Because of its simplicity every optimization-algorithm should be able to find its global minimum at x=[0, 0, ... , 0]
@@ -15,7 +15,7 @@ Because of its simplicity every optimization-algorithm should be able to find it
Kenneth De Jong. An analysis of the behaviour of a class of genetic adaptive systems. Dissertation, University of Michigan, 1975. Diss. Abstr. Int. 36(10), 5140B, University Microflims No. 76-9381. diff --git a/resources/F2Problem.html b/resources/F2Problem.html index 7397650e..e40272a2 100644 --- a/resources/F2Problem.html +++ b/resources/F2Problem.html @@ -2,19 +2,19 @@
-This function i unimodal and continuous, but the global optimum is hard to find, because of independence through the term (x_(i+1) - x_i*x_i)^2 between contiguous parameters. +This function is unimodal and continuous, but the global optimum is hard to find, because of independence through the term (x_(i+1) - x_i*x_i)^2 between contiguous parameters.
Rosenbrock's function within the co-domain -5 <= x <= 5.
-The global optimum is located in a prabolic formed valley (among the curve x^2 = x_1^2), which has a flatten ground.
+The global optimum is located in a parabolic formed valley (among the curve x^2 = x_1^2), which has a flat ground.
diff --git a/resources/F3Problem.html b/resources/F3Problem.html
index a082d759..7b187e07 100644
--- a/resources/F3Problem.html
+++ b/resources/F3Problem.html
@@ -2,19 +2,19 @@
-The idea of this function is the implementation of a flat plateau (slope 0)in an underlying continuous function.Its harder for optimization algortihms to find optimums because minor changes of the object variables don't affect the fitness. Therefore no conclusions about the search direction can be made. +The idea of this function is the implementation of a flat plateau (slope 0)in an underlying continuous function. It's harder for optimization algortihms to find optima because minor changes of the object variables don't affect the fitness. Therefore no conclusions about the search direction can be made.
The step function is symmetric considering the underlying function (here: f(x,y) = f(y,x)), but between the bulk constant plateau-areas not continuously differentiable.
-Its minimum-area is located in the intervalls: f(x)=f([-5.12,-5), ... , [-5.12,-5))=0. +Its minimum-area is located in the intervals: f(x)=f([-5.12,-5), ... , [-5.12,-5))=0.
-Schwefel's double sum is a quadratic minimization problem which difficulty increases by the dimension n in O(n˛). It is used for analysis of correlating mutations. +Schwefel's double sum is a quadratic minimization problem. Its difficulty increases by the dimension n in O(n^2). It is used for analysis of correlating mutations.
It possesses specific symmetrical properties:
diff --git a/resources/F6Problem.html b/resources/F6Problem.html
index 70abac76..7d5bb872 100644
--- a/resources/F6Problem.html
+++ b/resources/F6Problem.html
@@ -2,15 +2,15 @@
-Rastrigin's function is symmetric. It is based on the simple sphere function (called f_1 in the JavaEvaŠ context), but it is multimodal because a modulation term on the basis of the cosine function is added. This evokes hills and valleys which are misleading local optimums. +Rastrigin's function is symmetric. It is based on the simple parabola function (called f1 in the JavaEvA context), but it is multimodal because a modulation term on the basis of the cosine function is added. This evokes hills and valleys which are misleading local optima.
-Values are used for the following illustrations: A=10, ω=2*π, n=2.
+Values used for the following illustrations: A=10, ω=2*π, n=2.
diff --git a/resources/F8Problem.html b/resources/F8Problem.html
index 64f45238..44bb50ea 100644
--- a/resources/F8Problem.html
+++ b/resources/F8Problem.html
@@ -2,16 +2,18 @@
-Ackley's function is intense multimodal and symmetrical. It refers to an exponential function which is modulated through a cosine function. The outside region is almost planar by the growing influence of the exponential function. In the center it possesses a hole by the influence of the cosine function.
+Ackley's function is multimodal and symmetrical. It is based on an exponential function and modulated by a cosine function.
+The outside region is almost planar as to the growing influence of the exponential function.
+In the center there is a steep hole as to the influence of the cosine function.
Its minimum is at: f(x)=f([0, 0, ... , 0])=0.
-The difficulty for an optmization algorithm is mid-graded because a simple optimization-algorithm like hill-climbing would get stuck in a local minimum. The optimization algorithm has to search a broader environ to overcome the local minimum and get closer to the global optima. +The difficulty for an optimization algorithm is mid-graded because a simple optimization-algorithm like hill-climbing would get stuck in a local minimum. The optimization algorithm has to search a broader environ to overcome the local minimum and get closer to the global optima.
diff --git a/resources/GOParameters.html b/resources/GOParameters.html index a76b4b03..2d9c1d82 100644 --- a/resources/GOParameters.html +++ b/resources/GOParameters.html @@ -8,12 +8,12 @@ The GO parameter class is used to change main GO optimization settings. You may: