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agomez |
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/* Nonlinear Optimization using the algorithm of Hooke and Jeeves */
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/* 12 February 1994 author: Mark G. Johnson */
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/* Find a point X where the nonlinear function f(X) has a local */
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/* minimum. X is an n-vector and f(X) is a scalar. In mathe- */
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/* matical notation f: R^n -> R^1. The objective function f() */
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/* is not required to be continuous. Nor does f() need to be */
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/* differentiable. The program does not use or require */
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/* derivatives of f(). */
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/* The software user supplies three things: a subroutine that */
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/* computes f(X), an initial "starting guess" of the minimum point */
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/* X, and values for the algorithm convergence parameters. Then */
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/* the program searches for a local minimum, beginning from the */
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/* starting guess, using the Direct Search algorithm of Hooke and */
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/* Jeeves. */
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/* This C program is adapted from the Algol pseudocode found in */
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/* "Algorithm 178: Direct Search" by Arthur F. Kaupe Jr., Commun- */
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/* ications of the ACM, Vol 6. p.313 (June 1963). It includes the */
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/* improvements suggested by Bell and Pike (CACM v.9, p. 684, Sept */
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/* 1966) and those of Tomlin and Smith, "Remark on Algorithm 178" */
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/* (CACM v.12). The original paper, which I don't recommend as */
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/* highly as the one by A. Kaupe, is: R. Hooke and T. A. Jeeves, */
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/* "Direct Search Solution of Numerical and Statistical Problems", */
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/* Journal of the ACM, Vol. 8, April 1961, pp. 212-229. */
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/* Calling sequence: */
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/* int hooke(nvars, startpt, endpt, rho, epsilon, itermax) */
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/* */
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/* nvars {an integer} */
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/* This is the number of dimensions in the domain of f(). */
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/* It is the number of coordinates of the starting point */
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/* (and the minimum point.) */
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/* startpt {an array of doubles} */
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/* This is the user-supplied guess at the minimum. */
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/* endpt {an array of doubles} */
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/* This is the calculated location of the local minimum */
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/* rho {a double} */
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/* This is a user-supplied convergence parameter (more */
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/* detail below), which should be set to a value between */
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/* 0.0 and 1.0. Larger values of rho give greater */
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/* probability of convergence on highly nonlinear */
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/* functions, at a cost of more function evaluations. */
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/* Smaller values of rho reduces the number of evaluations */
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/* (and the program running time), but increases the risk */
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/* of nonconvergence. See below. */
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/* epsilon {a double} */
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/* This is the criterion for halting the search for a */
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/* minimum. When the algorithm begins to make less and */
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/* less progress on each iteration, it checks the halting */
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/* criterion: if the stepsize is below epsilon, terminate */
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/* the iteration and return the current best estimate of */
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/* the minimum. Larger values of epsilon (such as 1.0e-4) */
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/* give quicker running time, but a less accurate estimate */
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/* of the minimum. Smaller values of epsilon (such as */
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/* 1.0e-7) give longer running time, but a more accurate */
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/* estimate of the minimum. */
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/* itermax {an integer} A second, rarely used, halting */
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/* criterion. If the algorithm uses >= itermax */
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/* iterations, halt. */
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/* The user-supplied objective function f(x,n) should return a C */
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/* "double". Its arguments are x -- an array of doubles, and */
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/* n -- an integer. x is the point at which f(x) should be */
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/* evaluated, and n is the number of coordinates of x. That is, */
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/* n is the number of coefficients being fitted. */
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/* rho, the algorithm convergence control */
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/* The algorithm works by taking "steps" from one estimate of */
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/* a minimum, to another (hopefully better) estimate. Taking */
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/* big steps gets to the minimum more quickly, at the risk of */
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/* "stepping right over" an excellent point. The stepsize is */
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/* controlled by a user supplied parameter called rho. At each */
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/* iteration, the stepsize is multiplied by rho (0 < rho < 1), */
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/* so the stepsize is successively reduced. */
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/* Small values of rho correspond to big stepsize changes, */
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/* which make the algorithm run more quickly. However, there */
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/* is a chance (especially with highly nonlinear functions) */
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/* that these big changes will accidentally overlook a */
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/* promising search vector, leading to nonconvergence. */
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/* Large values of rho correspond to small stepsize changes, */
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/* which force the algorithm to carefully examine nearby points */
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/* instead of optimistically forging ahead. This improves the */
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/* probability of convergence. */
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/* The stepsize is reduced until it is equal to (or smaller */
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/* than) epsilon. So the number of iterations performed by */
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/* Hooke-Jeeves is determined by rho and epsilon: */
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/* rho**(number_of_iterations) = epsilon */
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/* In general it is a good idea to set rho to an aggressively */
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/* small value like 0.5 (hoping for fast convergence). Then, */
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/* if the user suspects that the reported minimum is incorrect */
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/* (or perhaps not accurate enough), the program can be run */
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/* again with a larger value of rho such as 0.85, using the */
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/* result of the first minimization as the starting guess to */
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/* begin the second minimization. */
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/* Normal use: */
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/* (1) Code your function f() in the C language */
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/* (2) Install your starting guess {or read it in} */
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/* (3) Run the program */
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/* (4) {for the skeptical}: Use the computed minimum */
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/* as the starting point for another run */
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/* Data Fitting: */
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/* Code your function f() to be the sum of the squares of the */
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/* errors (differences) between the computed values and the */
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/* measured values. Then minimize f() using Hooke-Jeeves. */
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/* EXAMPLE: you have 20 datapoints (ti, yi) and you want to */
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/* find A,B,C such that (A*t*t) + (B*exp(t)) + (C*tan(t)) */
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/* fits the data as closely as possible. Then f() is just */
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/* f(x) = SUM (measured_y[i] - ((A*t[i]*t[i]) + (B*exp(t[i])) */
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/* + (C*tan(t[i]))))^2 */
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/* where x[] is a 3-vector consisting of {A, B, C}. */
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/* The author of this software is M.G. Johnson. */
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/* Permission to use, copy, modify, and distribute this software */
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/* for any purpose without fee is hereby granted, provided that */
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/* this entire notice is included in all copies of any software */
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/* which is or includes a copy or modification of this software */
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/* and in all copies of the supporting documentation for such */
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/* software. THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT */
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/* ANY EXPRESS OR IMPLIED WARRANTY. IN PARTICULAR, NEITHER THE */
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/* AUTHOR NOR AT&T MAKE ANY REPRESENTATION OR WARRANTY OF ANY */
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/* KIND CONCERNING THE MERCHANTABILITY OF THIS SOFTWARE OR ITS */
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/* FITNESS FOR ANY PARTICULAR PURPOSE. */
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/* JMB this has been modified to work with the gadget object structure */
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/* This means that the function has been replaced by a call to ecosystem */
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/* object, and we can use the vector objects that have been defined */
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#include "gadget.h" |
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#include "optinfo.h" |
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#include "mathfunc.h" |
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#include "doublevector.h" |
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#include "intvector.h" |
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#include "errorhandler.h" |
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#include "ecosystem.h" |
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#include "global.h" |
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extern Ecosystem* EcoSystem;
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/* given a point, look for a better one nearby, one coord at a time */
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double OptInfoHooke::bestNearby(DoubleVector& delta, DoubleVector& point, double prevbest, IntVector& param) {
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double minf, ftmp;
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int i;
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DoubleVector z(point);
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minf = prevbest;
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for (i = 0; i < point.Size(); i++) {
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z[param[i]] = point[param[i]] + delta[param[i]];
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ftmp = EcoSystem->SimulateAndUpdate(z);
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if (ftmp < minf) {
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minf = ftmp;
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} else {
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delta[param[i]] = 0.0 - delta[param[i]];
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z[param[i]] = point[param[i]] + delta[param[i]];
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ftmp = EcoSystem->SimulateAndUpdate(z);
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if (ftmp < minf)
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minf = ftmp;
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else
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z[param[i]] = point[param[i]];
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}
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}
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for (i = 0; i < point.Size(); i++)
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point[i] = z[i];
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return minf;
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}
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void OptInfoHooke::OptimiseLikelihood() {
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double oldf, newf, bestf, steplength, tmp;
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int i, offset;
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int rchange, rcheck, rnumber; //Used to randomise the order of the parameters
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handle.logMessage(LOGINFO, "\nStarting Hooke & Jeeves optimisation algorithm\n");
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int nvars = EcoSystem->numOptVariables();
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DoubleVector x(nvars);
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DoubleVector trialx(nvars);
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DoubleVector bestx(nvars);
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DoubleVector lowerb(nvars);
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DoubleVector upperb(nvars);
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DoubleVector init(nvars);
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DoubleVector initialstep(nvars, rho);
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DoubleVector delta(nvars);
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IntVector param(nvars, 0);
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IntVector lbound(nvars, 0);
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IntVector rbounds(nvars, 0);
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IntVector trapped(nvars, 0);
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EcoSystem->scaleVariables();
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EcoSystem->getOptScaledValues(x);
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EcoSystem->getOptLowerBounds(lowerb);
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EcoSystem->getOptUpperBounds(upperb);
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EcoSystem->getOptInitialValues(init);
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for (i = 0; i < nvars; i++) {
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// Scaling the bounds, because the parameters are scaled
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lowerb[i] = lowerb[i] / init[i];
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upperb[i] = upperb[i] / init[i];
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if (lowerb[i] > upperb[i]) {
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tmp = lowerb[i];
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lowerb[i] = upperb[i];
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upperb[i] = tmp;
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}
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bestx[i] = x[i];
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trialx[i] = x[i];
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param[i] = i;
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delta[i] = ((2 * (rand() % 2)) - 1) * rho; //JMB - randomise the sign
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}
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bestf = EcoSystem->SimulateAndUpdate(trialx);
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if (bestf != bestf) { //check for NaN
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handle.logMessage(LOGINFO, "Error starting Hooke & Jeeves optimisation with f(x) = infinity");
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converge = -1;
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iters = 1;
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return;
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}
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offset = EcoSystem->getFuncEval(); //number of function evaluations done before loop
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newf = bestf;
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oldf = bestf;
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steplength = lambda;
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if (isZero(steplength))
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steplength = rho;
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while (1) {
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if (isZero(bestf)) {
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iters = EcoSystem->getFuncEval() - offset;
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handle.logMessage(LOGINFO, "Error in Hooke & Jeeves optimisation after", iters, "function evaluations, f(x) = 0");
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converge = -1;
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return;
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}
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/* randomize the order of the parameters once in a while */
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rchange = 0;
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while (rchange < nvars) {
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rnumber = rand() % nvars;
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rcheck = 1;
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for (i = 0; i < rchange; i++)
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if (param[i] == rnumber)
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rcheck = 0;
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if (rcheck) {
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param[rchange] = rnumber;
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rchange++;
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}
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}
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/* find best new point, one coord at a time */
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for (i = 0; i < nvars; i++)
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trialx[i] = x[i];
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newf = this->bestNearby(delta, trialx, bestf, param);
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/* if too many function evaluations occur, terminate the algorithm */
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iters = EcoSystem->getFuncEval() - offset;
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if (iters > hookeiter) {
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handle.logMessage(LOGINFO, "\nStopping Hooke & Jeeves optimisation algorithm\n");
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handle.logMessage(LOGINFO, "The optimisation stopped after", iters, "function evaluations");
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handle.logMessage(LOGINFO, "The steplength was reduced to", steplength);
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handle.logMessage(LOGINFO, "The optimisation stopped because the maximum number of function evaluations");
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handle.logMessage(LOGINFO, "was reached and NOT because an optimum was found for this run");
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score = EcoSystem->SimulateAndUpdate(trialx);
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handle.logMessage(LOGINFO, "\nHooke & Jeeves finished with a likelihood score of", score);
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for (i = 0; i < nvars; i++)
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bestx[i] = trialx[i] * init[i];
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EcoSystem->storeVariables(score, bestx);
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return;
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}
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/* if we made some improvements, pursue that direction */
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while (newf < bestf) {
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for (i = 0; i < nvars; i++) {
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/* if it has been trapped but f has now gotten better (bndcheck) */
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/* we assume that we are out of the trap, reset the counters */
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/* and go back to the stepsize we had when we got trapped */
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if ((trapped[i]) && (newf < oldf * bndcheck)) {
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trapped[i] = 0;
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lbound[i] = 0;
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rbounds[i] = 0;
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delta[i] = initialstep[i];
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} else if (trialx[i] < (lowerb[i] + verysmall)) {
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lbound[i]++;
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trialx[i] = lowerb[i];
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if (!trapped[i]) {
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initialstep[i] = delta[i];
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trapped[i] = 1;
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}
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/* if it has hit the bounds 2 times then increase the stepsize */
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if (lbound[i] >= 2)
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delta[i] /= rho;
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| 299 : |
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|
} else if (trialx[i] > (upperb[i] - verysmall)) {
|
| 300 : |
|
|
rbounds[i]++;
|
| 301 : |
|
|
trialx[i] = upperb[i];
|
| 302 : |
|
|
if (!trapped[i]) {
|
| 303 : |
|
|
initialstep[i] = delta[i];
|
| 304 : |
|
|
trapped[i] = 1;
|
| 305 : |
|
|
}
|
| 306 : |
|
|
/* if it has hit the bounds 2 times then increase the stepsize */
|
| 307 : |
|
|
if (rbounds[i] >= 2)
|
| 308 : |
|
|
delta[i] /= rho;
|
| 309 : |
|
|
}
|
| 310 : |
|
|
}
|
| 311 : |
|
|
|
| 312 : |
|
|
for (i = 0; i < nvars; i++) {
|
| 313 : |
|
|
/* firstly, arrange the sign of delta[] */
|
| 314 : |
|
|
if (trialx[i] < x[i])
|
| 315 : |
|
|
delta[i] = 0.0 - fabs(delta[i]);
|
| 316 : |
|
|
else
|
| 317 : |
|
|
delta[i] = fabs(delta[i]);
|
| 318 : |
|
|
|
| 319 : |
|
|
/* now, move further in this direction */
|
| 320 : |
|
|
tmp = x[i];
|
| 321 : |
|
|
x[i] = trialx[i];
|
| 322 : |
|
|
trialx[i] = trialx[i] + trialx[i] - tmp;
|
| 323 : |
|
|
}
|
| 324 : |
|
|
|
| 325 : |
|
|
/* only move forward if this is really an improvement */
|
| 326 : |
|
|
oldf = newf;
|
| 327 : |
|
|
newf = EcoSystem->SimulateAndUpdate(trialx);
|
| 328 : |
|
|
if ((isEqual(newf, oldf)) || (newf > oldf)) {
|
| 329 : |
|
|
newf = oldf; //JMB no improvement, so reset the value of newf
|
| 330 : |
|
|
break;
|
| 331 : |
|
|
}
|
| 332 : |
|
|
|
| 333 : |
|
|
/* OK, it's better, so update variables and look around */
|
| 334 : |
|
|
bestf = newf;
|
| 335 : |
|
|
for (i = 0; i < nvars; i++)
|
| 336 : |
|
|
x[i] = trialx[i];
|
| 337 : |
|
|
newf = this->bestNearby(delta, trialx, bestf, param);
|
| 338 : |
|
|
if (isEqual(newf, bestf))
|
| 339 : |
|
|
break;
|
| 340 : |
|
|
|
| 341 : |
|
|
/* if too many function evaluations occur, terminate the algorithm */
|
| 342 : |
|
|
iters = EcoSystem->getFuncEval() - offset;
|
| 343 : |
|
|
if (iters > hookeiter) {
|
| 344 : |
|
|
handle.logMessage(LOGINFO, "\nStopping Hooke & Jeeves optimisation algorithm\n");
|
| 345 : |
|
|
handle.logMessage(LOGINFO, "The optimisation stopped after", iters, "function evaluations");
|
| 346 : |
|
|
handle.logMessage(LOGINFO, "The steplength was reduced to", steplength);
|
| 347 : |
|
|
handle.logMessage(LOGINFO, "The optimisation stopped because the maximum number of function evaluations");
|
| 348 : |
|
|
handle.logMessage(LOGINFO, "was reached and NOT because an optimum was found for this run");
|
| 349 : |
|
|
|
| 350 : |
|
|
score = EcoSystem->SimulateAndUpdate(trialx);
|
| 351 : |
|
|
handle.logMessage(LOGINFO, "\nHooke & Jeeves finished with a likelihood score of", score);
|
| 352 : |
|
|
for (i = 0; i < nvars; i++)
|
| 353 : |
|
|
bestx[i] = trialx[i] * init[i];
|
| 354 : |
|
|
EcoSystem->storeVariables(score, bestx);
|
| 355 : |
|
|
return;
|
| 356 : |
|
|
}
|
| 357 : |
|
|
}
|
| 358 : |
|
|
|
| 359 : |
|
|
iters = EcoSystem->getFuncEval() - offset;
|
| 360 : |
|
|
if (newf < bestf) {
|
| 361 : |
|
|
for (i = 0; i < nvars; i++)
|
| 362 : |
|
|
bestx[i] = x[i] * init[i];
|
| 363 : |
|
|
bestf = newf;
|
| 364 : |
|
|
handle.logMessage(LOGINFO, "\nNew optimum found after", iters, "function evaluations");
|
| 365 : |
|
|
handle.logMessage(LOGINFO, "The likelihood score is", bestf, "at the point");
|
| 366 : |
|
|
EcoSystem->storeVariables(bestf, bestx);
|
| 367 : |
|
|
EcoSystem->writeBestValues();
|
| 368 : |
|
|
|
| 369 : |
|
|
} else
|
| 370 : |
|
|
handle.logMessage(LOGINFO, "Checking convergence criteria after", iters, "function evaluations ...");
|
| 371 : |
|
|
|
| 372 : |
|
|
/* if the step length is less than hookeeps, terminate the algorithm */
|
| 373 : |
|
|
if (steplength < hookeeps) {
|
| 374 : |
|
|
handle.logMessage(LOGINFO, "\nStopping Hooke & Jeeves optimisation algorithm\n");
|
| 375 : |
|
|
handle.logMessage(LOGINFO, "The optimisation stopped after", iters, "function evaluations");
|
| 376 : |
|
|
handle.logMessage(LOGINFO, "The steplength was reduced to", steplength);
|
| 377 : |
|
|
handle.logMessage(LOGINFO, "The optimisation stopped because an optimum was found for this run");
|
| 378 : |
|
|
|
| 379 : |
|
|
converge = 1;
|
| 380 : |
|
|
score = bestf;
|
| 381 : |
|
|
handle.logMessage(LOGINFO, "\nHooke & Jeeves finished with a likelihood score of", score);
|
| 382 : |
|
|
EcoSystem->storeVariables(bestf, bestx);
|
| 383 : |
|
|
return;
|
| 384 : |
|
|
}
|
| 385 : |
|
|
|
| 386 : |
|
|
steplength *= rho;
|
| 387 : |
|
|
handle.logMessage(LOGINFO, "Reducing the steplength to", steplength);
|
| 388 : |
|
|
for (i = 0; i < nvars; i++)
|
| 389 : |
|
|
delta[i] *= rho;
|
| 390 : |
|
|
}
|
| 391 : |
|
|
}
|
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