A Novel Grey Wolf Optimizer with Random Walk Strategies for Constrained Engineering Design

Efficient sampling of complex network with modified random walk strategies

The Grey Wolf Optimization (GWO) Algorithm is a heuristic evolutionary algorithm inspired by the hunting and leadership mechanisms of the natural grey wolf. However, its location update equation has the disadvantages of strong development ability and weak exploration ability. To improve these shortcomings, we propose the RWCA-GWO algorithm. It occurs inspired by the random walk strategy and enhances the exploration ability of the leading wolves. Inspired by the analytic hierarchy process, a procedure for setting the weights of α, β, and δ are proposed. Besides, to promote the global convergence speed of the GWO algorithm, the initial population is generated by the chaotic initialization method. The simulation experiments are carried out with 11 test functions. The results show that for most cases, the performance of RWCA-GWO algorithm is significantly better than the standard grey wolf algorithm and other improved grey wolf algorithms under the same maximum fitness function evaluation times.

Meta-path-based random walk strategy has attracted tremendous attention in heterogeneous network representation, which can capture network semantics with heterogeneous neighborhoods of nodes. Despite the success of meta-path-based random walk strategy in plain heterogeneous networks which contain no attributes, it remains unexplored how meta-path-based random walk strategy could be utilized on attributed heterogeneous networks to simultaneously capture structural heterogeneity and attribute proximity. Moreover, the importance of node attributes and structural relations generally varies across data sets, thus requiring careful considerations when they are incorporated into representations. To tackle these problems, we propose a novel method, Attributed Heterogeneous Network embedding based on Aggregate-path (AHNA), which generates aggregate-path-based random walks on attributed heterogeneous networks and adaptively fuses topological structures and node attributes based on the learned importance. Specifically, AHNA first converts node attributes to additional links in the network to deal with the heterogeneity of structures and attributes, which is followed by an adaptive random walk strategy to strike the importance balance between node attributes and topological structures, thereby generating high-quality representations. Extensive experiments are conducted on three real-world data sets, where AHNA outperforms state-of-the-art approaches by up to 22.7%, 2.6%, and 2.3% on link prediction, community detection, and node classification, respectively. Moreover, our qualitative analysis indicates that AHNA can capture different balances of topological structures and node attributes on various data sets and thus boost the quality of node representations.

An optimization based framework for region wise optimal clusters in MR images using hybrid objective

In this paper, we explore different Markovian random walk strategies on networks with transition probabilities between nodes defined in terms of functions of the Laplacian matrix. We generalize random walk strategies with local information in the Laplacian matrix, that describes the connections of a network, to a dynamic determined by functions of this matrix. The resulting processes are non-local allowing transitions of the random walker from one node to nodes beyond its nearest neighbors. We find that only two types of Laplacian functions are admissible with distinct behaviors for long-range steps in the infinite network limit: type (i) functions generate Brownian motions, type (ii) functions Lévy flights. For this asymptotic long-range step behavior only the lowest non-vanishing order of the Laplacian function is relevant, namely first order for type (i), and fractional order for type (ii) functions.In the first part, we discuss spectral properties of the Laplacian matrix and a series of relations that are maintained by a particular type of functions that allow to define random walks on any type of undirected connected networks. Once described general properties, we explore characteristics of random walk strategies that emerge from particular cases with functions defined in terms of exponentials, logarithms and powers of the Laplacian as well as relations of these dynamics with non-local strategies like Lévy flights and fractional transport. Finally, we analyze the global capacity of these random walk strategies to explore networks like lattices and trees and different types of random and complex networks.

Salp Swarm Algorithm (SSA) is a new type of metaheuristic and has shown superiority over other well-known algorithms such as Particle Swarm Optimization and Grey Wolf Optimizer in solving challenging optimization problems. Despite its superior performance, SSA still has problems such as insufficient convergence speed. Moreover, its local optima avoidance ability is not as good as those evolutionary algorithms using crossover operators. In this paper, we propose a modified Salp Swarm Algorithm (m-SSA) which improves the exploitation and exploration of SSA by integrating random walk strategy and especially enhances exploration by adding a new controlling parameter. In addition, a simulated annealing-type acceptance criterion is adopted to accept the fittest follower position as the new best leader position. The performance of the proposed algorithm is benchmarked on a set of classical functions and CEC2014 test suite. The proposed algorithm (m-SSA) outperforms SSA significantly on most test functions. When compared with other state-of-the-art metaheuristics, it also presents very competitive results. Besides, we apply the proposed algorithm on training feedforward neural networks (FNNs) and the results prove the effectiveness and efficiency of m-SSA.

Grey Wolf Optimizer (GWO) is competitive to other population-based algorithms. However, considering that the conventional GWO has inadequate global search capacity, a GWO variant based on multiple strategies, i.e., adaptive Evolutionary Population Dynamics (EPD) strategy, differential perturbation strategy, and greedy selection strategy, named as ADGGWO, is proposed in this paper. Firstly, the adaptive EPD strategy is adopted to enhance the search capacity by updating the position of the worst wolves according to the best ones. Secondly, the exploration capacity is extended by the use of differential perturbation strategy. Thirdly, the greedy selection improves the exploitation capacity, contributing to the balance between exploration and exploitation capacity. ADGGWO has been examined on a suite from CEC2014 and compared with the traditional GWO as well as its three latest variants. The significance of the results is evaluated by two non-parametric tests, Friedman test and Wilcoxon test. Furthermore, constrained portfolio optimization is applied in this paper to investigate the performance of ADGGWO on real-world problems. The experimental results demonstrate that the proposed algorithm, which integrates multiple strategies, outperforms the traditional GWO and other GWO variants in terms of both accuracy and convergence. It can be proved that ADGGWO is not only effective for function optimization but also for practical problems.

Meta-heuristic algorithms are widely viewed as feasible techniques to solve continuous large-scale numerical optimization problems. Grey wolf optimizer (GWO) is a relatively new stochastic algorithm with only a few parameters to adjust that can be easily used for global optimization. This paper presents an efficient and robust GWO (ERGWO) variant to solve large-scale numerical optimization problems. Inspired by particle swarm optimization, a nonlinearly adjustment strategy for parameter control is designed to balance exploration and exploitation. Additionally, a modified position-updating equation is presented to improve convergence speed. The performance of ERGWO is verified on 18 benchmark large-scale numerical optimization problems with dimensions ranging from 30 to 10,000, 30 benchmarks from CEC 2014, 30 functions in CEC 2017, respectively. Numerical experiments are performed to compare ERGWO to the basic GWO algorithm, other GWO variants, and other well-known meta-heuristic search techniques. Simulations demonstrate that the proposed ERGWO algorithm can find high quality solutions with low computational cost and very fast convergence.

Magnetic target state estimation is a widely applied technology, but it also faces many challenges in practical applications. One of the most critical challenges is the issue of estimation accuracy. The Grey Wolf Optimizer (GWO) is one of the more successful swarm intelligence algorithms in recent years, but its shortcomings have also been exposed when facing increasingly complex problems. Therefore, a Multi-Strategy Improved Grey Wolf Optimizer (MSIGWO) algorithm has been proposed to enhance the accuracy of magnetic target state estimation. In the initialization phase, Tent chaos mapping is introduced to enhance population diversity, prevent falling into local optima, and improve convergence speed. Multi-population fusion evolution strategies enhance population diversity, convergence accuracy, and global search ability. Nonlinear convergence factors better balance exploration and exploitation behaviors. Dynamic weight strategies increase the diversity of search samples and reduce the likelihood of falling into local optima. Adaptive dimensional learning better balances local and global searches, enhancing population diversity. Adaptive Levy flight enhances the ability to jump out of local optima and ensures convergence speed. In the CEC2018 benchmark function set of 29 benchmark function problems and magnetic target state estimation problems, the proposed MSIGWO was tested, and statistical indicators and Friedman test results show that compared with GWO and its advanced variants, the MSIGWO algorithm has superior performance. The application of this algorithm in magnetic target state estimation problems has proven its effectiveness and applicability.

Sub-population improved grey wolf optimizer with Gaussian mutation and Lévy flight for parameters identification of photovoltaic models

Over the recent decades, there are many nature inspired optimization algorithms have been introduced. In this study, a newly algorithm namely Grey Wolf Optimizer (GWO) is employed for gasoline price forecasting. The performance of GWO is compared against the results produced by Artificial Bee Colony (ABC) algorithm and Differential Evolution (DE) algorithm. Measured based on Mean Absolute Percentage Error (MAPE) and prediction accuracy, the GWO is proven to produce significantly better results as compared to the identified algorithms.

We study the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. We deduce analytical expressions for the stationary occupation probability and for the mean and global first passage times. This general approach allows us to characterize the effect of resetting on the capacity of random walk strategies to reach a particular target or to explore the network. Our formalism holds for ergodic random walks and can be implemented from the spectral properties of the random walk without resetting, providing a tool to analyze the efficiency of search strategies with resetting to multiple nodes. We apply the methods developed here to the dynamics with two reset nodes and derive analytical results for normal random walks and Lévy flights on rings. We also explore the effect of resetting to multiple nodes on a comb graph, Lévy flights that visit specific locations in a continuous space, and the Google random walk strategy on regular networks.

Recent researches on multiview learning have received widespread attention due to the increasing generalization of multiview data. As an effective probabilistic model, random walk has also shown encouraging performance in various fields. To further exploit the potential of utilizing random walk schemes to address multiview learning problems, this article proposes a simple yet efficient multigraph random walk scheme for both multiview clustering and semisupervised classification tasks. The proposed model integrates random walk with multiview learning, and recursively learns a globally stable probability distribution matrix from multiple views, on the basis of which the label indicator is obtained in the scene of clustering or semisupervised classification. Furthermore, an adaptive weight vector is learned to incorporate the diversity and complementarity of multiview data. Besides, the relationships between the proposed scheme and spectral clustering, neighborhood embedding and manifold embedding are analyzed theoretically. Finally, comprehensive comparative experiments are conducted with several state-of-the-art multiview clustering and semisupervised classification methods on eight real-world datasets. The experimental results demonstrate the superiority of the proposed method in terms of both clustering and classification performance.

A newly hybrid nature inspired algorithm called HPSOGWO is presented with the combination of Particle Swarm Optimization (PSO) and Grey Wolf Optimizer (GWO). The main idea is to improve the ability of exploitation in Particle Swarm Optimization with the ability of exploration in Grey Wolf Optimizer to produce both variants’ strength. Some unimodal, multimodal, and fixed-dimension multimodal test functions are used to check the solution quality and performance of HPSOGWO variant. The numerical and statistical solutions show that the hybrid variant outperforms significantly the PSO and GWO variants in terms of solution quality, solution stability, convergence speed, and ability to find the global optimum.

Secure and economical operation of distribution networks needs the management of reactive power resources. Optimal Reactive Power Dispatch (ORPD) optimally manages the reactive power scheduling of generators and distribution generations as well as the Reactive Power Compensation (RPC) devices. This paper investigates the effect of load models on the multi-objective ORPD problem in active distribution networks. Moreover, a modified Grey Wolf Optimizer (GWO), which is called in this paper as Civilized GWO (CGWO), is introduced to solve the ORPD problem. The proposed strategy including multi-objective function, various load models, DG’s reactive power, RPCs and the introduced CGWO, is tested on standard IEEE 33- and 69-bus distribution systems. The obtained results indicate the load models have significant impact on the cost function amount. Moreover, the performance of the proposed algorithm is evaluated using ten standard benchmark functions. The optimization results demonstrate the robustness of the introduced optimization algorithm and its ability in finding the better solutions compared to the Particle Swarm Optimization (PSO), Exchange Market Algorithm (EMA), and original GWO.