# An Improved Particle Swarm Optimization Algorithm for Data Classification
## 1 Introduction
In addition, many modifications have been made to the PSO algorithm to improve its convergence. Inertia weight is introduced and gives more control over the particle capabilities for exploration (searching the entire space to gain a solution) and exploitation (searching the neighbourhood of the fittest solution). [PERSON] [27] introduced the concept of Opposition-Based Learning (OBL), which has so far been used to accelerate backpropagation learning on neural networks [28] and reinforcement learning. The purpose of OBL is to check the estimate (random guess) and its corresponding opposite estimate (opposite guess) at the same time to obtain a more approximate value for the current candidate solution [29]. It is used to generate opposite populations that inspire the real world's opposite. The probability of finding the best solution is increased through the opposite solution. It improves algorithms' performance and finds the best possible solution in search space [30]. OBL is used in many areas, such as agriculture for preserving water crops, soil purification, medical fields for disease diagnosis, scheduling of agricultural work [31]. It is applied in many well-known algorithms such as the Bat algorithm [32; 33], PSO [34], Grey Wolf Optimizer (GWO) [35], Harmony Search (HS) [36], Differential Evolution (DE) [37] and Artificial Neural Networks (ANNs). The distribution of random numbers is divided into three major categories: probability sequences, i.e., Exponential, Beta, Gamma, Lognormal, Quasi-random sequence, i.e., Halton, Van der corput, Hamersley, Sobol, Faure [38], and the pseudo-random sequences Multiply with-carry, Linear congruential generator, Mersenne twister, Philox, and Threefry [39]. A probability sequence is a sequence of continuous probabilities according to a particular distribution's scale factor and shape [40]. Pseudo-random sequences and quasi-randomsequences outperform for a globally optimal solution due to cover all search spaces. We used QRS (Sobol sequence (S), Halton sequence (H), Faure sequence (F), Gaussian (G), and Lognormal (LN)) for the initialisation of the population. This behavior is more persevering and intolerable for multimodal problems, as it contains many local and global optimums. The most considerable factor for this deprived performance can be the insufficient distribution of the population in the search area, i.e., to conclude that if the initial population does not search the complete search space adeptly, it is difficult to locate the robust solution points, and thus the results omit the global best solution. This problem can be overcome by adding the most structured and organized random distribution for population initialization. Random number sequences vary with respect to the nature of their morphological design, i.e., quasi-random sequences, pseudo-random sequences, and probability distribution. Due to this fact, a novel initialisation population method used a Quasi-random sequence (Faure) to create the initialisation of the swarm, and through the opposition-based method, an opposite swarm was generated. We proposed an Opposition rank-based inertia weight approach to adjust inertia weights of particles to increase the performance of the standard PSO. The proposed algorithm (ORIW-PSO-F) has been tested to optimise the weight of the feed-forward neural network for fifteen data sets taken from UCI. This paper proposes new variants of the PSO algorithm, Faure, with opposition-based PSO-ranked inertia weight (ORIW-PSO-F). The proposed algorithms improve global search ability and solve real-world classification problems. The proposed algorithms have two main effective improvements in initialisation strategies (Faure) with Opposition based learning and rank-based inertia weight. We present a new Quasi-random initialisation strategy (Faure) to initialise the search space particles, and opposite particles generated using Opposition-based learning. Particle inertia weight was updated with opposition rank-based inertia weight-balancing exploration and exploitation.