An Improved Whale Optimization Algorithm Based on Different Searching Paths and Perceptual Disturbance

Through the research and analysis of a relatively novel natural heuristic, meta-heuristic swarm intelligence optimization algorithm, this swarm intelligence algorithm is defined as a whale optimization algorithm. The algorithm builds a mathematical model by simulating a social behavior of humpback whales. This optimization algorithm was inspired by the bubble-like net hunting phenomenon that humpback whales prey on. By analyzing the four benchmark optimization problems with or without offset and rotation, the convergence performance of the whale optimization algorithm and the ability to solve the optimization problem are proved. The performance of the whale optimization algorithm is based on the computer simulation technology. Through the convergence curve obtained from the experiment, we can see that the whale optimization algorithm performs best for the five benchmark optimization problems without rotation.

Near infrared spectroscopic variable selection by a novel swarm intelligence algorithm for rapid quantification of high order edible blend oil

Clustering is a fundamental data analysis task that presents challenges. Choosing proper initialization centroid techniques is critical to the success of clustering algorithms, such as k-means. The current work investigates six established methods (random, Forgy, k-means++, PCA, hierarchical clustering, and naive sharding) and three innovative swarm intelligence-based approaches—Spider Monkey Optimization (SMO), Whale Optimization Algorithm (WOA) and Grey Wolf Optimizer (GWO)—for k-means clustering (SMOKM, WOAKM, and GWOKM). The results on ten well-known datasets strongly favor swarm intelligence-based techniques, with SMOKM consistently outperforming WOAKM and GWOKM. This finding provides critical insights into selecting and evaluating centroid techniques in k-means clustering. The current work is valuable because it provides guidance for those seeking optimal solutions for clustering diverse datasets. Swarm intelligence, especially SMOKM, effectively generates distinct and well-separated clusters, which is valuable in resource-constrained settings. The research also sheds light on the performance of traditional methods such as hierarchical clustering, PCA, and k-means++, which, while promising for specific datasets, consistently underperform swarm intelligence-based alternatives. In conclusion, the current work contributes essential insights into selecting and evaluating initialization centroid techniques for k-means clustering. It highlights the superiority of swarm intelligence, particularly SMOKM, and provides actionable guidance for addressing various clustering challenges.

Using swarm intelligence algorithms to detect influential individuals for influence maximization in social networks

A rising meta-heuristic swarm intelligent computation algorithm, the Whale optimization Algorithm (WOA), which has been proved competitive with other intelligent optimization algorithms in solving different optimization problems. To accelerate the convergence rate of WOA, this paper has proposed a new improved whale optimization algorithm, called Chaos Regulation Whale optimization Algorithm (CRWOA). The chaotic map generator composed with three kinds of chaotic maps has been used to initialize the population. Furthermore, Cauchy distribution and Gauss distribution are introduced to regulate the position in each iteration. To analyze the superiority of CRWOA further, ten single-objective benchmark test functions are chosen. Through the comparison and analysis of the optimal results, CRWOA is demonstrated superior in general. It has faster convergence speed and better results than the other algorithms when less iteration number, less population quantity and wider ranges of variables are set.

A hybrid modified step Whale Optimization Algorithm with Tabu Search for data clustering

In order to protect the environment, an increasing number of people are paying attention to the recycling and remanufacturing of EOL (End-of-Life) products. Furthermore, many companies aim to establish their own closed-loop supply chains, encouraging the integration of disassembly and assembly lines into a unified closed-loop production system. In this work, a hybrid production line that combines disassembly and assembly processes, incorporating human–machine collaboration, is designed based on the traditional disassembly line. A mathematical model is proposed to address the human–machine collaboration disassembly and assembly hybrid line balancing problem in this layout. To solve the model, an evolutionary learning-based whale optimization algorithm is developed. The experimental results show that the proposed algorithm is significantly faster than CPLEX, particularly for large-scale disassembly instances. Moreover, it outperforms CPLEX and other swarm intelligence algorithms in solving large-scale optimization problems while maintaining high solution quality.

To address the insufficient global search efficiency of the original Whale Optimization Algorithm (WOA), this paper proposes an enhanced variant (ImWOA) integrating three strategies. First, a dynamic cluster center-guided search mechanism based on K-means clustering divides the population into subgroups that conduct targeted searches around dynamically updated centroids, with real-time centroid recalculation enabling evolutionary adaptation. This strategy innovatively combines global optima with local centroids, significantly improving global exploration while reducing redundant searches. Second, a dual-modal diversity-driven adaptive mutation mechanism simultaneously evaluates spatial distribution and fitness-value diversity to comprehensively characterize population heterogeneity. It dynamically adjusts mutation probability based on diversity states, enhancing robustness. Finally, a pattern search strategy (GPSPositiveBasis2N algorithm) is embedded as a periodic optimization module, synergizing WOA's global exploration with GPSPositiveBasis2N's local precision to boost solution quality and convergence. Evaluated on the CEC2017 benchmark against the original WOA, eight state-of-the-art metaheuristics, and five advanced WOA variants, ImWOA achieves: (1) optimal mean values for 20/29 functions in 30D tests; (2) optimal mean values for 26/29 functions in 100D tests; and (3) first rank in 3D-TSP validation, demonstrating superior capability for complex optimization.

With the growing emphasis on intelligent and sustainable manufacturing, the flexible job shop scheduling problem (FJSP) has emerged as a critical optimization challenge due to its capability to model complex and dynamic production environments. As an NP-hard problem, FJSP poses significantly greater complexity than the classical job shop scheduling problem, particularly in high-precision domains such as aerospace manufacturing, where traditional optimization methods often fall short. To overcome the limitations of the standard Whale Optimization Algorithm (WOA)–namely its continuous search paradigm and inadequate local search mechanisms–this paper proposes a genetic-operator-integrated whale optimization algorithm (GOI-WOA) tailored for discrete scheduling tasks. The GOI-WOA employs a two-layer discrete encoding strategy to represent operations and machine assignments, and introduces genetic operators, a critical-path-based neighborhood search, and a temporal-entropy-based local search to enhance solution diversity and local exploitation. Furthermore, an elite information-sharing mechanism is incorporated to facilitate the diffusion of high-quality solutions within the population. Comprehensive experiments conducted on standard benchmark instances demonstrate that GOI-WOA consistently outperforms baseline WOA and other state-of-the-art methods in terms of makespan minimization, convergence stability, and computational efficiency. These results validate the effectiveness and robustness of GOI-WOA as a competitive solution framework for complex manufacturing scheduling problems.

During recent decades, evolutionary algorithms have been widely studied in optimization problems. The multi-objective whale optimization algorithm based on multi-leader guiding is proposed in this paper, which attempts to offer a proper framework to apply whale optimization algorithm and other swarm intelligence algorithms to solving multi-objective optimization problems. The proposed algorithm adopts several improvements to enhance optimization performance. First, search agents are classified into leadership set and ordinary set by grid mechanism, and multiple leadership solutions guide the population to search the sparse spaces to achieve more homogeneous exploration in per iteration. Second, the differential evolution and whale optimization algorithm are employed to generate the offspring for the leadership and ordinary solutions, respectively. In addition, a novel opposition-based learning strategy is developed to improve the distribution of the initial population. The performance of the proposed algorithm is verified in contrast to 10 classic or state-of-the-arts algorithms on 20 bi-objective and tri-objective unconstrained problems, and experimental results demonstrate the competitive advantages in optimization quality and convergence speed. Moreover, it is tested on load distribution of hot rolling, and the result proves its good performance in real-world applications. Thus, all of the aforementioned experiments have indicated that the proposed algorithm is comparatively effective and efficient.

The application of swarm intelligence (SI) in the optimization field has been gaining much popularity, and various SI algorithms have been proposed in last decade. However, with the increased number of SI algorithms, most research focuses on the implementation of a specific choice of SI algorithms, and there has been rare research analyzing the common features among SI algorithms coherently. More importantly, no general principles for the implementation and improvement of SI algorithms exist for solving various optimization problems. In this research, aiming to cover such a research gap, a unified framework towards SI is proposed inspired by the in-depth analysis of SI algorithms. The unified framework consists of the most frequently used operations and strategies derived from typical examples of SI algorithms. Following the proposed unified framework, the intrinsic features of SI algorithms can be understood straightforwardly and the implementation and improvement of SI algorithms can be achieved effortlessly, which is of great importance in practice. The numerical experiments examine the effects of the possible strategies employed in the unified framework, and provide pilot attempts to validate the performance of different combinations of strategies, which can not only facilitate specific SI algorithm application, but also can motivate SI algorithm innovation.

In the field of asset allocation, how to balance the returns of an investment portfolio and its fluctuations is the core issue. Capital asset pricing model, arbitrage pricing theory, and Fama–French three-factor model were used to quantify the price of individual stocks and portfolios. Based on the second-order stochastic dominance rule, the higher moments of return series, the Shannon entropy, and some other actual investment constraints, we construct a multiconstraint portfolio optimization model, aiming at comprehensively weighting the returns and risk of portfolios rather than blindly maximizing its returns. Furthermore, the whale optimization algorithm based on FTSE100 index data is used to optimize the above multiconstraint portfolio optimization model, which significantly improves the rate of return of the simple diversified buy-and-hold strategy or the FTSE100 index. Furthermore, extensive experiments validate the superiority of the whale optimization algorithm over the other four swarm intelligence optimization algorithms (gray wolf optimizer, fruit fly optimization algorithm, particle swarm optimization, and firefly algorithm) through various indicators of the results, especially under harsh constraints.

Solid particle erosion prediction in elbows based on machine learning and swarm intelligence algorithm

In order to solve the problems of slow convergence speed, insufficient accuracy, and easily falling into the local optimum of the traditional whale optimization algorithm (WOA) in mobile robot path planning, an improved whale optimization algorithm (IWOA) combined with the bird navigation mechanism was proposed. Specific improvement measures include using logical chaos mapping to initialize the population to enhance the randomness and diversity of the initial solution, designing a nonlinear convergence factor to prevent the algorithm from prematurely entering the shrinking surround phase and extending the global search time, introducing an adaptive spiral shape constant to dynamically adjust the search range to balance exploration and development capabilities, optimizing the individual update strategy in combination with the bird navigation mechanism, and optimizing the algorithm through companion position information, thereby improving the stability and convergence speed of the algorithm. Path planning simulations were performed on 30 × 30 and 50 × 50 grid maps. The results show that compared with WOA, MSWOA, and GA, in the 30 × 30 map, the path length of IWOA is shortened by 3.23%, 7.16%, and 6.49%, respectively; in the 50 × 50 map, the path length is shortened by 4.88%, 4.53%, and 28.37%, respectively. This study shows that IWOA has significant advantages in the accuracy and efficiency of path planning, which verifies its feasibility and superiority.

Value function approximation, such as Q-learning, is widely used in the discrete control rather than the continuous one because the optimal action in the discrete setting is more easily selected. Optimizing the action is a non-convex optimization problem with respect to the complex value function. Some notable studies simplify the non-convex optimization problem by assuming the value function as quadratic in the actions or by discretizing the action space. However, the performance of the output policy will decline if these studies’ premises do not hold. In order to address the problem, we propose a framework that combines swarm intelligence algorithms with value-based Reinforcement Learning, where the swarm intelligence algorithms are employed to search for the optimal action with respect to the state and the value function. To ensure the correctness of this framework, we conditionally claim the convergence rate of swarm intelligence algorithms with high probability. We then implement it by searching the batch optimal actions to various states on the GPU platform for the batch training. Furthermore, we employ the population-based atomic actions for the compatibility with the existing related work about solving discrete control problems. Four classical control models and four robot simulation environments are utilized in the comparisons. According to empirical results, our framework outputs a policy comparable with that of the policy-based algorithms by 10% timesteps in the continuous control. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the exploration-exploitation dilemma of Reinforcement Learning to solve continuous control tasks. To balance the exploration and exploitation, the stochastic exploration and the prioritized exploration are roughly two feasible ways, where the prioritized one is a better choice due to the higher data efficiency than the stochastic one, e.g. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon$</tex-math> </inline-formula> -greedy. Normally, the prioritized exploration works well in the value-based Reinforcement Learning algorithms rather than the policy-based ones; meanwhile, the policy-based algorithms are more suitable to continuous control tasks than the value-based ones. To tackle this conflict, we especially design a particle swarm optimization to maximize the Q-value of action in Q-learning. Our design can be hybridized by various swarm intelligence and value-based Reinforcement Learning algorithms. Also, it can be embedded in most intelligent control systems easily. The aim of this study is to solve the continuous control tasks by value-based algorithms as the first step of applying the prioritized exploration. The simulative results verify the effectiveness and efficiency of our design.