Update cmaes_sourcecode_page.html

Author: nikohansen

cmaes_sourcecode_page.html

@@ -146,7 +146,8 @@ <H3><A name="boundaries">Boundary and Constraint Handling</A></H3>
 For a very short and general overview on boundary and constraints handling (as of 2014 not entirely up-to-date though) in connection with CMA-ES, see the appendix of <A HREF="http://arxiv.org/abs/1604.00772"><I>The CMA Evolution Strategy: A Tutorial</I></A>, p.34f. 
 
 <H3><A name="initial">Initial Values</A></H3>
-After the encoding of variables, see above, the initial solution point <I>x</I><sub>0</sub> and the initial standard deviation (step-size) &sigma;<sub>0</sub> must be chosen. In a practical application, one often wants to start by trying to improve a given solution locally. In this case we choose a rather small &sigma;<sub>0</sub> (say in [0.001, 0.1], given the <I>x</I>-values "live" in [0,10]). Thereby we can also check, whether the initial solution is possibly a local optimum. When a global optimum is sought-after on rugged or multimodal landscapes, &sigma;<sub>0</sub> should be chosen such that the final desirable location (or at least some of its domain of attraction) is not far outside of <I>x</I><sub>0</sub> &pm; 2&sigma;<sub>0</sub> in each coordinate. (Remark that in <I>R<SUP>n</SUP></I>, if each boundary domain is in distance &sigma;, then the boundary corner is &sigma; &radic;<span style="text-decoration:overline"><I>n</I></span> away, which poses a slight dilemma for larger <I>n</I>.) 
+After the encoding of variables, see above, the initial solution point <I>x</I><sub>0</sub> and the initial standard deviation (step-size) &sigma;<sub>0</sub> must be chosen. In a practical application, one often wants to start by trying to improve a given solution locally. In this case we choose a rather small &sigma;<sub>0</sub> (say in [0.001, 0.1], given the <I>x</I>-values "live" in [0,10]). Thereby we can also check, whether the initial solution is possibly a local optimum. When a global optimum is sought-after on rugged or multimodal landscapes, &sigma;<sub>0</sub> should be chosen such that the global optimum or final desirable location (or at least some of its domain of attraction)
+  is expected not to be (far) outside of <I>x</I><sub>0</sub> &pm; 2&sigma;<sub>0</sub> in each coordinate. (Remark that in <I>R<SUP>n</SUP></I>, if each boundary domain is in distance &sigma;, then the boundary corner is &sigma; &radic;<span style="text-decoration:overline"><I>n</I></span> away, which poses a slight dilemma for larger <I>n</I>.) 
 
 <H3><A name="plotting">Plotting</A></H3>
 The source code from this page writes output data that can be plotted either with the respective code or with the following stand-alone versions (the data formats are largely inter-compatible):