An artificial neural network consists While Turing and von Neumann environmental selection.
of interconnected artificial neurons.³¹ dreamed of understanding the brain, Evolutionary systemshavefirstbeen
Modeled after the natural neurons, and possibly designing an intelligent viewed as optimization processes in the
each artificial neuron A has n real-val- computer that works like the brain, evo- 1930s. The basic idea of viewing evolu-
ued inputs, x₁, x₂, …, x_n, and it computes lutionary computation⁶ emerged as an- tion as a computational process gained
its own primitive function f_A as follows. other computation paradigm that drew momentum in the 1960s, and evolved
Usually, the inputs have associated its inspiration from a completely dif- along three main branches.¹³ Evolution
weights, w₁, w₂, …, w_n. Upon receiving ferent part of biology: Darwinian evolu- strategies use evolutionary processes
the n inputs, the artificial neuron A tion. Rather than emulating features of to solve parameter optimization prob-
produces the output f_A(w₁x₁ + w₂x₂ + … a single biological organism, evolution- lems, and are today used for real-val-
+ w_nx_n). An artificial neural network is ary computation draws its inspiration ued as well as discrete and mixed types
a network of such neurons, and thus from the dynamics of an entire species of parameters. Evolutionary program-
a network of their respective primitive of organisms. An artificial evolution- ming originally aimed at achieving the
functions. Someneuronsareselectedto ary system is a computational system goals of artificial intelligence via evo-
be the output neurons, and the network based on the notion of simulated evo- lutionary techniques, namely by evolv-
function is a vectorial function that, for lution. It features a constant- or vari- ing populations of intelligent agents
n inputvalues, associatestheoutputsof able-size population of individuals, a modeled, for example, as finite-state
the m output neurons. Note that differ- fitness criterion according to which the machines. Today, these algorithms
ent selections of the weights produce individuals of the population are being are also often used for real-valued pa-
rameter optimization problems. Ge-
netic algorithms originally featured a

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population of individuals encoded as fixed-length bit strings, wherein mutations consisted of bit-flips according to a typically small, uniform mutation rate, the recombination of two parents consisted of a cut-and-paste of a prefix of one parent with a suffix of the other, and the fitness function was problem-dependent. If the initial individuals were to encode possible solutions to a given problem, and the fitness function were designed to measure the op-timality of a candidate solution, then such a system would, in time, evolve to produce a near-optimal solution to the initial problem. Today, genetic algorithms are also modified heavily for

different network functions for the evaluated, and genetically inspired op- applications to real-valued parameter same inputs. Based on given input-out- erators that produce the next genera- optimization problems as well as many put pairs, the network can “learn” the tion from the current one. In an evolu- types of combinatorial tasks such as, weights w₁, …, w_n. Thus, there are three tionary system, the initial population of for example, permutation-based prob-important features of any artificial neu- individuals is generated at random or lems. As another application, if the ral network: the primitive function of heuristically. At each evolutionary step, individuals were computer programs, each neuron, the topology of the net- the individuals are evaluated according then the genetic algorithm technique work, and the learning algorithm used to a given fitness function. To form the would result in “the fittest” computer to find the weights of the network. One next generation, offspring are first gen- programs, as is the goal of genetic pro- of the many examples of such learning erated from selected individuals by us- gramming.²² algorithms is the “backwards propaga- ing operators such as mutation of a par- Cellular automata, neural compu-tion of errors.” Back-propagation is a ent, or recombination of pairs or larger tation, and evolutionary computation supervised learning method by which subsets of parents. The choice of par- are the most established “classical” the weights of the connections in the ents for recombination can be guided areas of natural computing. Several network are repeatedly adjusted so as by a fitness-based selection operator, other bio-inspired paradigms emerged to minimize the difference between the thus reflecting the biological principle more recently, among them swarm in-actual output vector of the net and the of mate selection. Secondly, individu- telligence, artificial immune systems, desired output vector. Artificial neural als of the next generation are selected artificial life, membrane computing, networks have proved to be a fruitful from the set of newly created offspring, and amorphous computing. paradigm, leading to successful novel sometimes also including the old par- A computational paradigm strad-applications in both new and estab- ents, according to their fitness—a pro- dling at times evolutionary computa-lished application areas. cess reflecting the biological concept of tion and neural computation is swarm