Harris hawks optimization (HHO) is a newly developed swarm-based algorithm and the most popular optimizer in the recent year, which mimics the cooperation behavior of Harris hawks. Although the original HHO has a specific weight compared to other state-of-the-art methods when working on the local exploitation of feasible solutions, it still may fail to achieve an excellent set of scales between locally accurate exploitation and globally exploratory search. This imbalanced behavior forms an overall perspective, which can be experienced by slow convergence, inaccuracy or inadequate search coverage, and quickly dropping into local solutions. In order to strengthen the performance of the HHO, two strategies of Gaussian mutation and a dimension decision strategy observed in the cuckoo search method are introduced into this optimizer. The mechanism of cuckoo search is very useful in improving the convergence speed of the search agents as well as sufficient excavation of the solutions in the search area, while the Gaussian mutation strategy performs well in increasing the accuracy and jumping out of the local optimum. In order to verify the remarkable performance of the proposed method, the enhanced paradigm is compared with other mate-heuristic algorithms on 30 IEEE CEC2017 benchmark functions and three typical engineering problems. The experimental results illustrate that the novel developed GCHHO has an excellent ability to achieve superior performance in competition with the original HHO as well as other well-established optimizers. Open source codes and information on original HHO algorithm is available at: https://aliasgharheidari.com/HHO.html . Supportive data and info for this research will be publicly provided in http://aliasgharheidari.com .

Dimension decided Harris hawks optimization with Gaussian mutation: Balance analysis and diversity patterns

In this paper, a novel swarm-based metaheuristic algorithm inspired from the behaviors of beluga whales, called beluga whale optimization (BWO), is presented to solve optimization problem. Three phases of exploration, exploitation and whale fall are established in BWO, corresponding to the behaviors of pair swim, prey, and whale fall, respectively. The balance factor and probability of whale fall in BWO are self-adaptive which play significant roles to control the ability of exploration and exploitation. Besides, the Levy flight is introduced to enhance the global convergence in the exploitation phase. The effectiveness of the proposed BWO is tested using 30 benchmark functions, with qualitative, quantitative and scalability analysis, and the statistical results are compared with 15 other metaheuristic algorithms. According to the results and discussion, BWO is a competitive algorithm in solving unimodal and multimodal optimization problems, and the overall rank of BWO is the first in the scalability analysis of benchmark functions among compared metaheuristic algorithms through the Friedman ranking test. Finally, four engineering problems demonstrate the merits and potential of BWO in solving complex real-world optimization problems. The source code of BWO is currently available to public: https://ww2.mathworks.cn/matlabcentral/fileexchange/112830-beluga-whale-optimization-bwo/ . • A novel metaheuristic algorithm named as Beluga Whale Optimization (BWO) is proposed. • The behaviors of swim, prey and whale fall are designed on BWO algorithm. • The BWO is tested on 30 well-known benchmark functions and 4 engineering problems. • The BWO is compared with 15 well-known metaheuristic algorithms. • The BWO outperforms comparing algorithms in benchmark functions, especially for scalability of dimension. 

Beluga whale optimization: A novel nature-inspired metaheuristic algorithm

The first-order reliability method (FORM) is a prevalent method in the structural reliability community. However, when solving the high-dimensional problem with a highly nonlinear limit state function, FORM usually encounters non-convergence or divergence. In this study, an improved FORM combining Harris Hawks Optimization (HHO-FORM) is presented for high-dimensional reliability analysis. HHO is a meta-heuristic algorithm mimicking the predatory behavior of Harris hawks, and efficient in finding the global optimum of high-dimensional problems. In HHO-FORM, the reliability index is firstly formulated as the solution of a constrained optimization problem according to the FORM theory. Then, the constraints are handled with the exterior penalty function method. In addition, the optimal reliability index is determined by the Harris Hawks Optimization that accelerates the convergence by the population-based mechanism and the strategy of Levy Flight. The HHO-FORM does not require the derivatives of the limit state functions that reduce the computational burden for high-dimensional problems. So the simplicity of HHO-FORM greatly improves the efficiency in solving high-dimensional reliability problems. The HHO-FORM is firstly tested on three challenging numerical high-dimensional problems and then applied to two high-dimensional engineering problems to verify its performance. Four gradient-based FORM algorithms and four heuristic-based FORM algorithms are also compared with the proposed method. The experimental results demonstrate that HHO-FORM provides good accuracy and efficiency for high-dimensional reliability problems.

First-order reliability method based on Harris Hawks Optimization for high-dimensional reliability analysis

Optimization and estimation in system reliability allocation problem

Harris hawks optimization (HHO) is a novel metaheuristic algorithm which has strong convergence for unconstrained optimization problems. However, HHO may encounter premature or local stagnation for constrained optimization problems. In this paper, a hybrid HHO algorithm named comprehensive learning harris hawks-equilibrium optimization (CLHHEO) is presented for solving constrained optimization problems, with the help of three operators: comprehensive learning, equilibrium optimizer, and terminal replacement mechanism. In the proposed algorithm, comprehensive learning strategy is incorporated with HHO to make search agents share their knowledge to enhance the convergence capacity. The operator of equilibrium optimizer is utilized to improve the exploration capacity of HHO. Besides, the terminal replacement mechanism is incorporated in the proposed algorithm to avoid local stagnation. The proposed CLHHEO is tested on 15 unconstrained and 10 real-world constrained optimization problems, and compared with 10 state-of-the-art metaheuristic algorithms, including PSO, CLPSO, BBBC, GWO, DA, WOA, SSA, HHO, SOA and AOA. From the experimental results, it is observed that CLHHEO outperforms HHO and other comparing metaheuristic algorithms in terms of solution quality. The results also demonstrate that the ensemble strategies of CLHHEO can enhance the performance of HHO for constrained optimization problems. 

Changting Zhong

Papers

Beluga whale optimization: A novel nature-inspired metaheuristic algorithm

First-order reliability method based on Harris Hawks Optimization for high-dimensional reliability analysis

Structural reliability assessment by salp swarm algorithm–based FORM

A hybrid teaching–learning slime mould algorithm for global optimization and reliability-based design optimization problems

A self-adaptive quantum equilibrium optimizer with artificial bee colony for feature selection