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.

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.

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.