Методы оптимизации
Математика
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Clerc M. Particle Swarm Optimization
ISTE Ltd, 2006. – 244 p.

This book is the first to deal exclusively with particle swarm optimization. In his Swarm Intelligence [KEN 01], originally entitled Particle Swarm Optimization (PSO), my friend Jim Kennedy has devoted three chapters out of eleven to this subject, above all as an illustration of the more general concept of collective intelligence without dwelling on the details of practical implementation.
For this book, my goal was simpler: to give you the concepts and tools necessary and sufficient for the resolution of problems of optimization, including the codes of various programs.
After having assimilated the contents of the first and more important part, you should be able to apply PSO to practically any problem of minimization of an assessable function in a continuous, discrete or mixed search space. You will also be able to deal with multi-objective problems, either as such, or as methods of taking into account complex constraints of a mono-objective problem.

The book is structured in two parts. The first describes PSO in detail, from a very simple primitive parametric version to an adaptive version that does not require the user to supply parameters. The discussion thread is a benchmark set of six test functions which enable us to compare the influence of the parameters and search strategies. The final chapter of this part focuses on some more realistic problems.
The second part is entitled Outlines, indicating that the items discussed are not dealt with in detail, as this would go beyond the scope of this book. It is primarily about parallelism, the canonical PSO (a basis, among others, of the combinatorial PSO) and the dynamics of the swarms. The final chapter very briefly presents some techniques and alteatives such as the stop-reset, the multi-swarm and the dynamic PSO (optimization of a function changing during the very process of search). The interested reader will be able to refer to the documents cited.
Many chapters end with a more mathematical part. This part specifies or justifies some of the assertions made in the body of the text but is by no means necessary for the comprehension of those ideas. It can thus be comfortably skipped if you do not have the taste or the time for it.
Various versions of PSO are studied, some in a very thorough manner, others very briefly. The diagram below shows the links between them and the levels of detail of the presentations. In particular, the significant field of specific implementations of PSOs is only skimmed through. It would be, in itself, worth a later work, particularly as the methods implemented are very often hybrid, i.e. use several methods of optimization jointly, in particular for difficult combinational problems.
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