval;
cs /= lratio; //JMB save processing time
for (i = 0; i < tempcheck; i++)
fstar[i] = funcval;
Siman s(seed, seedM, seedP, nvars, nt, ns, param, &x, &lowerb, &upperb, vm, t, rt, (1.0 / ns),
tempcheck, simanneps, fstar, lratio, uratio, cs, &bestx, scale, &converge, &score);
ReproducibleSearch<Siman, DoubleVector, ControlClass, evaluate_f, buildNewParams_f>
pa(s, x, simanniter);
#ifndef NO_OPENMP
// OpenMP parallelization
int numThr = omp_get_max_threads ( );
pa.paral_opt_omp(funcval,numThr,numThr);
#else
// sequential code
pa.seq_opt(funcval);
#endif
}
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