/* 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 SPECULATIVE #include #endif extern Ecosystem* EcoSystem; #ifdef _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]; //// } // // //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; // } // //Accept the new point if the new function value better // 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++; // } // } // // 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 SPECULATIVE 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, quit; int rchange, rcheck, rnumber; //Used to randomise the order of the parameters // store the info of the different threads 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(); int numThr = omp_get_max_threads ( ); for(i = 0; i < numThr; i++) // scale the variables for the ecosystem of every thread EcoSystems[i]->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; 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= 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 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 // calcule a new point void OptInfoSimann::newValue(int nvars, int l, IntVector& param, DoubleVector& trialx, DoubleVector& x, DoubleVector& lowerb, DoubleVector& upperb, DoubleVector& vm) { 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]; } } /*################################################################################ * code use in the template (seq_optimize_template.h) ################################################################################*/ //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; #ifdef _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(); #ifdef _OPENMP int numThr = omp_get_max_threads ( ); for(i = 0; i < numThr; i++) // scale the variables for the ecosystem of every thread 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 pa(s, x, simanniter); #ifdef _OPENMP // OpenMP parallelization int numThr = omp_get_max_threads ( ); pa.paral_opt_omp(funcval,numThr,numThr); #else // sequential code pa.seq_opt(funcval); #endif }