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88 I.K. Nikolos et al.

Fig. 1. A quadratic (p = 2) 2-dimensional B-Spline curve, produced using a uniform
non-periodic knot vector, and its control polygon

2.2 Fundamentals of Evolutionary Algorithms (EAs)

EAs are a class of search methods with remarkable balance between exploita-
tion of the best solutions and exploration of the search space. They combine
elements of directed and stochastic search and, therefore, are more robust
than directed search methods. Additionally, they may be easily tailored to
the specific application of interest, taking into account the special character-
istics of the problem under consideration [38, 39, 30].
The natural selection process is simulated in EAs, using a number (popu-
lation) of individuals (candidate solutions to the problem) to evolve through
certain procedures. Each individual is represented through chromosome -a
string of numbers (bit strings, integers or floating point numbers), in a sim-
ilar way with chromosomes in nature; it contains the design variables of the
optimization problem. Each individual’s quality is represented by a fitness
function tailored to the problem under consideration.
Classic Genetic Algorithms (GAs) use binary coding for the representation
of the genotype. However, floating point coding moves EAs closer to the prob-
lem space, allowing the operators to be more problem specific; this provides a
better physical representation of the space constraints. Additionally, directed
search techniques gain physical meaning and they are easily applicable.
In general, EA starts by generating, randomly, the initial chromosome
population with their genes (the design variables in the case of floating point
coding) taking values inside the desired constrained space of each design vari-
able. The lower and higher constraints of each gene may be chosen in a way
that specific undesirable solutions may be avoided. Although the shortening of
the search space reduces the computation time, it may also lead to sub-optimal
solutions, due to the lower variability between the potential solutions.