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Community discovery (CD) under complex networks is a hot discussion issue in network science research. Recently, many evolutionary methods have been introduced to detect communities of networks. However, evolutionary optimization-based community discovery still suffers from two problems. First, the initialization population quality of the current evolutionary algorithm is not good, resulting in slow convergence speed, and the final performance needs to be further improved. Another important issue is that current methods of CD have inconsistent network detection performance at different scales, showing a dramatic drop as the network scale increases. To address such issues, this paper proposes an algorithm based on the novel initial method and improved gray wolf optimization (NIGWO) to tackle the above two problems at the same time. In this paper, a novel initialization strategy is proposed to generate a high-quality initial population and greatly accelerate the convergence speed of population evolution. The strategy effectively fused the elite substructure of the community and different features based on the dependency and other features among nodes. Moreover, an improved GWO is presented with two new search strategies. An improved hunting prey stage is proposed to retain the excellent substructures of populations and quickly improve the community structure. Furthermore, new mutation strategies from node level to community level are designed in an improved encircling prey stage. Specifically, boundary nodes are mutated according to a proposed function to improve the search efficiency and save the computation assumption. Numerous experiments have proven our method obtains more excellent performance in most networks compared with 11 state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Reporting the empirical results of swarm and evolutionary computation algorithms is a challenging task with many possible difficulties. These difficulties stem from the stochastic nature of such algorithms, as well as their inability to guarantee an optimal solution in polynomial time. This research deals with measuring the performance of stochastic optimization algorithms, as well as the confidence intervals of the empirically obtained statistics. Traditionally, the arithmetic mean is used for measuring average performance, but we propose quantiles for measuring average, peak and bad-case performance, and give their interpretations in a relevant context for measuring the performance of the metaheuristics. In order to investigate the differences between arithmetic mean and quantiles, and to confirm possible benefits, we conducted experiments with 7 stochastic algorithms and 20 unconstrained continuous variable optimization problems. The experiments showed that median was a better measure of average performance than arithmetic mean, based on the observed solution quality. Out of 20 problem instances, a discrepancy between the arithmetic mean and median happened in 6 instances, out of which 5 were resolved in favor of median and 1 instance remained unresolved as a near tie. The arithmetic mean was completely inadequate for measuring average performance based on the observed number of function evaluations, while the 0.5 quantile (median) was suitable for that task. The quantiles also showed to be adequate for assessing peak performance and bad-case performance. In this paper, we also proposed a bootstrap method to calculate the confidence intervals of the probability of the empirically obtained quantiles. Considering the many advantages of using quantiles, including the ability to calculate probabilities of success in the case of multiple executions of the algorithm and the practically useful method of calculating confidence intervals, we recommend quantiles as the standard measure of peak, average and bad-case performance of stochastic optimization algorithms. [ABSTRACT FROM AUTHOR]

Formation control is one of the most concerning topics within the realm of swarm intelligence. This paper presents a metaheuristic approach that leverages a natural co-evolutionary strategy to solve the formation control problem for a swarm of missiles. The missile swarm is modeled by a second-order system with a heterogeneous reference target, and the exponential of the resultant error is accumulated to be the objective function such that the swarm converges to optimal equilibrium states satisfying specific formation requirements. Focusing on the issue of the local optimum and unstable evolution, we incorporate a novel model-based policy constraint and a population adaptation strategy that significantly alleviates the performance degradation of the existing natural co-evolutionary strategy in terms of slow training and instability of convergence. With application of the Molloy–Reed criterion in the field of network communication, we developed an adaptive topology method that assures connectivity under node failure, and its effectiveness is validated theoretically and experimentally. The experimental results demonstrate that the accuracy of formation flight achieved by this method is competitive with that of conventional control methods and is much more adaptable. More significantly, we show that it is feasible to treat the generic formation control problem as an optimal control problem for finding a Nash equilibrium strategy and solving it through iterative learning. [ABSTRACT FROM AUTHOR]

The Teaching Learning-Based Algorithm (TLBA) is a powerful and effective optimization approach. TLBA mimics the teaching-learning process in a classroom, where TLBA's iterative computing process is separated into two phases, unlike standard evolutionary algorithms and swarm intelligence algorithms, and each phase conducts an iterative learning operation. Advanced technologies of Voltage Source Converters (VSCs) enable greater active and reactive power regulation in these networks. Various objectives are addressed for optimal energy management, with the goal of attaining economic and technical advantages by decreasing overall production fuel costs and transmission power losses in AC-DC transmission networks. In this paper, the TLBA is applied for various sorts of nonlinear and multimodal functioning of hybrid alternating current (AC) and multi-terminal direct current (DC) power grids. The proposed TLBA is evaluated on modified IEEE 30-bus and IEEE 57-bus AC-DC networks and compared to other published methods in the literature. Numerical results demonstrate that the proposed TLBA has great effectiveness and robustness indices over the others. Economically, the reduction percentages of 13.84 and 21.94% are achieved for the IEEE 30-bus and IEEE 57-bus test systems when the fuel costs are minimized. Technically, significant improvement in the transmission power losses with reduction 28.01% and 69.83%, are found for the IEEE 30-bus and IEEE 57-bus test system compared to the initial case. Nevertheless, TLBA has faster convergence, higher quality for the final optimal solution, and more power for escaping from convergence to local optima compared to other published methods in the literature. [ABSTRACT FROM AUTHOR]