any PSO topology. The aims are to improve the performance of PSO overall, including faster global convergence, higher solution quality, and stronger robustness. However, such studies do not provide theoretical evidence to actually prove their claims. Adaptive mechanisms Without the need for a trade-off between convergence ('exploitation') and divergence ('exploration'), an adaptive mechanism can be introduced. Adaptive particle swarm optimization (APSO) features better search efficiency than standard PSO. APSO can perform global search over the entire search space with a higher convergence speed. It enables automatic control of the inertia weight, acceleration coefficients, and other algorithmic parameters at the run time, thereby improving the search effectiveness and efficiency at the same time. Also, APSO can act on the globally best particle to jump out of the likely local optima. However, APSO will introduce new algorithm parameters, it does not introduce additional design or implementation complexity nonetheless. Variants Numerous variants of even a basic PSO algorithm are possible. For example, there are different ways to initialize the particles and velocities (e.g. start with zero velocities instead), how to dampen the velocity, only update pi and g after the entire swarm has been updated, etc. 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." The latest is Standard PSO 2011 (SPSO-2011). Hybridization 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.g., combined PSO with biogeography-based optimization, and the incorporation of an effective learning method. Alleviate premature convergence Another research trend is to try and alleviate premature convergence (that is, optimization stagnation), e.g. by reversing or perturbing the movement of the PSO particles, another approach to deal with premature convergence is the use of multiple swarms (multi-swarm optimization). The multi-swarm approach can also be used to implement multi-objective optimization. Finally, there are developments in adapting the behavioural parameters of PSO during optimization. Simplifications