In response to sudden high-traffic signal demand caused by massive device access in urban Internet of Things environments, Unmanned Aerial Base Stations (UAV-BSs), as dynamic network nodes, can effectively enhance the coverage capacity and quality of communication network services. However, how to efficiently deploy UAV-BSs in complex urban environments while meeting the differentiated communication needs of common and special areas remains an urgent challenge. In this paper, we propose an Average Hamming Distance Modified Particle Swarm Optimization (AHDPSO) algorithm based on the similarity calculation of DNA sequences, which firstly matrices the position and velocity information, and then calculates the average Hamming distance between particles using DNA mapping sequences to identify ’outlier points’. Further, the search guidance coefficientc3is introduced to quantify the guiding effect of ’outlier points’ on the global search, and the values ofc1,c2, andc3are dynamically adjusted by combining with the chaotic mapping, so as to balance the exploratory and developmental capabilities of the algorithm. Compared with the original particle swarm optimization algorithm, matrix particle swarm optimization algorithm, and seven other improved particle swarm optimization algorithms, the experimental results show that AHDPSO can quickly converge to the optimal solution. Compared with the traditional PSO algorithm, the absolute improvement values in the coverage of the entire region and special regions are 7.82% and 7.29%, respectively. It also shows good stability in different scenarios, indicating that the proposed algorithm has significant advantages in convergence speed, coverage, and stability.

Cognitive diagnosis (CD) is a fundamental task within computational social systems, essential for personalizing learning in intelligent education by assessing a learner’s fine-grained knowledge proficiency. A critical dilemma exists in designing cognitive diagnosis models (CDMs): conventional psychometric models are interpretable but often simplistic, while complex deep learning models achieve high accuracy at the cost of becoming uninterpretable “opaque models.” This lack of transparency is a major barrier to trust and adoption in real-world educational social systems. To address this challenge, this article introduces probabilistic model-building for cognitive architecture search (PMB-CAS), a novel framework that automates the discovery of CDMs that balance diagnostic accuracy with structural interpretability. We reframe the design process as a multi-objective optimization problem, balancing diagnostic performance [area under the curve (AUC)] with a refined, operator-weighted model interpretability score (MIS) that fairly assesses topological complexity. The framework navigates a flexible, tree-based search space using a probabilistic model-building strategy to efficiently discover promising architectures. Extensive experiments on benchmark datasets demonstrate that PMB-CAS discovers a portfolio of Pareto-optimal models that not only achieve state-of-the-art accuracy, outperforming established baselines, but also offer varying degrees of structural transparency. This work provides educators and stakeholders with a spectrum of trustworthy solutions and establishes a new paradigm for developing effective and verifiable models for computational social systems.

In multi-objective evolutionary neural architecture search (NAS), existing predictor-based methods commonly suffer from the rank disorder issue that a candidate high-performance architecture may have a poor ranking compared with the worse architecture in terms of the trained predictor.To alleviate the above issue, we aim to train a Pareto-wise end-to-end ranking classifier to simplify the architecture search process by transforming the complex multi-objective NAS task into a simple classification task. To this end, a classifier-based Pareto evolution approach is proposed, where an online classifier is trained to directly predict the dominance relationship between the candidate and reference architectures. Besides, an adaptive clustering method is designed to select reference architectures for the classifier, and an α-domination assisted approach is developed to address the imbalance issue of positive and negative samples. The proposed approach is compared with a number of state-of-the-art NAS methods on widely-used test datasets, and computation results show that the proposed approach is able to alleviate the rank disorder issue and outperforms other methods. Especially, the proposed method is able to find a set of promising network architectures with different model sizes ranging from 2M to 5M under diverse objectives and constraints.

In brain storm optimization (BSO), the convergent operation utilizes a clustering strategy to group the population into multiple clusters, and the divergent operation uses this cluster information to generate new individuals. However, this mechanism is inefficient to regulate the exploration and exploitation search. This article first analyzes the main factors that influence the performance of BSO and then proposes an orthogonal learning framework to improve its learning mechanism. In this framework, two orthogonal design (OD) engines (i.e., exploration OD engine and exploitation OD engine) are introduced to discover and utilize useful search experiences for performance improvements. In addition, a pool of auxiliary transmission vectors with different features is maintained and their biases are also balanced by the OD decision mechanism. Finally, the proposed algorithm is verified on a set of benchmarks and is adopted to resolve the quantitative association rule mining problem considering the support, confidence, comprehensibility, and netconf. The experimental results show that the proposed approach is very powerful in optimizing complex functions. It not only outperforms previous versions of the BSO algorithm but also outperforms several famous OD-based algorithms.

Swarm intelligence algorithms have been widely and successfully used to optimize many science and engineering problems, the collective behavior of the agents lead to the emergence of intelligence. These interactions among agents can be classified into three categories: exploring, emulating and learning. Brain Storm Optimization (BSO) is a novel swarm intelligence algorithm which is inspired by the human brainstorming process, and generates new ideas by emulating existing ideas. In this paper, a new BSO algorithm with an adaptive learning strategy (BSOAL) is proposed. By considering the evolutionary speed factor of each individual and the aggregation degree of the swarm, the proposed BSO-AL generates new individuals by exploring, emulating or learning adaptively. Comparative experiments were conducted on a set of benchmark functions with different dimensions. The experimental results show that the proposed BSO-AL algorithm outperforms the classic BSO algorithm and the other two state-of-the-art algorithms, which demonstrates the effectiveness of the learning strategy.

Combining large-scale biological data, using computational methods to mine potential disease-gene associations is a popular strategy. At the same time, bio-inspired intelligent optimization has always been a hot research field of intelligent computing. In this study, we apply the pigeon-inspired optimization (PIO) algorithm to the identification of human disease-genes. The problem of predicting disease-genes is translated into a single-objective optimization problem. A reasonable objective function is designed to measure the association between genes and inquiring diseases in a heterogeneous network, and the corresponding probability matrix is generated. The experimental results show that the proposed method (PDG-PIO) can accurately identify disease-genes.

The benchmark problems have played a fundamental role in verifying the algorithm's search ability. A dynamic multimodal optimization (DMO) problem is defined as an optimization problem with multiple global optima and characteristics of global optima which are changed during the search process. Two cases are used to illustrate the application scenario of DMO. A set of benchmark functions on DMO, which contains eight problems, are proposed to show the difficulty of DMO. The properties of the proposed benchmark problems, such as the distribution of solutions, the scalability, the number of global/local optima, are discussed.

Parameter control is critical to the performance of any evolutionary algorithm (EA). In this paper, we propose a Q-Learning-based Particle Swarm Optimization (QLPSO) algorithm, which uses the Reinforcement Learning (RL) to train the parameters in Particle Swarm Optimization (PSO) algorithm. The core of the QLPSO algorithm is a three-dimensional Q table which consists of a state plane and an action axis. The state plane includes the state of the particles in both of the decision space and the objective space. The action axis controls the exploration and exploitation of particles by setting different parameters. The Q table can help particles to select actions according to their states. Besides, the Q table should be updated by reward function which is designed according to the performance change of particles and the number of iterations. The main difference between the QLPSO algorithms for single-objective and multi-objective optimization lies in the evaluation of the solution performance. In single-objective optimization, we only compare the fitness values of solutions, while in multi-objective optimization, we need to discuss the dominant relationship between solutions with the help of Pareto front. The performance of QLPSO is tested based on 6 single-objective and 5 multi-objective benchmark functions. The experiment results reveal the competitive performance of QLPSO compared with other algorithms.

The brain storm optimization (BSO) algorithm is a new and promising swarm intellgience paradigm, inspired from the behaviors of the human process of brainstorming. The noverty of BSO lies in the clustering mechanism where the ideas are clustered into a set of groups and each idea learns from experiences of one inter-cluster or two intra-cluster neighbors. However, this mechanism is inefficient to deal with complex optimiaiton problems. In this paper, we propose an improved BSO algorithm called OSBSO using orthogonal experimental design (OED) strategy, which aims to discover useful search experiences for improving the convergence and solution accurancy. In OSBSO, two new clustering procedures are developed, i.e., orthogonal initialization and orthogonal clustering. The orthogonal initialization aims to improve the uniformity of the initial cluster centers in the objective space instead of the decision space, which can enhance the convergence performance. The orthogonal clustering uses the information between inter- cluster and intra-cluster indviduals to alleviate the evolution stagnation of clusters. Experiments are conducted on a set of the CEC2017 benchmark functions and the results verify the effectivenss and efficiency of OSBSO.

The development, implementation, variant, and future directions of a new swarm intelligence algorithm, brain storm optimization (BSO) algorithm, are comprehensively surveyed. Brain storm optimization algorithm is a new and promising swarm intelligence algorithm, which simulates the human brainstorming process. Through the convergent operation and divergent operation, individuals in BSO are grouped and diverged in the search space/objective space. To the best of our knowledge, there are 75 papers, 8 theses, and 5 patents in total on the development and application of the BSO algorithm. Every individual in the BSO algorithm is not only a solution to the problem to be optimized, but also a data point to reveal the landscape of the problem. Based on the developments of brain storm optimization algorithms, different kinds of optimization problems and real-world applications could be solved.

Recently, inspired by the human brainstorming process, a new kind of metaheuristic algorithm, called brain storm optimization (BSO) algorithm was proposed for global optimization. Experimental results have shown its excellent performance when solving optimization problems. In order to further improve the search ability of the BSO, this paper proposes an improved BSO (IBSO) algorithm by introducing graph theory into it. In IBSO, new individuals will be generated to replace some old individuals when the BSO algorithm is in a poor status. Whether a BSO algorithm is in a poor status is determined by the length of Hamiltonian cycle, which can be obtained by transferring all the individuals into an undirected weight graph. A Hamiltonian cycle and its length will be computed according to a modified cycle algorithm. The proposed IBSO algorithm is tested on twelve benchmarks, and the experimental results illustrate its effectiveness.

The learning strategy in the canonical particle swarm optimization (PSO) algorithm is often blamed for being the primary reason for loss of diversity. Population diversity maintenance is crucial for preventing particles from being stuck into local optima. In this paper, we present an improved PSO algorithm with an interswarm interactive learning strategy (IILPSO) by overcoming the drawbacks of the canonical PSO algorithm's learning strategy. IILPSO is inspired by the phenomenon in human society that the interactive learning behavior takes place among different groups. Particles in IILPSO are divided into two swarms. The interswarm interactive learning (IIL) behavior is triggered when the best particle's fitness value of both the swarms does not improve for a certain number of iterations. According to the best particle's fitness value of each swarm, the softmax method and roulette method are used to determine the roles of the two swarms as the learning swarm and the learned swarm. In addition, the velocity mutation operator and global best vibration strategy are used to improve the algorithm's global search capability. The IIL strategy is applied to PSO with global star and local ring structures, which are termed as IILPSO-G and IILPSO-L algorithm, respectively. Numerical experiments are conducted to compare the proposed algorithms with eight popular PSO variants. From the experimental results, IILPSO demonstrates the good performance in terms of solution accuracy, convergence speed, and reliability. Finally, the variations of the population diversity in the entire search process provide an explanation why IILPSO performs effectively.

The aim of multimodal optimization is to locate multiple peaks/optima in a single run and to maintain these found optima until the end of a run. The results of seven variants of particle swarm optimization (PSO) algorithms on IEEE Congress on Evolutionary Computation (CEC) 2015 single objective multi-niche optimization problems are reported in this paper. The PSO algorithms include PSO with star structure, PSO with ring structure, PSO with four clusters structure, PSO with Von Neumann structure, social-only PSO with star structure, social-only PSO with ring structure, and cognition-only PSO. The experimental tests are conducted on fifteen benchmark functions. Based on the experimental results, the conclusions could be made that the PSO with ring structure performs better than the other PSO variants on multimodal optimization. To obtain good performance on the multimodal optimization problems, an algorithm needs to converge the candidate solutions to the global optima while keep the population diversity during whole search process.

Swarm intelligence suffers the premature convergence, which happens partially due to the solutions getting clustered together, and not diverging again. The brain storm optimization (BSO), which is a young and promising algorithm in swarm intelligence, is based on the collective behavior of human being, that is, the brainstorming process. Premature convergence also happens in the BSO algorithm. The solutions get clustered after a few iterations, which indicate that the population diversity decreases quickly during the search. A definition of population diversity in BSO algorithm to measure the change of solutions' distribution is proposed in this paper. The algorithm's exploration and exploitation ability can be measured based on the change of population diversity. Two kinds of partial re-initialization strategies are utilized to improve the population diversity in BSO algorithm. The experimental results show that the performance of the BSO is improved by these two strategies.

Portfolio optimization is an important problem based on the modern portfolio theory (MPT) in the finance field. The idea is to maximize the portfolio expected return as well as minimizing portfolio risk at the same time. In this work, we propose a combinatorial algorithm for the portfolio optimization problem with the cardinality and bounding constraints. The proposed algorithm hybridizes a metaheuristic approach (particle swarm optimization, PSO) and a mathematical programming method where PSO is used to deal with the cardinality constraints and the math programming method is used to deal with the rest of the model. Computational results are given for the benchmark datasets from the OR-library and they indicate that it is a useful strategy for this problem. We also present the solutions obtained by the CPLEX mixed integer program solver for these instances and they can be used as the criteria for the comparison of algorithms for the same problem in the future.

In swarm intelligence algorithms, premature convergence happens partially due to the solutions getting clustered together, and not diverging again. However, solution clustering is not always harmful for optimization. The solution clustering strategy is utilized in brain storm optimization (BSO) to guide individuals to move toward the better and better areas. The information of clusters indicates the solutions' distribution in the search space, which could be utilized to reveal the landscapes and other proprieties of problems being optimized. In this paper, the solution clustering, and other properties of the brain storm optimization algorithm are analyzed and discussed. Experimental results show that brain storm optimization is a very promising algorithm for solving different kinds of problems.

In this paper, the nearest neighbor method on Chinese text categorization is formulated as an optimization problem. The particle swarm optimization is utilized to optimize a nearest neighbor classifier to solve the Chinese text categorization problem. The parameter k was first optimized to obtain the minimum error, then the categorization problem is formulated as a discrete, constrained, and single objective optimization problem. Each dimension of solution vector is dependent on each other in the solution space. The parameter k and the number of labeled examples for each class are optimized together to reach the minimum categorization error. In the experiment, with the utilization of particle swarm optimization, the performance of a nearest neighbor algorithm can be improved, and the algorithm can obtain the minimum categorization error rate.

Particle swarm optimization (PSO) may lose search efficiency when the problem's dimension increases to large scale. For high dimensional search space, an algorithm may not be easy to locate at regions which contain good solutions. The exploitation ability is also reduced due to high dimensional search space. The “No Free Lunch” theorem implies that we can make better algorithm if an algorithm knows the information of the problem. Algorithms should have an ability of learning to solve different problems, in other words, algorithms can adaptively change to suit the landscape of problems. In this paper, the strategy of dynamical exploitation space reduction is utilized to learn problems' landscapes. While at the same time, partial re-initialization strategy is utilized to enhance the algorithm's exploration ability. Experimental results show that a PSO with these two strategies has better performance than the standard PSO in large scale problems. Population diversities of variant PSOs, which include position diversity, velocity diversity and cognitive diversity, are discussed and analyzed. From diversity analysis, we can conclude that an algorithm's exploitation ability can be enhanced by exploitation space reduction strategy.

For many large scale learning problems, acquiring a large amount of labeled training data is expensive and time-consuming. Semi-supervised learning is a machine learning paradigm which deals with utilizing unlabeled data to build better classifiers. However, unlabeled data with wrong predictions will mislead the classifier. In this paper, we proposed a particle swarm optimization based semi-learning classifier to solve Chinese text categorization problem. This classifier utilizes an iterative strategy, and the result of classifier is determined by a document's previous prediction and its neighbors' information. The new classifier is tested on a Chinese text corpus. The proposed classifier is compared with the k nearest neighbor method, the k weighted nearest neighbor method, and the self-learning classifier.

Premature convergence happens in Particle Swarm Optimization (PSO) partially due to improper search information propagation. Fast propagation of search information will lead particles get clustered together quickly. Determining a proper search information propagation mechanism is important in optimization algorithms to balance between exploration and exploitation. In this paper, we attempt to figure out the relationship between search information propagation and the population diversity change. Firstly, we analyze the different characteristics of search information propagation in PSO with four kinds of topologies: star, ring, four clusters, and Von Neumann. Secondly, population diversities of PSO, which include position diversity, velocity diversity, and cognitive diversity, are utilized to monitor particles' search during optimization process. Position diversity, velocity diversity, and cognitive diversity, represent distributions of current solutions, particles' “moving potential”, and particles' “moving target”, respectively. From the observation of population diversities, the effect of search information propagation on PSO's optimization performance is discussed at last.