An Improved Chaotic Grey Wolf Optimization Algorithm (CGWO)

Grey Wolf Optimization (GWO) is a new type of swarm-based technique for dealing with realistic engineering design constraints and unconstrained problems in the field of metaheuristic research. Swarm-based techniques are a type of population-based algorithm inspired by nature that can produce low-cost, quick, and dependable solutions to a wider variety of complications. It is the best choice when it can achieve faster convergence by avoiding local optima trapping. This work incorporates chaos theory with the standard GWO to improve the algorithm's performance due to the ergodicity of chaos. The proposed methodology is referred to as Chaos-GWO (CGWO). The CGWO improves the search space's exploration and exploitation abilities while avoiding local optima trapping. Using different benchmark functions, five distinct chaotic map functions are examined, and the best chaotic map is considered to have great mobility and ergodicity characteristics. The results demonstrated that the best performance comes from using the suitable chaotic map function, and that CGWO can clearly outperform standard GWO

Parallelization of adaptive Bayesian cubature using multimodal optimization algorithms

PurposeBayesian cubature (BC) has emerged to be one of most competitive approach for estimating the multi-dimensional integral especially when the integrand is expensive to evaluate, and alternative acquisition functions, such as the Posterior Variance Contribution (PVC) function, have been developed for adaptive experiment design of the integration points. However, those sequential design strategies also prevent BC from being implemented in a parallel scheme. Therefore, this paper aims at developing a parallelized adaptive BC method to further improve the computational efficiency.Design/methodology/approachBy theoretically examining the multimodal behavior of the PVC function, it is concluded that the multiple local maxima all have important contribution to the integration accuracy as can be selected as design points, providing a practical way for parallelization of the adaptive BC. Inspired by the above finding, four multimodal optimization algorithms, including one newly developed in this work, are then introduced for finding multiple local maxima of the PVC function in one run, and further for parallel implementation of the adaptive BC.FindingsThe superiority of the parallel schemes and the performance of the four multimodal optimization algorithms are then demonstrated and compared with the k-means clustering method by using two numerical benchmarks and two engineering examples.Originality/valueMultimodal behavior of acquisition function for BC is comprehensively investigated. All the local maxima of the acquisition function contribute to adaptive BC accuracy. Parallelization of adaptive BC is realized with four multimodal optimization methods.</jats:sec

Enhanced Parallel Sine Cosine Algorithm for Constrained and Unconstrained Optimization

The sine cosine algorithm’s main idea is the sine and cosine-based vacillation outwards or towards the best solution. The first main contribution of this paper proposes an enhanced version of the SCA algorithm called as ESCA algorithm. The supremacy of the proposed algorithm over a set of state-of-the-art algorithms in terms of solution accuracy and convergence speed will be demonstrated by experimental tests. When these algorithms are transferred to the business sector, they must meet time requirements dependent on the industrial process. If these temporal requirements are not met, an efficient solution is to speed them up by designing parallel algorithms. The second major contribution of this work is the design of several parallel algorithms for efficiently exploiting current multicore processor architectures. First, one-level synchronous and asynchronous parallel ESCA algorithms are designed. They have two favors; retain the proposed algorithm’s behavior and provide excellent parallel performance by combining coarse-grained parallelism with fine-grained parallelism. Moreover, the parallel scalability of the proposed algorithms is further improved by employing a two-level parallel strategy. Indeed, the experimental results suggest that the one-level parallel ESCA algorithms reduce the computing time, on average, by 87.4% and 90.8%, respectively, using 12 physical processing cores. The two-level parallel algorithms provide extra reductions of the computing time by 91.4%, 93.1%, and 94.5% with 16, 20, and 24 processing cores, including physical and logical cores. Comparison analysis is carried out on 30 unconstrained benchmark functions and three challenging engineering design problems. The experimental outcomes show that the proposed ESCA algorithm behaves outstandingly well in terms of exploration and exploitation behaviors, local optima avoidance, and convergence speed toward the optimum. The overall performance of the proposed algorithm is statistically validated using three non-parametric statistical tests, namely Friedman, Friedman aligned, and Quade tests.This research was supported by the Spanish Ministry of Science, Innovation and Universities and the Research State Agency under Grant RTI2018-098156-B-C54 cofinanced by FEDER funds and the Ministry of Science and Innovation and the Research State Agency under Grant PID2020-120213RB-I00 cofinanced by FEDER funds

Applied Metaheuristic Computing

For decades, Applied Metaheuristic Computing (AMC) has been a prevailing optimization technique for tackling perplexing engineering and business problems, such as scheduling, routing, ordering, bin packing, assignment, facility layout planning, among others. This is partly because the classic exact methods are constrained with prior assumptions, and partly due to the heuristics being problem-dependent and lacking generalization. AMC, on the contrary, guides the course of low-level heuristics to search beyond the local optimality, which impairs the capability of traditional computation methods. This topic series has collected quality papers proposing cutting-edge methodology and innovative applications which drive the advances of AMC

Heuristic optimization of electrical energy systems: Refined metrics to compare the solutions

Many optimization problems admit a number of local optima, among which there is the global optimum. For these problems, various heuristic optimization methods have been proposed. Comparing the results of these solvers requires the definition of suitable metrics. In the electrical energy systems literature, simple metrics such as best value obtained, the mean value, the median or the standard deviation of the solutions are still used. However, the comparisons carried out with these metrics are rather weak, and on these bases a somehow uncontrolled proliferation of heuristic solvers is taking place. This paper addresses the overall issue of understanding the reasons of this proliferation, showing a conceptual scheme that indicates how the assessment of the best solver may result in the unlimited formulation of new solvers. Moreover, this paper shows how the use of more refined metrics defined to compare the optimization result, associated with the definition of appropriate benchmarks, may make the comparisons among the solvers more robust. The proposed metrics are based on the concept of first-order stochastic dominance and are defined for the cases in which: (i) the globally optimal solution can be found (for testing purposes); and (ii) the number of possible solutions is so large that practically it cannot be guaranteed that the global optimum has been found. Illustrative examples are provided for a typical problem in the electrical energy systems area – distribution network reconfiguration. The conceptual results obtained are generally valid to compare the results of other optimization problem

Enhancement of Metaheuristic Algorithm for Scheduling Workflows in Multi-fog Environments

Whether in computer science, engineering, or economics, optimization lies at the heart of any challenge involving decision-making. Choosing between several options is part of the decision- making process. Our desire to make the "better" decision drives our decision. An objective function or performance index describes the assessment of the alternative's goodness. The theory and methods of optimization are concerned with picking the best option. There are two types of optimization methods: deterministic and stochastic. The first is a traditional approach, which works well for small and linear problems. However, they struggle to address most of the real-world problems, which have a highly dimensional, nonlinear, and complex nature. As an alternative, stochastic optimization algorithms are specifically designed to tackle these types of challenges and are more common nowadays. This study proposed two stochastic, robust swarm-based metaheuristic optimization methods. They are both hybrid algorithms, which are formulated by combining Particle Swarm Optimization and Salp Swarm Optimization algorithms. Further, these algorithms are then applied to an important and thought-provoking problem. The problem is scientific workflow scheduling in multiple fog environments. Many computer environments, such as fog computing, are plagued by security attacks that must be handled. DDoS attacks are effectively harmful to fog computing environments as they occupy the fog's resources and make them busy. Thus, the fog environments would generally have fewer resources available during these types of attacks, and then the scheduling of submitted Internet of Things (IoT) workflows would be affected. Nevertheless, the current systems disregard the impact of DDoS attacks occurring in their scheduling process, causing the amount of workflows that miss deadlines as well as increasing the amount of tasks that are offloaded to the cloud. Hence, this study proposed a hybrid optimization algorithm as a solution for dealing with the workflow scheduling issue in various fog computing locations. The proposed algorithm comprises Salp Swarm Algorithm (SSA) and Particle Swarm Optimization (PSO). In dealing with the effects of DDoS attacks on fog computing locations, two Markov-chain schemes of discrete time types were used, whereby one calculates the average network bandwidth existing in each fog while the other determines the number of virtual machines existing in every fog on average. DDoS attacks are addressed at various levels. The approach predicts the DDoS attack’s influences on fog environments. Based on the simulation results, the proposed method can significantly lessen the amount of offloaded tasks that are transferred to the cloud data centers. It could also decrease the amount of workflows with missed deadlines. Moreover, the significance of green fog computing is growing in fog computing environments, in which the consumption of energy plays an essential role in determining maintenance expenses and carbon dioxide emissions. The implementation of efficient scheduling methods has the potential to mitigate the usage of energy by allocating tasks to the most appropriate resources, considering the energy efficiency of each individual resource. In order to mitigate these challenges, the proposed algorithm integrates the Dynamic Voltage and Frequency Scaling (DVFS) technique, which is commonly employed to enhance the energy efficiency of processors. The experimental findings demonstrate that the utilization of the proposed method, combined with the Dynamic Voltage and Frequency Scaling (DVFS) technique, yields improved outcomes. These benefits encompass a minimization in energy consumption. Consequently, this approach emerges as a more environmentally friendly and sustainable solution for fog computing environments