Multimodal optimization problems (MMOPs) are common in real-world applications and involve identifying multiple optimal solutions for decision makers to choose from. The core requirement for dealing with such problems is to balance the ability of exploration in the global space and exploitation in the multiple optimal areas. In this paper, based on the differential evolution (DE), we propose a novel algorithm focusing on the formulation, balance, and keypoint of species for MMOPs, called FBK-DE. First, nearest-better clustering (NBC) is used to divide the population into multiple species with minimum size limitations. Second, to avoid placing too many individuals into one species, a species balance strategy is proposed to adjust the size of each species. Third, two keypoint-based mutation operators named DE/keypoint/1 and DE/keypoint/2 are proposed to evolve each species together with traditional mutation operators. The experimental results of FBK-DE on 20 benchmark functions are compared with 15 state-of-the-art multimodal optimization algorithms. The comparisons show that the proposed FBK-DE performs competitively with these algorithms.

Dynamic constrained optimization problems (DCOPs) are difficult to solve because both objective function and constraints can vary with time. Although DCOPs have drawn attention in recent years, little work has been performed to solve DCOPs with multiple dynamic feasible regions from the perspective of locating and tracking multiple feasible regions in parallel. Moreover, few benchmarks have been proposed to simulate the dynamics of multiple disconnected feasible regions. In this paper, first, the idea of tracking multiple feasible regions, originally proposed by Nguyen and Yao, is enhanced by specifically adopting multiple subpopulations. To this end, the dynamic species-based particle swam optimization (DSPSO), a representative multipopulation algorithm, is adopted. Second, an ensemble of locating and tracking feasible regions strategies is proposed to handle different types of dynamics in constraints. Third, two benchmarks are designed to simulate the DCOPs with dynamic constraints. The first benchmark, including two variants of G24 (called G24v and G24w), could control the size of feasible regions. The second benchmark, named moving feasible regions benchmark (MFRB), is highly configurable. The global optimum of MFRB is calculated mathematically for experimental comparisons. Experimental results on G24, G24v, G24w, and MFRB show that the DSPSO with the ensemble of strategies performs significantly better than the original DSPSO and other typical algorithms.

Multimodal optimization problems (MMOPs) are common problems with multiple optimal solutions. In this article, a novel method of population division, called nearest-better-neighbor clustering (NBNC), is proposed, which can reduce the risk of more than one species locating the same peak. The key idea of NBNC is to construct the raw species by linking each individual to the better individual within the neighborhood, and the final species of the population is formulated by merging the dominated raw species. Furthermore, a novel algorithm is proposed called NBNC-PSO-ES, which combines the advantages of better exploration in particle swarm optimization (PSO) and stronger exploitation in the covariance matrix adaption evolution strategy (CMA-ES). For the purpose of demonstrating the performance of NBNC-PSO-ES, several state-of-the-art algorithms are adopted for comparisons and tested using typical benchmark problems. The experimental results show that NBNC-PSO-ES performs better than other algorithms.

Most of the community detection methods require the global information of the original network to be available, however, it is often expensive (even no way) to obtain the global information of the network in many real-world networks. So, the local community detection, only based on the local information, becomes especially important. The local community is the community in the network to which a given starting node belongs. Some local community detection methods have been proposed. However, these methods did not consider the characteristics of the local community during the local community formation. In this paper, we analyze the formation of the local community and propose two local community detection algorithms based on the dynamic membership function. Each of the algorithms is divided into three stages: 1) the initial stage, 2) the middle stage, and 3) the closing stage. At the initial stage, we design a dynamical membership function to detect local community and nodes with the greatest neighborhood intersect rate could be added to the local community. At the middle stage, we design another dynamical membership function, and the goal of this stage is to make the connection of the node in the local community closest. At the closing stage, the third dynamical membership function is provided, and the local community is further improved by collecting some nodes that should not be omitted. We test our algorithms on several synthetic datasets and real datasets; the results show that the local communities detected by our method are closer to the real local communities.

Recently, dynamic optimization has received much attention from the swarm and evolutionary computation community. However, few studies have investigated data-driven evolutionary dynamic optimization, and most algorithms for evolutionary dynamic optimization are based on analytical mathematical functions. In this paper, we investigate data-driven evolutionary dynamic optimization. First, we develop a surrogate-assisted evolutionary framework for solving data-driven dynamic optimization problems (DD-DOPs). Second, we employ a benchmark based on the typical dynamic optimization problems set in order to verify the performance of the proposed framework. The experimental results demonstrate that the proposed framework is effective for solving DD-DOPs.