**The Particle Swarm**

The chapter starts out by talking about some concepts that were covered in the first half of the book, and why they make the particle swarm an obvious solution. The area they cover with the largest amount of depth is the adaptive culture model. When discussing this area they talk about the three primary concepts of the sociocognitive underpinnings, which are evaluate, compare, and imitate. Then, they go into discussion about each of these aspects.

The next area of focus is the model of binary decision. They begin by talking about what a binary decision model is. Then, they discuss the two types of neighborhoods that are used in binary modes: lbest (local), and gbest (global). They go into depth about each of these methods, and then begin talking about how you evaluate binary strings. There is then discussion of the reasoned action model; this is addressed when trying to figure out how to improve cognitive fitness. From there, they begin developing mathematical models for determining the probability of and individual deciding yes or no. After discussing the aspects of the mathematical backings, they give an example algorithm for optimizing goodness.

The next area of discussion is the testing of the binary algorithm using the De Jong test suite. In this section they look at several different functions, their dimensionality, and the performance of the binary swarm on the different functions. There are some bit string examples in order to help understand some of the work done by the binary particle swarm on the functions.

As in any field, there is some controversy regarding the evaluation of an algorithm. The discussion says that a majority of this strife is created by David Wolperet and William Macready, whom state that the performance of all algorithms is the same when averaged over all possible problems (or costs). The “no free lunch” theorem shows how all algorithms can be considered equal when averaged across the problem space. The section then describes the NFL problem, and then proceeds to defend itself against the argument, stating that you can determine which algorithm is better towards finding a goal, even if it is not necessarily good at finding answers to questions that no one would ever ask.

The next area of discussion is multimodality. In this context they are referring to problems that have more than one solution (or global optimum). After discussion what a multimodal problem is, they go into discussion as to why these problems are difficult for genetic algorithms to handle. They talk about three forms of genetic algorithms (mutation and crossover, crossover only, and mutation only), and how they perform on various problems against number evaluations and their peak fitness. Then, just for kicks they try to show how particle swarm can handle these problems better, and illustrate the PS performance against the GA’s performance.

“Minds as parallel constraint satisfaction networks” is the next focus of interest. They start out by talking about Hopfield, and his contributions to the field. Next, they begin discussion of binary and continuous Hopfield networks. They begin talking about having setup a binary particle swarm to optimize the network structure proposed by Hutchins. They then go into an example and explain the way the PS optimized Hutchins’ problem.

The next section deals with particles swarms that handle continuous numbers. The section begins by explain how this is the “real” particle swarm, and sets up for the explanation. The first area they discuss is the particle swarm in real number space. Essentially, particles in a real number space are connected to topographical neighbors, and neighbors tend to cluster in the same regions of search space. After that discussion they go into some mathematical background. There is then discussion of pseudocode for particle swarm optimization in continuous numbers. The next area they address, are the issues associated with the implementation of this version of the particle swarm. Having setup the foundation they go into an example of the particle swarm optimization of neural net weights. The section continues with a discussion of real world applications of the particle swarm. In this case they are referring to PSO for “training” neural nets rather than using back propagation.

The next section focuses on the hybrid particle swarm. They begin by briefly explain what a hybrid system would consist of, and then try to explain why you might want to implement such a system. They use a system that would diagnosis various abdominal diseases, and explain how some sections are more easily computed using binary PS, whereas more complex symptoms are computed using real PS. The presentation is merely hypothetical, and the hybrid system is still considered and on going research area.

The following section takes a look at science as a collaborative search. The section talks about null hypothesis testing, and confirmation bias. There is also discussion about the difference between truth and certainty. Then they talk about the establishment of paradigms in the scientific community. There is then discussion about mistakes that have been done when dealing with human social search, and problem space, which they believe is due to tendency of individuals to move towards self and social confirmation of hypotheses. The premise of which is logically invalid, results in excellent information processing capabilities.

The final section takes a quick look at emergent culture, and immergent intelligence. They begin by talking about trends that develop throughout multiple iterations within the population of the PS. Then, they talk about polarization, and optimal solutions either consuming lesser solutions, or compromising and thus moving away from an optimum. Then they begin to talk about he emergence of cultures within the programs, and how they are not hard coded, and care difficult to predict. Next, they discussed the process of the immergence of cognitive adaptation among the individuals. The section is ended with their perspective on the importance of the emulation of cognitive positions allowing individuals to adapt.