# Particle Swarm Optimization Based on a Novel Evaluation of Diversity
## 1 Introduction
[PERSON]'s group [35; 36] presented a dynamic multi-swarm PSO with small sub-swarms frequently regrouped using various schedules. [PERSON] et al. [37] hybridized the dynamic multi-swarm PSO with a new cooperative learning strategy in which the worst two particles learned from the two better sub-swarms. [PERSON] et al. [21] proposed a dynamic multi-swarm PSO with a differential learning strategy. It combined the differential mutation into PSO and employed Quasi-Newton method as a local searcher. PSO with hybrid strategies: To improve the performances of PSO, combining excellent strategies into PSO has been shown to be an effective approach. For example, [PERSON] et al. [38] combined PSO with gravitational search algorithm for efficiently training feedforward neural networks. [PERSON] et al. [39] combined PSO with a back-propagation algorithm to efficiently train the weights of feedforward neural networks. [PERSON] et al. [40] developed a hybrid of dynamic multi-swarm PSO with a gravitational search algorithm for improving the performance of PSO. [PERSON] et al. [41] combined PSO with orthogonal experimental design to discover an excellent exemplar from which the swarm can quickly learn and speed up the searching process. [PERSON] et al. [31] hybridized PSO with a covariance matrix adaptation strategy to improve the solutions in the latter phases of the searching process. [PERSON] [42] combined PSO with genetic algorithms (GA): creating a new population by replacing weak particles with excellent ones via selection, crossover, and mutation operators. [PERSON] and [PERSON] [43] combined PSO with a gradient-based quasi-Newton SQP algorithm for optimizing engineering structures. [PERSON] and [PERSON] [44] combined PSO with grey wolf optimizer for improving the convergence rate of the iterations. [PERSON] et al. [45] combined PSO with a bacterial foraging optimization for 3D printing parameters of complicated models. [PERSON] and [PERSON] [46] combined PSO and the simulated annealing algorithm for processing dynamic task scheduling. [PERSON] [47] introduced opposition-based learning (OBL) into PSO to improve the swarm's performance in noisy environments. [PERSON] et al. [48] embedded the comprehensive learning particle swarm optimizer (CLPSO) with local search (CL) to take advantage of both the exploration ability of CLPSO and the exploitation ability of CL. Many scholars have conducted intensive research on the theory and applications of the PSO algorithms. However, there are still some shortcomings. For example, the parameter adaptive adjustment strategy cannot truly reflect the evolution of the population, and the particle swarm cannot effectively jump out of local optimal areas. To address these issues, a particle swarm optimization variant based on a novel evaluation of diversity (PSO-ED) is proposed in this paper and the major innovation is listed as follows:We propose a novel approach to compute swarm diversity based on the particles' positions. By a series of encoding operations on the sub-space of the search space and the aid of hash table, the diversity can be determined in \(O(N_{s}D)\) time, and it can reflect the distribution of the swarm without any information compression. Section 3.2.1 details the related techniques. 2. We proposed a novel notion of exploration degree based on the diversity in the exploration, exploitation, and convergence states. It reflects the degree of demand for the swarm's dispersion, and it can be used to realize adaptive update of the inertial weight of the PSO's velocity function. Section 3.2.3 details the related techniques. 3. We proposed a disturbance update mode based on the particles' fitness. We replace the positions of the poor particles with new positions obtained by disturbing the best position. It saves the cost of function evaluations and improves convergence efficiency. Section 3.5 details the related techniques.