Talk:Particle swarm optimization

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    Comments of First Reviewer

    I think this is a well written short introduction to PSO. The article is balanced and does not mainly concentrate on the works of the authors (different from a few other articles in scholarpedia). I have just one remark concerning the external links: I do not think that there is a single main journal that publishes on PSO. The corresponding statement should be modified. Also Applied Soft Computing publishes much more on PSO than “Soft Computing”.

    Author's Answers to First Reviewer

    We agree with the reviewer that there is not a single main journal devoted to PSO research; however, Swarm Intelligence is a new journal that was started with the main objective of archiving the most important advancements in swarm-related fields. We have changed the sentence to include the Applied Soft Computing journal and to clarify the role of the Swarm Intelligence journal.

    Comments of Second Reviewer

    I also think that this is a compact and fairly accurate article. The origins of the algorithm are well explained, there is a breif overview of applications and alternative forms and the short list of references is well chosen. A few simple changes would enhance the article:

    1. The picture of the fully-connected topology is confusing. The drawing is too small for me to see what is connected to what.

    2. An over-reliance on strict mathematical notation neither makes the article more rigourous, nor more readable.

    3. \(\vec{U}^{\,t}_1\) and \(\vec{U}^{\,t}_2\) are *pseudorandom* numbers, and regeneration does not exclude \(\vec{U}^{\,t+1}_i\) = \(\vec{U}^{\,t}_i\)

    4. The asynchronous mode is more commonly used, and is easier to show here since there is only one loop over \(i\)

    5. Initial particle velocities are commonly chosen as vectors in the whole search space

    6. The algorithm is quite sensitive to the boundary conditions at the edge of the feasible search space. Since the feasible search space is usually a subspace of the infinite search space (assumed here), the algorithm description must describe what happens if the update rule put the particle outside the feasible space. Kennedy recommends "let them fly" i.e. no function evaluations outside the box, but don't inhibit the dynamics.

    Author's Answers to Second Reviewer

    1. We have reduced the number of particles (from 20 to 9) in order to help the reader to better understand the figure.

    2. We believe that many of the concepts behind the algorithm can be better described and understood using vectorial notation than using a verbose description of the implementation details.

    3. We agree with the reviewer in this point. The condition \(\vec{U}^{\,t+1}_i \neq \vec{U}^{\,t}_i\) has been removed.

    4. The asynchonous version is indeed more efficient; however, we believe that the synchronous version is easier to understand to non-experts (which represents most of the potential audience of this article).

    5. We agree with the reviewer that initializing the particles' velocities over the whole search space is the most common practice. This is now said in the article. Nevertheless, we say that velocities can also be initialized to zero or to small random numbers which is justified given the fact that particles' positions are already initialized randomly. When velocities are initialized randomly, care should be taken not to have too large initial velocities, as step size then might be too large, and particles may leave the search space.

    6. We added a short description of the constraint handling problem and a reference to existing approaches to tackle it.

    Comments of Third Reviewer

    This is a good introductory article on particle swarms. There are a couple of places that might need modification.

    Under the social psychology discussion in the "History" section, I think it would be appropriate to give credit to social impact theory, and in particular cite the paper by Nowak, Szamrej, and Latane (1990) in Psychological Review. I don't have the entire reference at hand, it's easy to find. That paper affected dynamical systems science well beyond particle swarms, and the simulations reported there were one of the most important antecedents to particle swarms.

    I am glad to see the population topology presented correctly. On the other hand, saying "Alternatively, the neighborhood best can be selected as the current best particle" is unclear. Do you mean to compare the evaluations of all the particles' current positions, or their previous bests? The former would be CPU-intensive and highly unorthodox. If the latter, the gbest arrangement is not really an "alternative," it is simply what happens in the topology where all particles are connected to each other. I suspect the formula in that sentence is not what you intend, especially the \(f(x_j)\). I see you use \(f(b_j)\) in your pseudocode, which is right.

    "The three terms in the velocity update rule characterize the local, simple behaviors that particles follow." -- the rules are simple, the behaviors of the particles are not.

    In the Bare-bones formula, since you give a superscript for \(t\), you may as well give \(ij\) subscripts to \(\mu\) and \(\sigma\) for clarity.

    Author's Answers to Third Reviewer

    We added a reference to Nowak et al.'s article and a reference to a text where James Kennedy mentions it as an inspiration source.

    We removed the sentence concerning the alternative selection method of a particle's best neighbor.

    We removed the adjective "simple" used to qualify the particles' behavior.

    We added the subscripts \(ij\) to the Bare-bones PSO formula.

    Additional comments of First Reviewer

    I am a bit confused because you say that "We agree with the reviewer that there is not a single main journal devoted to PSO research" and that "Swarm Intelligence is a new journal that was started with the main objective of archiving the most important advancements in swarm-related fields" and you have clarifies the role of Swarm Intelligence. But in the version of the article that I can seen it still says "it is the main journal on Swarm Intelligence" so only PSO is exchanged by the broader area of Swarm Intelligence. But nothing like "it is a journal that has the objective ....".

    Answer to additional comments of First Reviewer

    We have now modified the sentence, which becomes: Swarm Intelligence (whose main objective is to archive the most important advancements in the swarm intelligence field) regularly publishes articles on PSO. We also introduced a few minor stylistic improvements.

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