## 1 Introduction
These methods improve PSO's ability to find the optimum; however, many come at the expense of notably larger preprocessing requirements or by superficially increasing the population size. The aim of DPSO is to improve the fitness with relatively small increases in computational demand by limiting the scale of the modifications. DPSO's approach is less complicated, randomly selecting dimensions to apply global and local best attractions based on a fixed probability value. The selection of dimensions is not of a fixed number, nor is it based on pre-processed information about the local search space, thus maintaining a relatively low computational cost. The binary nature of DPSO's attractors is closer to casting a net-like structure of potential attraction points on the search space solely based on the particles' current location and the location of the local and global best points; i.e., it does not require pre-processing or a look-ahead feature. The velocity limitations imposed on DPSO are similar to the boundary restrictions of the population migration PSO's (PMPSO). However, DPSO's limits do not change in scale over time and only restrict each particle's maximum viable search space for the next iteration relative to its current location [12]. Velocity restriction-based improvised PSO (VRIPSO) uses a dynamic method of limiting velocity and relies on an escape velocity mechanism to explore beyond its velocity limit [13]. Alternatively, DPSO warps individuals who appear to be stagnating, while VRIPSO occasionally allows particles to escape the imposed velocity limit. Warping has been applied to all algorithms in this article as a general rule to ensure that it does not become a primary difference in results. Although VRIPSO's approach may allow for faster convergence in some circumstances, DPSO's warping condition recycles particles to increase the exploration of dimensions that may not have been sufficiently covered. Tabu search PSO has an interesting feature, where the fitness results of particles and the respective locations are saved for a specified number of iterations [8]. This type of logging has been applied for all algorithms covered in this article but without removing older records. By recording the fitness of a location for later, it is possible to skip the function evaluation step and, over time, to significantly reduce the time spent on iterations with repeated positions. An element of reserving the position was also included in all algorithms to ensure that multiple particles on the same position would only require one shared evaluation. Another feature found in VRIPSO is that it adjusts momentum over time [13]. Continuous PSO has a more in-depth version of this momentum feature in that it determines a gradient by which to adjust the momentum factors, encouraging movement in directions with greater improvements and not just in the current direction [14]. Though these dynamic methods are appealing, DPSO was limited to using random noise injection, which can either dampen or excite the particle's movement irrespective of the perceived gradient or its direction of travel. These random perturbations allow for greater degrees of exploration along the dimensions lacking in representation or for which movement has stagnated. Given that this research is interested in solving high-dimensional problems with relatively sparse population sizes, it is important to ensure that particles do not restrict themselves to a subset of searchable dimensions while neglecting the rest.