Soft Computing

Evolutionary algorithms (EAs) are a broad class of stochastic optimization algorithms, inspired by biology and in particular by those biological processes that allow populations of organisms to adapt to their surrounding environment: genetic inheritance and survival of the fittest. These concepts were introduced in the 19th century by Charles Darwin [50] and are still today widely acknowledged as valid, even though complemented with further details [52].

THE functioning of the brain has always fascinated people. The human brain, and also the brain of some animals, is indeed capable of astonishing achievements such as remembering, recognizing patterns, and associating, among many others. The way in which these tasks are performed appears to be quite different in nature from standard computation as we know it, that is, in the Turing sense [146]. Indeed, the brain is a massively parallel, highly connected assemblage of an astronomical number of slow processing units that collectively work on these difficult tasks and allow us to function smoothly and effortlessly. These units or cells are called neurons, they are of several different types, and they work in an analog way by propagating electrical currents of chemical origin along connections. The details of how neurons function are very intricate and need not concern us here but the main points are simple and worth some study. The neuron has three main components: the soma, the dendrites, and the axon (Figure 2.1).

Fuzzy set theory was initiated by Lotfi Zadeh in the mid-sixties. In 1965 Zadeh, then chair of the Electrical Engineering Department at the University of California at Berkeley, published a paper called “Fuzzy Sets” [257].

ONE of the reasons for the success of fuzzy logic is that the linguistic variables, values, and rules allow the engineer to seamlessly translate human knowledge into systems that work. What is a strength in some cases, however, is a weakness in others. If expert knowledge is not available, there is no ready made recipe to put together a fuzzy system from scratch, as is the case with more conventional techniques. This is where evolutionary algorithms come into play.

This Chapter deals with neuro-fuzzy systems, i. e., those soft computing methods that combine in various ways neural networks and fuzzy concepts. Each methodology has its particular strengths and weaknesses that make it more or less suitable in a given context. For example, fuzzy systems can reason with imprecise information and have good explanatory power. On the other hand, rules for fuzzy inference have to be explicitly built into the system or communicated to it in some way; in other words the system cannot learn them automatically. Neural networks represent knowledge implicitly, are endowed with learning capabilities, and are excellent pattern recognizers. But they are also notoriously difficult to analyze: to explain how exactly hey reach their conclusions is far from easy while the knowledge is explicitly represented through rules in fuzzy systems.

Synergy between evolutionary algorithms and fuzzy logic can occur in three complementary forms [220].

Many problem solving and heuristic techniques, including those typical of soft computing, have the distinctive feature of being directly or indirectly inspired by the observation of the natural world. If we look, for instance, into such processes as biological evolution or the functioning of the brain, we notice that many things are happening at the same time. The same can be said of many other natural systems such as insect societies and ecologies in general. In other words, these systems are natural massively parallel ones where more or less simple agents, such as nervous cells or ants, work jointly, in a distributed manner, to sustain the whole or to “solve” a problem. In short, many, if not all, natural systems work on a problem in a collective, concerted manner. Of course, collectively “solving” a problem does not have the same meaning in nature as in the sciences. Solving a problem might mean building a bee nest, firing a few million interconnected neurons in response to a stimulus, or just surviving in an animal ecology. There is no explicit concept of “optimizing” something, nor of finding a particular solution, just of adapting so as to maintain collective viability in the face of a changing environment.

The main theme of this book has been the integration and the synergistic cooperation of a few important soft computing methodologies that have their roots mainly in natural systems: artificial evolution, artificial neural networks, and fuzzy systems.