Low Convergence Accuracy Research Articles

Modified Harris Hawks Optimization Algorithm with Multi-strategy for Global Optimization Problem

<p>As a novel metaheuristic algorithm, the Harris Hawks Optimization (HHO) algorithm has excellent search capability. Similar to other metaheuristic algorithms, the HHO algorithm has low convergence accuracy and easily traps in local optimal when dealing with complex optimization problems. A modified Harris Hawks optimization (MHHO) algorithm with multiple strategies is presented to overcome this defect. First, chaotic mapping is used for population initialization to select an appropriate initiation position. Then, a novel nonlinear escape energy update strategy is presented to control the transformation of the algorithm phase. Finally, a nonlinear control strategy is implemented to further improve the algorithm’s efficiency. The experimental results on benchmark functions indicate that the performance of the MHHO algorithm outperforms other algorithms. In addition, to validate the performance of the MHHO algorithm in solving engineering problems, the proposed algorithm is applied to an indoor visible light positioning system, and the results show that the high precision positioning of the MHHO algorithm is obtained.</p> <p> </p>

Harris Hawks Algorithm Incorporating Tuna Swarm Algorithm and Differential Variance Strategy

Because of the low convergence accuracy of the basic Harris Hawks algorithm, which quickly falls into the local optimal, a Harris Hawks algorithm combining tuna swarm algorithm and differential mutation strategy (TDHHO) is proposed. The escape energy factor of nonlinear periodic energy decline balances the ability of global exploration and regional development. The parabolic foraging approach of the tuna swarm algorithm is introduced to enhance the global exploration ability of the algorithm and accelerate the convergence speed. The difference variation strategy is used to mutate the individual position and calculate the fitness, and the fitness of the original individual position is compared. The greedy technique is used to select the one with better fitness of the objective function, which increases the diversity of the population and improves the possibility of the algorithm jumping out of the local extreme value. The test function tests the TDHHO algorithm, and compared with other optimization algorithms, the experimental results show that the convergence speed and optimization accuracy of the improved Harris Hawks are improved. Finally, the enhanced Harris Hawks algorithm is applied to engineering optimization and wireless sensor networks (WSN) coverage optimization problems, and the feasibility of the TDHHO algorithm in practical application is further verified.

Multi-threshold Image Segmentation based on an improved Salp Swarm Algorithm: Case study of breast cancer pathology images

Breast cancer poses a significant risk to women’s health, and it is essential to provide proper diagnostic support. Medical image processing technology is a key component of all supporting diagnostic techniques, with Image Segmentation (IS) being one of its primary steps. Among various methods, Multilevel Image Segmentation (MIS) is considered one of the most effective and straightforward approaches. Many researchers have attempted to improve the quality of image segmentation by combining different metaheuristic algorithms with MIS. However, these methods often suffer from issues such as low convergence accuracy and a proclivity for converging towards Local Optima (LO). To overcome these challenges, this study introduces an integrated approach that combines the Salp Swarm Algorithm (SSA), Slime Mould Algorithm (SMA) and Differential Evolution (DE) algorithm. In this manuscript, we introduce an innovative hybrid MIS model termed SDSSA, which leverages elements from the SSA, SMA and DE algorithms. The SDSSA model fundamentally relies on non-local means 2D histogram and 2D Kapur’s entropy. To evaluate the proposed method effectively, we compare it initially with similar algorithms using the IEEE CEC2014 benchmark functions. The SDSSA showcases enhanced convergence velocity and precision relative to similar algorithms. Furthermore, this paper proposes an excellent MIS method. Subsequently, IS experiments were conducted separately at both low and high threshold levels. The test results demonstrate that the segmentation outcomes of MIS, at both low and high threshold levels, outperform other methods. This validates SDSSA as a superior segmentation technique that provides practical assistance for future research in breast cancer pathology image processing.

Adaptive Differential Evolutionary Algorithm for Innovative Teaching and Learning in High School Project-Based Courses

Abstract In this paper, for the innovative teaching of high school project-based courses, an adaptive differential evolutionary algorithm is used as one of the tools of the project to help students solve complex problems. The traditional adaptive differential evolution algorithm has the problems of local optimum and low convergence accuracy; to overcome these limitations, this paper proposes an enhanced reverse learning adaptive differential evolution algorithm. The OL-ADE algorithm is improved by introducing the reverse learning strategy in machine learning to extract the reverse elite individual population from the original individual population and select the better-adapted individuals for mutation operation. After the project-based teaching, the students’ works have high scores in layout color matching, technical operation, organization, information awareness, and information social responsibility, and their scores are 8.6, 9.75, 9, 9.35, and 8.75, respectively. Therefore, this paper proves the Adaptive Difference Evolution algorithm’s effectiveness in innovative teaching of high school project-based courses.

Improved Bat Algorithm Based on Fast Diving Strategy

<p>Bat algorithm has good global search ability, but it has some problems, such as slow convergence speed in local search stage, low convergence accuracy, easy to fall into local optimization and can not escape. In view of the above defects, inspired by Harris Hawks’s strategy of catching rabbits, this paper introduces the surrounding mechanism of prey, which can quickly approach the food and judge its quality, so as to achieve the purpose of rapid convergence and improve the convergence accuracy. The experiment shows that the improved algorithm of the fast diving strategy is tested by using the test function, and compared with the basic bat algorithm, backtracking bat algorithm and HABC. The improved bat algorithm of the fast diving strategy has better optimization accuracy, faster convergence speed, simple algorithm and higher success rate.</p> <p> </p>

Sand cat arithmetic optimization algorithm for global optimization engineering design problems

Abstract Sand cat swarm optimization (SCSO) is a recently introduced popular swarm intelligence metaheuristic algorithm, which has two significant limitations – low convergence accuracy and the tendency to get stuck in local optima. To alleviate these issues, this paper proposes an improved SCSO based on the arithmetic optimization algorithm (AOA), the refracted opposition-based learning and crisscross strategy, called the sand cat arithmetic optimization algorithm (SC-AOA), which introduced AOA to balance the exploration and exploitation and reduce the possibility of falling into the local optimum, used crisscross strategy to enhance convergence accuracy. The effectiveness of SC-AOA is benchmarked on 10 benchmark functions, CEC 2014, CEC 2017, CEC 2022, and eight engineering problems. The results show that the SC-AOA has a competitive performance.

A hybrid strategy-based GJO algorithm for robot path planning

Addressing the challenges of low convergence accuracy and stagnation at local optima in the application of the golden jackal optimizer (GJO) to mobile robot path planning, this paper proposes a hybrid strategy-based golden jackal optimizer (HGJO) algorithm. The improved algorithm employs a pre-decreasing slow nonlinear energy decay strategy to balance the global and local search capabilities. The roulette wheel selection algorithm and Lévy flight strategy are introduced into the position update of the GJO algorithm, so the proposed algorithm avoids stagnation at the local optimum. The HGJO algorithm is evaluated against some state-of-the-art optimizers on 23 benchmark functions and the CEC2021 benchmark function. It is also applied to ablation experiments for mobile robot path planning. The experimental results show that the HGJO algorithm improves the average path length in path planning by 0.21%, 82.4%, and 7.9% over the original algorithm in three different environments under 30 independent experiments.

Enhanced Grey Wolf Optimization Algorithm for Mobile Robot Path Planning

In this study, an enhanced hybrid Grey Wolf Optimization algorithm (HI-GWO) is proposed to address the challenges encountered in traditional swarm intelligence algorithms for mobile robot path planning. These challenges include low convergence accuracy, slow iteration speed, and vulnerability to local optima. The HI-GWO algorithm introduces several key improvements to overcome these limitations and enhance performance. To enhance the population diversity and improve the initialization process, Gauss chaotic mapping is applied to generate the initial population. A novel nonlinear convergence factor is designed to strike a balance between global exploration and local exploitation capabilities. This factor enables the algorithm to effectively explore the solution space while exploiting the promising regions to refine the search. Furthermore, an adaptive position update strategy is developed by combining Levy flight and golden sine. This strategy enhances the algorithm’s solution accuracy, global search capability, and search speed. Levy flight allows longer jumps to explore distant regions, while golden sine guides the search towards the most promising areas. Extensive simulations on 16 standard benchmark functions demonstrate the effectiveness of the proposed HI-GWO algorithm. The results indicate that the HI-GWO algorithm outperforms other state-of-the-art intelligent algorithms in terms of optimization performance. Moreover, the performance of the HI-GWO algorithm is evaluated in a real-world path planning experiment, where a comparison with the traditional grey wolf algorithm and ant colony algorithm validates the superior efficiency of the improved algorithm. It exhibits excellent optimization ability, robust global search capability, high convergence accuracy, and enhanced robustness in diverse and complex scenarios. The proposed HI-GWO algorithm contributes to advancing the field of mobile robot path planning by providing a more effective and efficient optimization approach. Its improvements in convergence accuracy, iteration speed, and robustness make it a promising choice for various practical applications.

PSO-Incorporated Hybrid Artificial Hummingbird Algorithm with Elite Opposition-Based Learning and Cauchy Mutation: A Case Study of Shape Optimization for CSGC-Ball Curves.

With the rapid development of the geometric modeling industry and computer technology, the design and shape optimization of complex curve shapes have now become a very important research topic in CAGD. In this paper, the Hybrid Artificial Hummingbird Algorithm (HAHA) is used to optimize complex composite shape-adjustable generalized cubic Ball (CSGC-Ball, for short) curves. Firstly, the Artificial Hummingbird algorithm (AHA), as a newly proposed meta-heuristic algorithm, has the advantages of simple structure and easy implementation and can quickly find the global optimal solution. However, there are still limitations, such as low convergence accuracy and the tendency to fall into local optimization. Therefore, this paper proposes the HAHA based on the original AHA, combined with the elite opposition-based learning strategy, PSO, and Cauchy mutation, to increase the population diversity of the original algorithm, avoid falling into local optimization, and thus improve the accuracy and rate of convergence of the original AHA. Twenty-five benchmark test functions and the CEC 2022 test suite are used to evaluate the overall performance of HAHA, and the experimental results are statistically analyzed using Friedman and Wilkerson rank sum tests. The experimental results show that, compared with other advanced algorithms, HAHA has good competitiveness and practicality. Secondly, in order to better realize the modeling of complex curves in engineering, the CSGC-Ball curves with global and local shape parameters are constructed based on SGC-Ball basis functions. By changing the shape parameters, the whole or local shape of the curves can be adjusted more flexibly. Finally, in order to make the constructed curve have a more ideal shape, the CSGC-Ball curve-shape optimization model is established based on the minimum curve energy value, and the proposed HAHA is used to solve the established shape optimization model. Two representative numerical examples comprehensively verify the effectiveness and superiority of HAHA in solving CSGC-Ball curve-shape optimization problems.

PECSO: An Improved Chicken Swarm Optimization Algorithm with Performance-Enhanced Strategy and Its Application.

To solve the problems of low convergence accuracy, slow speed, and common falls into local optima of the Chicken Swarm Optimization Algorithm (CSO), a performance enhancement strategy of the CSO algorithm (PECSO) is proposed with the aim of overcoming its deficiencies. Firstly, the hierarchy is established by the free grouping mechanism, which enhances the diversity of individuals in the hierarchy and expands the exploration range of the search space. Secondly, the number of niches is divided, with the hen as the center. By introducing synchronous updating and spiral learning strategies among the individuals in the niche, the balance between exploration and exploitation can be maintained more effectively. Finally, the performance of the PECSO algorithm is verified by the CEC2017 benchmark function. Experiments show that, compared with other algorithms, the proposed algorithm has the advantages of fast convergence, high precision and strong stability. Meanwhile, in order to investigate the potential of the PECSO algorithm in dealing with practical problems, three engineering optimization cases and the inverse kinematic solution of the robot are considered. The simulation results indicate that the PECSO algorithm can obtain a good solution to engineering optimization problems and has a better competitive effect on solving the inverse kinematics of robots.

HBWO-JS: jellyfish search boosted hybrid beluga whale optimization algorithm for engineering applications

Abstract Beluga whale optimization (BWO) algorithm is a recently proposed population intelligence algorithm. Inspired by the swimming, foraging, and whale falling behaviors of beluga whale populations, it shows good competitive performance compared to other state-of-the-art algorithms. However, the original BWO faces the challenges of unbalanced exploration and exploitation, premature stagnation of iterations, and low convergence accuracy in high-dimensional complex applications. Aiming at these challenges, a hybrid BWO based on the jellyfish search optimizer (HBWO-JS), which combines the vertical crossover operator and Gaussian variation strategy with a fusion of jellyfish search (JS) optimizer, is developed for solving global optimization in this paper. First, the BWO algorithm is fused with the JS optimizer to improve the problem that BWO tends to fall into the best local solution and low convergence accuracy in the exploitation stage through multi-stage exploration and collaborative exploitation. Then, the introduced vertical cross operator solves the problem of unbalanced exploration and exploitation processes by normalizing the upper and lower bounds of two stochastic dimensions of the search agent, thus further improving the overall optimization capability. In addition, the introduced Gaussian variation strategy forces the agent to explore the minimum neighborhood, extending the entire iterative search process and thus alleviating the problem of premature stagnation of the algorithm. Finally, the superiority of the proposed HBWO-JS is verified in detail by comparing it with basic BWO and eight state-of-the-art algorithms on the CEC2019 and CEC2020 test suites, respectively. Also, the scalability of HBWO-JS is evaluated in three dimensions (10D, 30D, 50D), and the results show the stable performance of the proposed algorithm in terms of dimensional scalability. In addition, three practical engineering designs and two Truss topology optimization problems demonstrate the practicality of HBWO-JS. The optimization results show that HBWO-JS has a strong competitive ability and broad application prospects.

A novel hybrid multi-verse optimizer with queuing search algorithm

Multi-verse optimizer (MVO) is a novel nature-inspired algorithm that has been applied to solve many practical optimization problems. Nevertheless, the original MVO has problems of low convergence speed and accuracy of final solutions. Besides, the failure to strike a balance between exploration and exploitation and the easiness of falling into local optimum in the early stages makes MVO hard to converge. In this paper, we propose a novel hybrid algorithm called Hybrid Queuing Search algorithm with MVO (HQS-MVO) by introducing Queuing Search Algorithm (QSA) and Metropolis rule to overcome these shortcomings. The introduction of QSA is to improve the accuracy of final solutions. At the same time, the Metropolis rule is employed to prevent the algorithm from falling into the local optimum, thus improving the convergence speed of the original MVO. Then, we compare the performance of HQS-MVO on 30 benchmark functions of CEC2014 and 10 benchmark functions of CEC2019 with the other four related algorithms and three latest algorithms. The results show that HQS-MVO has the most accurate solutions in most cases compared with other seven algorithms in most cases, and gains the lowest standard deviations. Moreover, we make convergence curve of the eight algorithms. Compared with other algorithms, HQS-MVO shows outstanding performances and converge faster in general. Finally, we apply the proposed algorithm in a real engineering optimization problem and compare its performance with other algorithms, the results show that HQS-MVO is still the best one in problem of designing of gear train.

Research on eye movement data classification using support vector machine with improved whale optimization algorithm

When performing eye movement pattern classification for different tasks, support vector machines are greatly affected by parameters. To address this problem, we propose an algorithm based on the improved whale algorithm to optimize support vector machines to enhance the performance of eye movement data classification. According to the characteristics of eye movement data, this study first extracts 57 features related to fixation and saccade, then uses the ReliefF algorithm for feature selection. To address the problems of low convergence accuracy and easy falling into local minima of the whale algorithm, we introduce inertia weights to balance local search and global search to accelerate the convergence speed of the algorithm and also use the differential variation strategy to increase individual diversity to jump out of local optimum. In this paper, experiments are conducted on eight test functions, and the results show that the improved whale algorithm has the best convergence accuracy and convergence speed. Finally, this paper applies the optimized support vector machine model of the improved whale algorithm to the task of classifying eye movement data in autism, and the experimental results on the public dataset show that the accuracy of the eye movement data classification of this paper is greatly improved compared with that of the traditional support vector machine method. Compared with the standard whale algorithm and other optimization algorithms, the optimized model proposed in this paper has higher recognition accuracy and provides a new idea and method for eye movement pattern recognition. In the future, eye movement data can be obtained by combining it with eye trackers to assist in medical diagnosis.

Improved Multi-Strategy Harris Hawks Optimization and Its Application in Engineering Problems

In order to compensate for the low convergence accuracy, slow rate of convergence, and easily falling into the trap of local optima for the original Harris hawks optimization (HHO) algorithm, an improved multi-strategy Harris hawks optimization (MSHHO) algorithm is proposed. First, the population is initialized by Sobol sequences to increase the diversity of the population. Second, the elite opposition-based learning strategy is incorporated to improve the versatility and quality of the solution sets. Furthermore, the energy updating strategy of the original algorithm is optimized to enhance the exploration and exploitation capability of the algorithm in a nonlinear update manner. Finally, the Gaussian walk learning strategy is introduced to avoid the algorithm being trapped in a stagnant state and slipping into a local optimum. We perform experiments on 33 benchmark functions and 2 engineering application problems to verify the performance of the proposed algorithm. The experimental results show that the improved algorithm has good performance in terms of optimization seeking accuracy, the speed of convergence, and stability, which effectively remedies the defects of the original algorithm.

A hybrid discrete state transition algorithm for combinatorial optimization problems

The discrete state transition algorithm (DSTA) has been wildly applied to deal with combinatorial optimization problems. However, its low convergence accuracy limits its application in large-scale optimization problems. Aiming at the convergence performance and search intensity of the algorithm, a hybrid discrete state transition algorithm (HDSTA) is proposed in this work by introducing tabu search and elite solution set. Firstly, a searching mechanism with the integration of DSTA and tabu search (TS) is established, which allows moving to adjacent solutions at an increased cost to escape from the local optimum. Specifically, a tabu list as adaptive memory is adopted to avoid the loop when deviating from local optima. Secondly, an elite solution set is introduced to integrate the information of the previous optimal solution and the global optimal solution, and the search strategy is modified to expand the range and diversity of candidate solutions. Finally, the proposed HDSTA is verified according to the real data on two well-known optimization problems (staff assignment problem and traveling salesman problem) and the real data of an industrial case. The experimental results show the effectiveness of the proposed algorithm in large-scale optimization problems.

An improved cooperation search algorithm for the multi-degree reduction in Ball Bézier surfaces

Cooperation search algorithm (CSA) is a new metaheuristic algorithm inspired from the team cooperation behaviors in modern enterprises and is characterized by fast convergence. However, for complex multimodal problems, it may get trapped into local optima and suffer from premature convergence for the shortcoming of population updating guided only by leading individuals. In this paper, the issue of low convergence efficiency and convergence accuracy of the CSA algorithm on complex multimodal problems is dramatically alleviated by integrating the mutation and crossover operators in DE algorithm. Experimental results demonstrate the better performance of CCSA on convergence speed and accuracy as compared to other existing optimizers. Furthermore, aiming at the problem that there is no universal approach for the multi-degree reduction in Ball Bézier surfaces under different interpolation constrains, we propose a new method to solve this problem by introducing metaheuristic methods, where the change of interpolation constrains is treated as the change of decision variables. The modeling examples show that the proposed method is effective and easy to implement under different interpolation constrains, which can achieve the multi-degree reduction in Ball Bézier surfaces at one time and can simplify the degree reduction procedure significantly.

DTCSMO: An efficient hybrid starling murmuration optimizer for engineering applications

Starling murmuration optimizer is a newly well-developed swarm intelligence algorithm inspired by the behavior of starlings during stunning murmuration and has performed competitively with other well-known methods. However, starling murmuration optimizer faces the issues of poor search capability, iterative stagnation, and low convergence accuracy when dealing with complex engineering optimization and high-dimensional problems. To ameliorate these deficiencies, an efficient hybrid starling murmuration optimizer that combines dynamic opposition, Taylor-based optimal neighborhood strategy, and crossover operator is developed in this paper. Firstly, introducing the Taylor-based optimal neighborhood strategy ensures a more careful and reasonable reliance on optimal individuals, thus reducing the possibility of falling into local optima. Meanwhile, dynamic opposition successfully balances the exploration and development phases by incorporating the ideas of quasi- and reflective opposition. In addition, the exploration-development capability is further enhanced by introducing the crossover operator. To ensure the adaptivity of the crossover factor, 12 different inertia weights are explored for crossover factors, and the sigmoidal decreasing inertia weights achieve optimality. Finally, the excellent performance of the proposed algorithm is verified by comparing it with the improved algorithm and the state-of-the-art search algorithms on 26 benchmark functions and the CEC2020 test suite, respectively. In addition, the proposed algorithm is used to optimize ten practical engineering optimization problems. Experimental results demonstrate that the proposed algorithm has strong competitiveness in this algorithm regarding computational power and convergence accuracy. Finally, the proposed algorithm is applied to two truss topology optimization designs. The experimental results demonstrate the applicability and potential of the proposed algorithm in practical applications. The proposed algorithm is a competitive optimization algorithm for solving optimization problems.

A chaos-based adaptive equilibrium optimizer algorithm for solving global optimization problems.

The equilibrium optimizer (EO) algorithm is a newly developed physics-based optimization algorithm, which inspired by a mixed dynamic mass balance equation on a controlled fixed volume. The EO algorithm has a number of strengths, such as simple structure, easy implementation, few parameters and its effectiveness has been demonstrated on numerical optimization problems. However, the canonical EO still presents some drawbacks, such as poor balance between exploration and exploitation operation, tendency to get stuck in local optima and low convergence accuracy. To tackle these limitations, this paper proposes a new EO-based approach with an adaptive gbest-guided search mechanism and a chaos mechanism (called a chaos-based adaptive equilibrium optimizer algorithm (ACEO)). Firstly, an adaptive gbest-guided mechanism is injected to enrich the population diversity and expand the search range. Next, the chaos mechanism is incorporated to enable the algorithm to escape from the local optima. The effectiveness of the developed ACEO is demonstrated on 23 classical benchmark functions, and compared with the canonical EO, EO variants and other frontier metaheuristic approaches. The experimental results reveal that the developed ACEO method remarkably outperforms the canonical EO and other competitors. In addition, ACEO is implemented to solve a mobile robot path planning (MRPP) task, and compared with other typical metaheuristic techniques. The comparison indicates that ACEO beats its competitors, and the ACEO algorithm can provide high-quality feasible solutions for MRPP.

Particle Swarm Optimization Algorithm With Adaptive Two-Population Strategy

The particle swarm optimization (PSO) algorithm is a swarm intelligence (SI) algorithm used to solve optimization problems. Owing to its advantages in simplicity, using only a few parameters, PSO has become one of the most popular optimization algorithms. However, the single structure of PSO leads to challenges in finding the appropriate optima, resulting in low convergence accuracy. To solve the defects of PSO, it is necessary to increase the diversity of the populations involved as well as enhance the ability of the algorithm to develop locally. In this study, we propose a PSO algorithm with an adaptive two-population strategy (PSO-ATPS), which adaptively divides a population into two groups representing excellent and ordinary populations. Inspired by animal hunting behavior, a new velocity–position update method is proposed for the general population. A velocity update formulation with decreasing inertia weights based on logistic chaotic mapping is applied to the excellent population. The algorithm increases the diversity of the population by continuously changing the search strategy of the particles. In addition, a new neighborhood search strategy (oscillation strategy) is proposed, in which a particle searches randomly in its own adaptive neighborhood when its motion is stagnant and updates the particle position using an elite strategy. Among several optimization strategies, PSO-ATPS achieved first place in 7, 8, and 9 groups of tests involving 10 test functions in 3 dimensions, indicating the accuracy and effectiveness of PSO-ATPS. The results show that the performance of PSO-ATPS is competitive, and many improvements developed for PSO can be applied to PSO-ATPS, demonstrating the potential for further development.

Path Planning for Autonomous Underwater Vehicles Based on an Improved Artificial Jellyfish Search Algorithm in Multi-Obstacle Ocean Current Environment

Path planning for autonomous underwater vehicles (AUVs) is a key research focus in the marine domain, requiring consideration of the underwater environment’s complexity and the efficiency of the planning algorithms. Firstly, this paper uses the grid method to construct a realistic ocean terrain for the underwater environment and incorporates obstacles and ocean currents. Also, the AUV’s movement strategy and posture are illustrated and constrained by a visual search strategy. Secondly, an improved artificial jellyfish search (IJS) algorithm is to overcome the drawbacks of low convergence accuracy and adaptability of the basic algorithm. The IJS algorithm determines the optimal path point by optimizing the objective function. This objective function not only takes into account factors such as path navigation time and path safety but also designs an ocean current disturbance model, which facilitates the AUV to successfully reach the target point while avoiding obstacles and strong side currents. Finally, the optimal smoothed path is output using a cubic spline midpoint interpolation method. Multiple simulation experiments are carried out on the constructed environment model. The comparison results show that the IJS algorithm with a short running time has the optimal time cost and ocean current penalty cost for the planned path. In addition, the IJS algorithm is also shown to be adaptable in the field of multi-AUV movements.