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Solving nonlinear equation systems (NESs) is one of the most important tasks in numerical computing. The NESs usually have multiple roots, and quickly locating their roots in a single algorithm run with a limited number of iterations has always been the algorithm improvement direction. In order to further enhance the efficiency of the existing methods, a density clustering-based differential evolution algorithm (DCDE) for the NESs problem solving is proposed in this paper. Firstly, density-based spatial clustering of applications with noise (DBSCAN) is used to divide the population into clusters and noises, which provides a better direction for population evolution. Secondly, a cluster evaluation factor is proposed, which not only divides the clusters into excellent clusters and non-excellent clusters, but also prevents the migration of excellent clusters and maintain the diversity of populations. Then, a migration strategy and individual generation mechanism are proposed to guide non-excellent clusters to migrate to promising regions. Finally, combined with an archive technique, the individuals which satisfy the solution requirements are archived and randomly initialized to further improve population diversity. To verify the effectiveness of the proposed algorithm, comparative experimental results of the propsoed DCDE with other state-of-the-art algorithms for thirty NESs problems solving show that the proposed DCDE is the most effective algorithm to locate more roots in a single run. [ABSTRACT FROM AUTHOR]

The paper presents a new balanced selection operator applied to the proposed Balanced Non-dominated Tournament Genetic Algorithm (B-NTGA) that actively uses archive to solve multi- and many-objective NP-hard combinatorial optimization problems with constraints. The primary motivation is to make B-NTGA more efficient in exploring Pareto Front Approximation (PFa), focusing on "gaps" and reducing some PFa regions' sampling too frequently. Such a balancing mechanism allows B-NTGA to be more adaptive and focus on less explored PFa regions. The proposed B-NTGA is investigated on two benchmark multi- and many-objective optimization real-world problems, like Thief Traveling Problem and Multi-Skill Resource-Constrained Project Scheduling Problem. The results of experiments show that B-NTGA has a higher efficiency and better performance than state-of-the-art methods. • New balanced GAP selection actively uses archive, focuses on Pareto Front 'gaps' to reduce too frequent sampling of regions. • B-NTGA bases and modifies NTGA2 (i.e., clone elimination, tournament as second selection) and adds balanced GAP selection. • B-NTGA is less time-consuming than NTGA2, uses fewer parameters, and is more efficient than NTGA2. • Experiments for NP-hard multi-objective optimization problems (TTP and MS-RCPSP) comparing B-NTGA to state-of-the-art methods. • Results of experiments showed that B-NTGA is highly effective for multi- and many-objective problems (like TTP and MS-RCPSP). [ABSTRACT FROM AUTHOR]

Various variants have been proposed to improve the search ability and efficiency of Differential Evolution (DE). However, the variants ignore the impact caused by the use of accumulated historical information, resulting in unpromising performance of the search. Furthermore, the global exploration and local exploitation ability of population is affected by the population number (NP), which commonly adapts with little adaptive control or with linear descendent only. To utilize more historical population information, we propose in this paper a novel adaptive population size-based DE (APSDE) by mining historical population information, to balance global exploration and local exploitation ability. APSDE uses historical population information to mine population distribution and extract information to assign parameters to the current population. Moreover, an archive is utilized to store the historical population information, where historical successful parameter information consists of scaling factor (F), crossover rate (CR) and NP for better balancing the search ability of population. To evaluate the performance of APSDE, we conduct experiments both on the 28 benchmark functions of CEC2017, the 10 benchmark functions of CEC2020, and a real-world application - the path planning of unmanned aerial vehicles (UAVs). The experimental results have demonstrated that APSDE achieves the promising performance in both convergence accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

Multimodal multi-objective optimization problems (MMOPs) contain multiple equivalent Pareto optimal sets (PSs) corresponding to the same Pareto front (PF). However, simultaneously locating well-distributed and well-converged multiple equivalent global PSs and PF remains challenging. Therefore, this paper proposes dynamic niching particle swarm optimization (PSO) with an external archive-guided (AG) mechanism, termed DNPSO-AG, for solving MMOPs. In DNPSO-AG, a clustering-based dynamic niching technique is integrated with PSO to divide the population into multiple niches. In addition, a leader updating method controls the updating of the leaders. Furthermore, a novel external archive-guided mechanism guides the evolution of multiple niches and enhances the distribution of solutions, which comprises two strategies: the adaptive division of the external archive strategy, which adaptively divides the external archive into multiple sub-archives, and the distance-based sub-archive and niche matching strategy, which assigns sub-archives to multiple niches for maintenance. The experimental results demonstrate that the proposed DNPSO-AG outperforms seven other state-of-the-art competitors on the CEC 2019 MMOP test suite in terms of the inverted generational distance (IGD) and IGD in the decision space (IGDX) metrics, with improvements of 21.3% and 9.1% over the best-performing competitor, respectively. [ABSTRACT FROM AUTHOR]