## 1 Introduction  
Particle swarm optimization (PSO) algorithms are reputed for optimizing complex multidimensional problems with a balanced trade-off between reliability of convergence and computational efficiency. PSO relies on momentum, local/personal best attraction, and global best attraction to find a global optima. Although PSO tends to be slightly slower than differential evolution (DE), it can produce similar or even slightly better convergence rates depending on the problem at hand [1,2]. PSO also tends to be faster and more efficient than genetic algorithms (GAs), which rely heavily on random mutation and cross-over. The work reported in this article builds on prior work where PSO was modified to optimize each dimension semi-independently [3]. This variant, called dimension-wise particle swarm optimization (DPSO), aims to increase the convergence reliability at the cost of some additional time complexity. The focus of the original article [3] was on how varying the ratio of particles to dimensions and per-dimension sensitivity--henceforth referred to as ill-conditioning--affected the algorithm's ability to find the global optimum. These evaluations were carried out with scarce populations, i.e., with more dimensions than particles, which increased the difficulty and importance of exploration. The same article also introduced self-tuning as a method of PSO parameter selection. These configurations are carried over to this work with some changes in the rules, an inclusion of DE and GA in the evaluation, and an increase in the number of functions to be optimized. An in-sample evaluation with some degree of similarity to each out-of-sample function is used for each optimizer's parameter optimization process. The most suitable optimizer parameters are determined using self-tuning. This way, the algorithm of interest can explore and change its parameters during the in-sample test should it find a statistically better set w.r.t. fitness. For the out-of-sample tests, each algorithm must rely on the generally optimized parameters derived from the self-tuning process. The results are evaluated based on the statistical mean and standard deviation of each algorithm's global optimum results for the 24 problem functions used. These benchmark functions are composed of 7-, 14-, and 21-dimensional spaces with randomly generated offsets, ill-conditioning, rotation, and overlaps. To ensure the results are reliable, each problem function is randomly generated and evaluated 30 times. Related WorkPSO has a wide range of modifications, which address specific aspects of the algorithm or the problem of interest. PSO can be improved by integrating other algorithms into its process--such as neural networks and support vector machines--or by modifying the fundamental rules for particle movement [4; 5; 6; 7; 8]. For relatively high dimensional problems, it is usually preferred to selectively optimize a subset of dimensions at a time [9]. By occasionally changing the subset, progressive convergence towards the overall global optimum can be improved. DPSO differs from other variants such as dual guest PSO (DGPSO) in that it does not rely on preprocessing steps to identify, order, and select the dimensions with the greatest sensitivity [9]. A simpler method of feature selection borrows from the GA, where crossover is used to combine the particle's current location, a predetermined relevant feature vector, the global best position, and its local best position. However, this approach uses a look-ahead approach, evaluating the three candidate locations before choosing the best one as the new individual, effectively tripling the population size during evaluation [10]. PSO with an enhanced learning strategy and crossover operator uses a weighted sum of local bests over all particles based on a normalized fitness distribution to achieve variations in attractor locations [11]. DGPSO's approach can be described as a divide-and-conquer approach, while PSO with crossover hybridizes features from GA into PSO.