-
-This class implements the IPOP (increased population size) restart strategy ES, which increases
-the ES population size (i.e., lambda) after phases of stagnation and then restarts the optimization
-by reinitializing the individuals and operators.
-Stagnation is for this implementation defined by a FitnessConvergenceTerminator instance
-which terminates if the absolute change in fitness is below a threshold (default 10e-12) for a
-certain number of generations (default: 10+floor(30*n/lambda) for problem dimension n).
-
-If the MutateESRankMuCMA mutation operator is employed, additional criteria are used for restarts, -such as numeric conditions of the covariance matrix. -Lambda is increased multiplicatively for every restart, and typical initial values are -mu=5, lambda=10, incFact=2. -The IPOP-CMA-ES won the CEC 2005 benchmark challenge. -Refer to Auger&Hansen 05 for more details. -
-
--Schwefel's (sine root) function is highly multimodal and has no global basin of attraction. The optimum at a fitness of f(x*)=0 lies at x*=420.9687. Schwefel's sine root is a tough challenge for any global optimizer due to the multiple distinct optima. Especially, there is a deceptive nearly optimal solution close to x=(-420.9687)n. - -
- -
-
-
-
-Schwefels's sine root function in 2D within the co-domain -500 <= x <= 500.
-
- -
-David. H. Ackley. A connection machine for genetic hillclimbing. Kluwer Academic Publishers, Boston, 1987. -
-Thomas Baeck. Evolutionary Algorithms in Theory and Practice. Oxford University Press, 1996. - - - diff --git a/resources/F1Problem.html b/resources/F1Problem.html deleted file mode 100644 index 1cfb1fe6..00000000 --- a/resources/F1Problem.html +++ /dev/null @@ -1,24 +0,0 @@ - -
-
--Because of its simplicity every optimization-algorithm should be able to find its global minimum at x=[0, 0, ... , 0] -
-
-
-
-
- -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. - - - \ No newline at end of file diff --git a/resources/F2Problem.html b/resources/F2Problem.html deleted file mode 100644 index 40dfaa06..00000000 --- a/resources/F2Problem.html +++ /dev/null @@ -1,36 +0,0 @@ - -
-
--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 domain -5 <= x <= 5.
-
-The global optimum is located in a parabolic formed valley (among the curve x^2 = x_1^2), which has a flat ground.
-
-
-
-The function close to its global optimum, which is: f(x) = f(1, 1, ... , 1) = 0.
-
-Rosenbrock' function is not symmetric, not convex and not linear. - -
-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. -
-Hans Paul Schwefel. Evolution and optimum seeking. Sixth-Generation Computer Technology Series. John Wiley & Sons, INC., 1995. -
-Darrell Whitley, Soraya Rana, John Dzubera, Keith E. Mathias. Evaluating Evolutionary Algorithms. Artificial Intelligence, 85(1-2):245-276. 1996. -
-Eberhard Schoeneburg, Frank Heinzmann, Sven Feddersen. Genetische Algorithmen und Evolutionstrategien - Eine Einfuehrung in Theorie und Praxis der simulierten Evolution. Addison-Wesley, 1994. - - \ No newline at end of file diff --git a/resources/F3Problem.html b/resources/F3Problem.html deleted file mode 100644 index 7b187e07..00000000 --- a/resources/F3Problem.html +++ /dev/null @@ -1,29 +0,0 @@ - -
-
--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 intervals: f(x)=f([-5.12,-5), ... , [-5.12,-5))=0. -
-
-
-Thomas Baeck, Evolutionary Algorithms in Theory and Practice. Oxford University Press, 1996. -
-Darrell Whitley, Soraya Rana, John Dzubera, Keith E. Mathias. Evaluating Evolutionary Algorithms. Artificial Intelligence, 85(1-2):245-276. 1996. -
-Eberhard Schoeneburg, Frank Heinzmann, Sven Feddersen. Genetische Algorithmen und Evolutionstrategien - Eine Einfuehrung in Theorie und Praxis der simulierten Evolution. Addison-Wesley, 1994. - - \ No newline at end of file diff --git a/resources/F5Problem.html b/resources/F5Problem.html deleted file mode 100644 index 9697f9f7..00000000 --- a/resources/F5Problem.html +++ /dev/null @@ -1,27 +0,0 @@ - -
-
--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:
-
-
-
-Its minimum is located at: f(x)=f([0, 0, ... , 0])=0 -
-
-
-
-Hans Paul Schwefel. Evolution and optimum seeking. Sixth-Generation Computer Technology Series. John Wiley & Sons, INC., 1995. - - - \ No newline at end of file diff --git a/resources/F6Problem.html b/resources/F6Problem.html deleted file mode 100644 index a5b7246a..00000000 --- a/resources/F6Problem.html +++ /dev/null @@ -1,42 +0,0 @@ - -
-
--Rastrigin's function is symmetric. It is based on the simple parabola function (called f1 in the EvA 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 used for the following illustrations: A=10, ω=2*π, n=2.
-
-
-
-
-
-
-Rastrigin's function within the co-domain -20>=x>=20
-
-
-
-
-
-Rastrigin's function within the co-domain -5>=x>=5
-
-
- -Like Ackley's function a simple evolutionary algorithm would get stuck in a local optimum, while a broader searching algorithm would get out of the local optimum closer to the global optimum, which in this case is: f(x) = f(0, 0, ... , 0) = 0. -
-
-Rastrigin's function close to its optimum.
-
-
-Darrell Whitley, Soraya Rana, John Dzubera, Keith E. Mathias. Evaluating Evolutionary Algorithms. Artificial Intelligence, 85(1-2):245-276. 1996. -
-Eberhard Schoeneburg, Frank Heinzmann, Sven Feddersen. Genetische Algorithmen und Evolutionstrategien - Eine Einfuehrung in Theorie und Praxis der simulierten Evolution. Addison-Wesley, 1994. - - \ No newline at end of file diff --git a/resources/F8Problem.html b/resources/F8Problem.html deleted file mode 100644 index 44bb50ea..00000000 --- a/resources/F8Problem.html +++ /dev/null @@ -1,36 +0,0 @@ - -
-
-
-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 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. - -
-
-
-
-Ackley's function within the co-domain -20 >= x >= 20, a=20, b=0.2, c=2*π, n=2.
-
-
-
-
-Ackley's function close to the optimum.
-
-David. H. Ackley. A connection machine for genetic hillclimbing. Kluwer Academic Publishers, Boston, 1987. -
-Thomas Baeck. Evolutionary Algorithms in Theory and Practice. Oxford University Press, 1996. - - - \ No newline at end of file diff --git a/resources/FitnessConvergenceTerminator.html b/resources/FitnessConvergenceTerminator.html deleted file mode 100644 index 099e963f..00000000 --- a/resources/FitnessConvergenceTerminator.html +++ /dev/null @@ -1,19 +0,0 @@ - -
-To represent generic constraints on real-valued functions, this class can parse -String expressions in prefix notation of the form: -
-<expr> ::= <constant-operator> | <functional-operator> "(" <arguments> ")"- - -Setting the constraint string: -Constant operators have an arity of zero. Examples are:
-<arguments> ::= <expr> | <expr> "," <arguments> -
-Additionally, any numerical strings can also be used; they are parsed to numeric constants. The literal n
-is parsed to the current number of problem dimensions.
-Notice that only the sum and prod operators may receive the literal X as input, standing
-for the full solution vector. Access to single solution components is possible by writing x0...x9
-for a problem with 10 dimensions.
-
-Thus you may write +(-(5,sum(X)),+sin(/(x0,pi)))
-and select 'lessEqZero' as relation to require valid solutions to fulfill 5-sum(X)+sin(x0/pi)<=0.
-
-Typical relations concerning constraints allow for g(x)<=0, g(x)==0, or g(x)>=0 for -constraint g. Notice that equal-to-zero constraints are converted to g(x)==0 <=> |g(x)-epsilon|<=0 for -customizable small values of epsilon. -
- -
-The handling method defines how EvA 2 copes with the constraint. Simplest variant is an
-additive penalty which is scaled by the penalty factor and then added directly to the fitness
-of an individual. This will work for any optimization strategy, but results will depend on
-the selection of penalty factors. Multiplicative penalty works analogously with the difference of
-being multiplied with the raw fitness.
-In the variant called specific tag, the constraint violation is stored in an extra field of any
-individual and may be regarded by the optimization strategy. However, not all strategies provide
-simple mechanisms of incorporating this specific tag.
-