Influence of Weighting factor and Crossover constant on the behavior of Differential Evolution Algorithms with a Penalty Function approach
Journal
ICT Innovations 2018, Web Proceedings
Date Issued
2018
Author(s)
Salkoski, Rasim
Abstract
Differential Evolution (DE) is one of the most popular evolutionary
optimization technique on continuous domains based on simplicity, effectiveness
and robustness. The weighting factor(F) and crossover constant(CR) allows the
construction of a new trial element based on the current and mutant elements.
The crossover constant controls which and how many components are mutated
in each element of the current population. The work in the present paper aims to
analyze the impact the weighting factor and the crossover constant, has on the
behavior of DE. The influence of the crossover constant on the distribution of the
number of mutated components and on the probability for a component to be
taken from mutant vector (mutation probability) is analyzed for several variants
of weighting factor and crossover factor, including classical binomial and
exponential strategies. For each weighting and crossover variant the relationship
between the crossover and mutation probability is identified and its impact on the
choice and adaptation of control parameters is analyzed numerically and
graphically. Ten different strategies (variations) of DE with penalty function
approach are analyzed with various population sizes, crossover and weighting
factors and applied to the problem of minimizing the cost of the active parts of
the power objects. Constraints resulting from international specifications are
taken into account. The Objective functions that are optimized are minimizations
dependent on multiple input variables. All constraints are normalized and
modeled as inequalities.
optimization technique on continuous domains based on simplicity, effectiveness
and robustness. The weighting factor(F) and crossover constant(CR) allows the
construction of a new trial element based on the current and mutant elements.
The crossover constant controls which and how many components are mutated
in each element of the current population. The work in the present paper aims to
analyze the impact the weighting factor and the crossover constant, has on the
behavior of DE. The influence of the crossover constant on the distribution of the
number of mutated components and on the probability for a component to be
taken from mutant vector (mutation probability) is analyzed for several variants
of weighting factor and crossover factor, including classical binomial and
exponential strategies. For each weighting and crossover variant the relationship
between the crossover and mutation probability is identified and its impact on the
choice and adaptation of control parameters is analyzed numerically and
graphically. Ten different strategies (variations) of DE with penalty function
approach are analyzed with various population sizes, crossover and weighting
factors and applied to the problem of minimizing the cost of the active parts of
the power objects. Constraints resulting from international specifications are
taken into account. The Objective functions that are optimized are minimizations
dependent on multiple input variables. All constraints are normalized and
modeled as inequalities.
Subjects
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