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## cmaes

CMA-ES (Evolution Strategy with Covariance Matrix Adaptation) optimization library.

## Usage

(require-extension cmaes)

## Documentation

The CMA-ES CMA-ES (Covariance Matrix Adaptation Evolution Strategy) is an evolutionary algorithm for difficult non-linear non-convex optimization problems in a continuous domain.

The Chicken `cmaes` library provides a Scheme interface to the core procedures of CMA-ES.

### High-level procedures

*[procedure]*

`init:: PARAMETERS -> [H FUNVALS]`

Creates a new optimization problem based on the given parameters. `PARAMETERS` is an alist of parameter values, as defined in the CMA-ES documentation.

*[procedure]*

`run:: FN * H * FUNVALS * SIGNALS [output-file: "all.dat"] [result-values: '(xbest xmean)] -> RESULT`

Executes the optimizer and returns the solution. `FN` is the objective function: it must take an SRFI-4 `f64vector` of state value and return the objective value corresponding to this state fector. `H` is the problem handle returned by `init`. `FUNVALS` is the initial state vector (must be SRFI-4 `f64vector`). `SIGNALS` is an alist of runtime signals to be evaluated.

### Initialization procedures

*[procedure]*

`init-from-file:: FILEPATH -> [H FUNVALS]`

*[procedure]*

`read-signals:: H * [PARAMETER1 ...] -> VOID`

*[procedure]*

`read-signals-from-file:: H * FILEPATH -> VOID`

### Core procedures

*[procedure]*

`sample-population:: H -> VECTOR`

Computes a population of lambda N-dimensional multivariate normally distributed samples.

*[procedure]*

`update-distribution:: H -> F64VECTOR`

Sets a new mean value and estimates the new covariance matrix and a new step size for the normal search distribution. Returns the new mean value.

### Support procedures

## Examples

### High-level procedures

(use srfi-4 cmaes) (define(minimize f N) (let-values (((h funvals) (init `((N . ,N) ;; Problem dimension (initialX 0.5e0) ;; Initial search point (typicalX 0.0) ;; Typical search point (useful for restarts) (initialStandardDeviations 0.3) ;; numbers should not differ by orders of magnitude ;; should be roughly 1/4 of the search interval ;; this number essentially influences the global ;; search ability (ie. the horizon where to search ;; at all) on multimodal functions (stopMaxFunEvals . 1e299) ;; max number of f-evaluations, 900*(N+3)*(N+3) is default (stopMaxIter . 1e299) ;; max number of iterations (generations), inf is default (stopTolFun . 1e-12) ;; stop if function value differences are ;; smaller than stopTolFun, default=1e-12 (stopTolFunHist . 1e-13) ;; stop if function value differences of best values are ;; smaller than stopTolFunHist, default was 0 (stopTolX . 1e-11) ;; stop if step sizes/steps in x-space are ;; smaller than TolX, default=0 (stopTolUpXFactor . 1e3) ;; stop if std dev increases more than by TolUpXFactor, default 1e3 (seed . 0) )))) (pp (run f h funvals `((print fewinfo 200) ;; print every 200 seconds (print few+clock 2 ) ;; clock: used processor time since start (write "iter+eval+sigma+0+0+xmean" outcmaesxmean.dat ) (write "iter+eval+sigma+0+fitness+xbest" outcmaesxrecentbest.dat ) ))) )) ;; an objective (fitness) function to be minimized (define(f1 x) (let((N (f64vector-length x))) (letrecur ((i 2) (sum (+ (* 1e4 (f64vector-ref x 0) (f64vector-ref x 0)) (* 1e4 (f64vector-ref x 1) (f64vector-ref x 1)) ))) (if(< i N) (recur (+ 1 i) (+ sum (* (f64vector-ref x i) (f64vector-ref x i)))) sum)) )) (minimize f1 22)

### Core procedures

(use srfi-4 cmaes) ;; the objective (fitness) function to be minimized (define(fitfun x N) (letrecur ((i 2) (sum (+ (* 1e4 (f64vector-ref x 0) (f64vector-ref x 0)) (* 1e4 (f64vector-ref x 1) (f64vector-ref x 1)) ))) (if(< i N) (recur (+ 1 i) (+ sum (* (f64vector-ref x i) (f64vector-ref x i)))) sum)) ) (let-values (((h funvals) (init-from-file "initials.par"))) (read-signals-from-file h "signals.par") (letrecur ((h h)) (let((stop (terminated? h))) (if(not stop) (let((pop (sample-population h)) (lam (get-parameter h 'lambda)) (n (get-parameter h 'dim))) (letinner-recur ((i 0)) (if(< i lam) (begin (f64vector-set! funvals i (fitfun (vector-ref pop i) n)) (inner-recur (+ 1 i))))) (update-distribution h funvals) (read-signals-from-file h "signals.par") (recur h) ) (print stop) ))) (write-to-file h 'all "allcmaes.dat") (let((xfinal (get-new h "xmean"))) (printf "xmean = ~A~%" xfinal) (terminate h) (free h) ))

## About this egg

### Author

The CMA-ES C library was written by Nikolaus Hansen. The Chicken Scheme `cmaes` library was written by Ivan Raikov.

### Version history

- 1.0
- Initial release

### License

CMA-ES C library is copyright 1996, 2003, 2007 Nikolaus Hansen. Chicken Scheme bindings for CMA-ES are copyright 2012 Ivan Raikov. This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License version 2 as published by the Free Software Foundation. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. A full copy of the GPL license can be found at <http://www.gnu.org/licenses/>.