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Exploratory Toolkit for Evolutionary and Swarm-Based Optimization\
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Cell["\<\
Namrata Khemka
Christian Jacob\
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"Optimization of parameters or \[OpenCurlyDoubleQuote]systems\
\[CloseCurlyDoubleQuote] in general plays an ever-increasing role in \
mathematics, economics, engineering, and the life sciences. As a result, a \
wide variety of both traditional mathematical and nontraditional algorithmic \
approaches have been introduced to solve challenging and practically relevant \
optimization problems. Evolutionary optimization methods\[LongDash]in the \
form of genetic algorithms, genetic programming, and evolution strategies\
\[LongDash]represent nontraditional optimization algorithms that draw \
inspiration from the processes of natural evolution. Particle swarm \
optimization is another set of more recently developed algorithmic optimizers \
inspired by social behaviors of organisms such as birds [",
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"] and social insects. These new evolutionary approaches in optimization are \
now entering the stage and are becoming very successful tools for solving \
real-world optimization problems [",
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Calgary [",
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"]. In this particular biomechanical application, numerical optimization \
algorithms are used to design equipment for sports activities. The involved \
simulations of muscle movements are very time consuming and high dimensional, \
thus making their evaluation costly and difficult. Simulating a soccer kick \
is an example of a model that investigates muscle activation patterns within \
the leg and foot when kicking a soccer ball toward the goal. The specific \
objective in this case is to obtain a high ball speed, in order to minimize \
the goal keeper\[CloseCurlyQuote]s chances of catching the ball. In 1998, \
Cole applied a ",
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learned from our comparison studies of the evolution- and swarm-based \
optimizers on a set of selected benchmark functions. These benchmark studies \
turned out to be extremely useful in understanding the intricacies in \
performance regarding three optimizers: (1) the originally used ",
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functions in two, four, and 10 dimensions. These findings are projected to \
performance characteristics that were found in the real-world application of \
the discussed soccer-kick model, which poses a 56-dimensional optimization \
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under study. Consequently, we gain a better understanding of the algorithms \
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Griewangk\[CloseCurlyQuote]s function has hundreds of local optima in the \
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