Numerous variants of even a basic PSO algorithm are possible. For example, there are different ways to initialize the particles and velocities e.
Particle swarm optimization - Wikipedia
Some of these choices and their possible performance impact have been discussed in the literature. A series of standard implementations have been created by leading researchers, "intended for use both as a baseline for performance testing of improvements to the technique, as well as to represent PSO to the wider optimization community. Having a well-known, strictly-defined standard algorithm provides a valuable point of comparison which can be used throughout the field of research to better test new advances.
New and more sophisticated PSO variants are also continually being introduced in an attempt to improve optimization performance. There are certain trends in that research; one is to make a hybrid optimization method using PSO combined with other optimizers,    e. Another research trend is to try and alleviate premature convergence that is, optimization stagnation , e.
The multi-swarm approach can also be used to implement multi-objective optimization. Another school of thought is that PSO should be simplified as much as possible without impairing its performance; a general concept often referred to as Occam's razor.
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Simplifying PSO was originally suggested by Kennedy  and has been studied more extensively,     where it appeared that optimization performance was improved, and the parameters were easier to tune and they performed more consistently across different optimization problems. Another argument in favour of simplifying PSO is that metaheuristics can only have their efficacy demonstrated empirically by doing computational experiments on a finite number of optimization problems.
This means a metaheuristic such as PSO cannot be proven correct and this increases the risk of making errors in its description and implementation. A good example of this  presented a promising variant of a genetic algorithm another popular metaheuristic but it was later found to be defective as it was strongly biased in its optimization search towards similar values for different dimensions in the search space, which happened to be the optimum of the benchmark problems considered.
This bias was because of a programming error, and has now been fixed.
Multi-objective Swarm Intelligence
Initialization of velocities may require extra inputs. Another simpler variant is the accelerated particle swarm optimization APSO ,  which also does not need to use velocity and can speed up the convergence in many applications. A simple demo code of APSO is available.
PSO has also been applied to multi-objective problems ,    in which the objective function comparison takes pareto dominance into account when moving the PSO particles and non-dominated solutions are stored so as to approximate the pareto front. As the PSO equations given above work on real numbers, a commonly used method to solve discrete problems is to map the discrete search space to a continuous domain, to apply a classical PSO, and then to demap the result. Such a mapping can be very simple for example by just using rounded values or more sophisticated.
However, it can be noted that the equations of movement make use of operators that perform four actions:. But all these mathematical objects can be defined in a completely different way, in order to cope with binary problems or more generally discrete ones , or even combinatorial ones. From Wikipedia, the free encyclopedia.
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