An Improved Brain Storm Optimization with Dynamic Clustering Strategy

Intelligence algorithms play an increasingly important role in the field of intelligent control. Brain storm optimization (BSO) is a new kind of swarm intelligence algorithm inspired by emulating the collective behavior of human beings in the problem solving process. To improve the performance of the original BSO, many variants of BSO are proposed. In this paper, an improved BSO algorithm with dynamic clustering strategy (BSO-DCS) is proposed as a variant of BSO for global optimization problems. The basic framework of BSO is firstly introduced. Then to reduce the time complexity of the original BSO, a new grouping method named dynamic clustering strategy (DCS) is proposed to improve the clustering method in the original BSO. To verify the effectiveness of the proposed BSO-DCS, it is tested on 12 benchmark functions of CEC 2005 with 30 dimensions. Experimental results show that DCS is an effective strategy to reduce the time complexity, and the improved BSO-DCS performs greatly better than the original BSO algorithm

Simplex search-based brain storm optimization

Through modeling human's brainstorming process, the brain storm optimization (BSO) algorithm has become a promising population-based evolutionary algorithm. However, BSO is pointed out that it possesses a degenerated L-curve phenomenon, i.e., it often gets near optimum quickly but needs much more cost to improve the accuracy. To overcome this question in this paper, an excellent direct search-based local solver, the Nelder-Mead Simplex method is adopted in BSO. Through combining BSO's exploration ability and NMS's exploitation ability together, a simplex search-based BSO (Simplex-BSO) is developed via a better balance between global exploration and local exploitation. Simplex-BSO is shown to be able to eliminate the degenerated L-curve phenomenon on unimodal functions, and alleviate significantly this phenomenon on multimodal functions. Large number of experimental results shows that Simplex-BSO is a promising algorithm for global optimization problems

Particle swarm optimization with state-based adaptive velocity limit strategy

Velocity limit (VL) has been widely adopted in many variants of particle swarm optimization (PSO) to prevent particles from searching outside the solution space. Several adaptive VL strategies have been introduced with which the performance of PSO can be improved. However, the existing adaptive VL strategies simply adjust their VL based on iterations, leading to unsatisfactory optimization results because of the incompatibility between VL and the current searching state of particles. To deal with this problem, a novel PSO variant with state-based adaptive velocity limit strategy (PSO-SAVL) is proposed. In the proposed PSO-SAVL, VL is adaptively adjusted based on the evolutionary state estimation (ESE) in which a high value of VL is set for global searching state and a low value of VL is set for local searching state. Besides that, limit handling strategies have been modified and adopted to improve the capability of avoiding local optima. The good performance of PSO-SAVL has been experimentally validated on a wide range of benchmark functions with 50 dimensions. The satisfactory scalability of PSO-SAVL in high-dimension and large-scale problems is also verified. Besides, the merits of the strategies in PSO-SAVL are verified in experiments. Sensitivity analysis for the relevant hyper-parameters in state-based adaptive VL strategy is conducted, and insights in how to select these hyper-parameters are also discussed.Comment: 33 pages, 8 figure

A Brain Storm Optimization with Multiinformation Interactions for Global Optimization Problems

The original BSO fails to consider some potential information interactions in its individual update pattern, causing the premature convergence for complex problems. To address this problem, we propose a BSO algorithm with multi-information interactions (MIIBSO). First, a multi-information interaction (MII) strategy is developed, thoroughly considering various information interactions among individuals. Specially, this strategy contains three new MII patterns. The first two patterns aim to reinforce information interaction capability between individuals. The third pattern provides interactions between the corresponding dimensions of different individuals. The collaboration of the above three patterns is established by an individual stagnation feedback (ISF) mechanism, contributing to preserve the diversity of the population and enhance the global search capability for MIIBSO. Second, a random grouping (RG) strategy is introduced to replace both the K-means algorithm and cluster center disruption of the original BSO algorithm, further enhancing the information interaction capability and reducing the computational cost of MIIBSO. Finally, a dynamic difference step-size (DDS), which can offer individual feedback information and improve search range, is designed to achieve an effective balance between global and local search capability for MIIBSO. By combining the MII strategy, RG, and DDS, MIIBSO achieves the effective improvement in the global search ability, convergence speed, and computational cost. MIIBSO is compared with 11 BSO algorithms and five other algorithms on the CEC2013 test suit. The results confirm that MIIBSO obtains the best global search capability and convergence speed amongst the 17 algorithms

A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization

[EN] In a multi-objective optimization problem, in addition to optimal solutions, multimodal and/or nearly optimal alternatives can also provide additional useful information for the decision maker. However, obtaining all nearly optimal solutions entails an excessive number of alternatives. Therefore, to consider the nearly optimal solutions, it is convenient to obtain a reduced set, putting the focus on the potentially useful alternatives. These solutions are the alternatives that are close to the optimal solutions in objective space, but which differ significantly in the decision space. To characterize this set, it is essential to simultaneously analyze the decision and objective spaces. One of the crucial points in an evolutionary multi-objective optimization algorithm is the archiving strategy. This is in charge of keeping the solution set, called the archive, updated during the optimization process. The motivation of this work is to analyze the three existing archiving strategies proposed in the literature (ArchiveUpdateP(Q,epsilon)D(xy), Archive_nevMOGA, and targetSelect) that aim to characterize the potentially useful solutions. The archivers are evaluated on two benchmarks and in a real engineering example. The contribution clearly shows the main differences between the three archivers. This analysis is useful for the design of evolutionary algorithms that consider nearly optimal solutions.This work was supported in part by the Ministerio de Ciencia, Innovacion y Universidades (Spain) (grant number RTI2018-096904-B-I00), by the Generalitat Valenciana regional government through project AICO/2019/055 and by the Universitat Politecnica de Valencia (grant number SP20200109).Pajares-Ferrando, A.; Blasco, X.; Herrero Durá, JM.; Martínez Iranzo, MA. (2021). A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization. Mathematics. 9(9):1-28. https://doi.org/10.3390/math9090999S1289