The idea can be described as follows: Most problems do not only have one unique minimum (maximum) but
+ * a number of local minima (maxima). To avoid to get stuck in a local minimum at the beginning of a search
+ * this threshold-acceptance function accepts also worse solution at the beginning (in contrary to a greedy
+ * approach which only accepts better solutions), and converges to a greedy approach at the end.
+ * The difficulty is to define (i) an appropriate initial threshold and (ii) a corresponding function describing
+ * how the threshold converges to zero, i.e. the greedy threshold.
+ *
+ *
ad i) The initial threshold is determined by a random walk through the search space. + * The random walk currently runs with the following algorithm: src/main/resources/randomWalk.xml. It runs + * as long as it is specified in nuOfWarmupIterations. In the first iteration or walk respectively the algorithm generates a solution. + * This solution in turn is the basis of the next walk yielding to another solution value ... and so on. + * Each solution value is memorized since the initial threshold is essentially a function of the standard deviation of these solution values. + * To be more precise: initial threshold = stddev(solution values) / 2. + * + *
ad ii) The threshold of iteration i is determined as follows: + * threshold(i) = initialThreshold * Math.exp(-Math.log(2) * (i / nuOfTotalIterations) / alpha) + * To get a better understanding of the threshold-function go to Wolfram Alpha and plot the following line + * (just copy and paste it into Wolfram's console: www.wolframalpha.com): + *
100. * exp(-log(2)* (x/1000) / 0.1) (x from 0 to 1000) (y from 0 to 100) + *
with
+ * initialThreshold = 100
+ * nuOfTotalIter = 1000
+ * alpha = 0.1
+ * x corresponds to i iterations and
+ * y to the threshold(i)
+ *
+ *
Gerhard Schrimpf, Johannes Schneider, Hermann Stamm- Wilbrandt, and Gunter Dueck (2000). + * Record breaking optimization results using the ruin and recreate principle. + * Journal of Computational Physics, 159(2):139 – 171, 2000. ISSN 0021-9991. doi: 10.1006/jcph.1999. 6413. + * URL http://www.sciencedirect.com/science/article/ pii/S0021999199964136 + * + *
Probably the determination of the initial threshold will be separated from the threshold-acceptance
+ * function (25.02.14 stefan)
+ *
+ * @author schroeder
+ *
+ */
public class SchrimpfAcceptance implements SolutionAcceptor, IterationStartsListener, AlgorithmStartsListener{
private static Logger logger = Logger.getLogger(SchrimpfAcceptance.class);
@@ -62,8 +100,6 @@ public class SchrimpfAcceptance implements SolutionAcceptor, IterationStartsList
logger.info("initialise " + this);
}
-
-
@Override
public boolean acceptSolution(Collection