Ameliorated elk herd optimizer for global optimization and engineering problems

A population-based optimizer called beluga whale optimization (BWO) depicts behavioral patterns of water aerobics, foraging, and diving whales. BWO runs effectively, nevertheless it retains numerous of deficiencies that has to be strengthened. Premature convergence and a disparity between exploitation and exploration are some of these challenges. Furthermore, the absence of a transfer parameter in the typical BWO when moving from the exploration phase to the exploitation phase has a direct impact on the algorithm’s performance. This work proposes a novel modified BWO (mBWO) optimizer that incorporates an elite evolution strategy, a randomization control factor, and a transition factor between exploitation and exploitation. The elite strategy preserves the top candidates for the subsequent generation so it helps generate effective solutions with meaningful differences between them to prevent settling into local maxima. The elite random mutation improves the search strategy and offers a more crucial exploration ability that prevents stagnation in the local optimum. The mBWO incorporates a controlling factor to direct the algorithm away from the local optima region during the randomization phase of the BWO. Gaussian local mutation (GM) acts on the initial position vector to produce a new location. Because of this, the majority of altered operators are scattered close to the original position, which is comparable to carrying out a local search in a small region. The original method can now depart the local optimal zone because to this modification, which also increases the optimizer’s optimization precision control randomization traverses the search space using random placements, which can lead to stagnation in the local optimal zone. Transition factor (TF) phase are used to make the transitions of the agents from exploration to exploitation gradually concerning the amount of time required. The mBWO undergoes comparison to the original BWO and 10 additional optimizers using 29 CEC2017 functions. Eight engineering problems are addressed by mBWO, involving the design of welded beams, three-bar trusses, tension/compression springs, speed reducers, the best design of industrial refrigeration systems, pressure vessel design challenges, cantilever beam designs, and multi-product batch plants. In both constrained and unconstrained settings, the results of mBWO preformed superior to those of other methods.

Computationally efficient and time‐memory saving compact algorithms become a keystone for solving global optimization problems, particularly the real world problems; which involve devices with limited memory or restricted use of battery power. Compact optimization algorithms represent a probabilistic view of the population to simulate the population behaviour as they broadly explores the decision space at the beginning of the optimization process and keep focus on to search the most promising solution, therefore narrows the search space, moreover few number of parameters need be stored in the memory thus require less space and time to compute efficiently. Role of population‐based algorithms remain inevitable as compact algorithms make use of the efficient search ability of these population based algorithms for optimization but only through a probabilistic representation of the population space in order to optimize the real world problems. Artificial bee colony (ABC) algorithm has shown to be competitive over other population‐based algorithms for solving optimization problems, however its solution search equation contributes to its insufficiency due to poor exploitation phase coupled with low convergence rate. This paper, presents a compact Artificial bee colony (cABC) algorithm with an improved solution search equation, which will be able to search an optimal solution to improve its exploitation capabilities, moreover in order to increase the global convergence of the proposed algorithm, an improved approach for population sampling is introduced through a compact distribution which helps in maintaining a good balance between exploration and exploitation search abilities of the proposed compact algorithm with least memory requirements, thus became suitable for limited hardware access devices. The proposed algorithm is evaluated extensively on a standard set of benchmark functions proposed at IEEE CEC'13 for large‐scale global optimization (LSGO) problems. Numerical results prove that the proposed compact algorithm outperforms other standard optimization algorithms.

Ideal solution candidate search for starling murmuration optimizer and its applications on global optimization and engineering problems

Monarch butterfly optimization is inspired by the migration of monarch butterflies in nature: monarch butterflies in eastern North America migrate southward from northern United States and southern Canada to Mexico every summer/autumn. It is a new swarm intelligence metaheuristic algorithm, which is called monarch butterfly optimization (MBO). In MBO, the monarch butterfly population is ideally divided into two populations, one is located in southern Canada and northern United States (land 1), and the other is located in Mexico (land 2). We update the individuals in the population through migration and butterfly shape adjustment. To maintain the diversity of the population and minimize the fitness value, the total number of butterflies generated by the operation should be equal to the original population. In the experiment, MBO is compared with five metaheuristic algorithms through 38 test functions, especially applied to solve a large-scale 0-1 knapsack (KP) problem. Three groups of 15 large-scale 0-1 KP cases from 800 to 2000 dimensions are used to test. It is proved that MBO has strong advantages in solving global numerical optimization and engineering problems, which provides a reference for further discussion of MBO in the future.

E-Pdo: An Enhanced Prairie Dog Optimization Algorithm with L´Evy Distribution and Dynamic Opposition-Based Learning for Global Optimization and Engineering Problems

Wireless sensor network (WSN) coverage optimization is a critical factor in improving network service quality, yet it faces challenges such as deployment uniformity, high-dimensional optimization, and the balance between exploration and exploitation under limited node resources. To address the shortcomings of the cultural historical optimization algorithm (CHOA), including insufficient global exploration, lack of dynamic regulation, and limited local exploitation accuracy, this paper proposes a film and television strategy-based multi-strategy cultural historical optimization algorithm (FTSCHOA). The proposed algorithm enhances performance through three synergistic mechanisms: a DE-style evolutionary operator that strengthens global exploration and population diversity; a film-and-television strategy that balances exploration and exploitation via random perturbations and adaptive parameter regulation; and a memory-based neighborhood local search that performs refined exploitation around high-quality solution sets to improve local optimization accuracy. Extensive experiments conducted on the CEC2017 and CEC2022 benchmark suites with dimensions of 10, 20, 30, and 50 demonstrate that FTSCHOA outperforms comparative algorithms in terms of optimization accuracy, convergence speed, and stability. The Friedman mean rank test indicates that FTSCHOA consistently achieves the best average ranking, while the Wilcoxon rank-sum test confirms that its performance differences with respect to competing algorithms are statistically significant (p<0.05). When applied to WSN coverage optimization in a 100 m×100 m monitoring region, FTSCHOA achieves coverage rates of 0.9351 and 0.9738 with 25 and 30 sensor nodes, respectively, which are significantly higher than those obtained by PSO, GWO, CHOA, and other algorithms. Moreover, the resulting node deployments exhibit greater uniformity, fewer coverage holes, and lower redundancy. The experimental results demonstrate that FTSCHOA effectively overcomes the limitations of traditional algorithms and provides an efficient and practical solution for WSN node deployment optimization, with strong potential for application in real-world scenarios such as environmental monitoring and smart agriculture.

This paper presents an improved beluga whale optimization (IBWO) algorithm, which is mainly used to solve global optimization problems and engineering problems. This improvement is proposed to solve the imbalance between exploration and exploitation and to solve the problem of insufficient convergence accuracy and speed of beluga whale optimization (BWO). In IBWO, we use a new group action strategy (GAS), which replaces the exploration phase in BWO. It was inspired by the group hunting behavior of beluga whales in nature. The GAS keeps individual belugas whales together, allowing them to hide together from the threat posed by their natural enemy, the tiger shark. It also enables the exchange of location information between individual belugas whales to enhance the balance between local and global lookups. On this basis, the dynamic pinhole imaging strategy (DPIS) and quadratic interpolation strategy (QIS) are added to improve the global optimization ability and search rate of IBWO and maintain diversity. In a comparison experiment, the performance of the optimization algorithm (IBWO) was tested by using CEC2017 and CEC2020 benchmark functions of different dimensions. Performance was analyzed by observing experimental data, convergence curves, and box graphs, and the results were tested using the Wilcoxon rank sum test. The results show that IBWO has good optimization performance and robustness. Finally, the applicability of IBWO to practical engineering problems is verified by five engineering problems.

Many key problems in science and engineering can be formulated and solved using global optimization techniques. In the particular case of computational biology, the development of dynamic (kinetic) models is one of the current key issues. In this context, the problem of parameter estimation (model calibration) remains as a very challenging task. The complexity of the underlying models requires the use of efficient solvers to achieve adequate results in reasonable computation times. Metaheuristics have been the focus of great consideration as an efficient way of solving hard global optimization problems. Even so, in most realistic applications, metaheuristics require a very large computation time to obtain an acceptable result. Therefore, several parallel schemes have been proposed, most of them focused on traditional parallel programming interfaces and infrastructures. However, with the emergence of cloud computing, new programming models have been proposed to deal with large-scale data processing on clouds. In this paper we explore the applicability of these new models for global optimization problems using as a case study a set of challenging parameter estimation problems in systems biology. We have developed, using Spark, an island-based parallel version of Differential Evolution. Differential Evolution is a simple population-based metaheuristic that, at the same time, is very popular for being very efficient in real function global optimization. Several experiments were conducted both on a cluster and on the Microsoft Azure public cloud to evaluate the speedup and efficiency of the proposal, concluding that the Spark implementation achieves not only competitive speedup against the serial implementation, but also good scalability when the number of nodes grows. The results can be useful for those interested in using parallel metaheuristics for global optimization problems benefiting from the potential of new cloud programming models.

The modeling and control of photovoltaic and other engineering systems highly depend on the accuracy of parameter identification. However, parameter extraction for photovoltaic equivalent models typically presents a high-dimensional, strongly nonlinear, and multimodal global optimization problem. Traditional analytical or gradient-based methods are sensitive to initial values and easily fall into local optima. To address this issue, this paper proposes a multi-strategy improvement teaching–learning-based optimization algorithm (SNTLBO). A social learning network structure with symmetric interaction topology is introduced into the classical TLBO framework to characterize the knowledge propagation relationships among individuals. Through this symmetric and balanced information exchange mechanism, learners can be guided not only by the teacher but also by multiple neighbors within the network, enabling more diverse and symmetric exploration of the search space and enhancing population diversity and global search capability. Furthermore, a teacher reputation mechanism is constructed, where historical performance is used to weight teacher influence, strengthening the guidance of high-quality solutions and accelerating convergence. Meanwhile, an adaptive teaching factor is designed to dynamically adjust the teaching intensity based on the distance between the teacher and students in the solution space, maintaining a dynamic balance (symmetry) between exploration and exploitation. To evaluate the performance of the proposed algorithm, SNTLBO is systematically compared with 11 advanced optimization algorithms on two benchmark test suites, CEC2017 (30D, 50D) and CEC2022 (10D, 20D). Non-parametric statistical tests are conducted to assess significance. The results demonstrate that SNTLBO shows competitive advantages in terms of convergence speed, solution accuracy, and stability. Finally, SNTLBO is applied to the parameter estimation of single-diode, double-diode, triple-diode, quadruple-diode, and photovoltaic module models. Experimental results show that the proposed algorithm achieves higher identification accuracy and robustness in terms of RMSE, IAE, and I–V/P–V curve fitting, verifying its effectiveness and practical value for complex global optimization and practical engineering applications.

Analysis of the dynamics of particle Swarm optimization

A dynamic chain-like agent genetic algorithm for global numerical optimization and feature selection

Bare-Bones Based Sine Cosine Algorithm for global optimization

Hybrid harmony search and artificial bee colony algorithm for global optimization problems

The osprey optimization algorithm (OOA) is a metaheuristic algorithm with a simple framework, which is inspired by the hunting process of ospreys. To enhance its searching capabilities and overcome the drawbacks of susceptibility to local optima and slow convergence speed, this paper proposes a modified osprey optimization algorithm (MOOA) by integrating multiple advanced strategies, including a Lévy flight strategy, a Brownian motion strategy and an RFDB selection method. The Lévy flight strategy and Brownian motion strategy are used to enhance the algorithm’s exploration ability. The RFDB selection method is conducive to search for the global optimal solution, which is a symmetrical strategy. Two sets of benchmark functions from CEC2017 and CEC2022 are employed to evaluate the optimization performance of the proposed method. By comparing with eight other optimization algorithms, the experimental results show that the MOOA has significant improvements in solution accuracy, stability, and convergence speed. Moreover, the efficacy of the MOOA in tackling real-world optimization problems is demonstrated using five engineering optimization design problems. Therefore, the MOOA has the potential to solve real-world complex optimization problems more effectively.

This paper proposes a multi-strategy Secretary Bird Optimization Algorithm (MS-SBOA) for solving global optimization problems and 3D wireless sensor network deployment. While preserving the original two-phase search framework of SBOA, the proposed algorithm achieves a dynamic balance between global exploration and local exploitation through the synergistic integration of multiple enhancement strategies, including a hybrid initialization scheme combining Latin hypercube sampling and quasi-opposition-based learning, a success-history-based adaptive parameter learning mechanism, a finance-inspired market-state trading operator, and an elite-guided population regulation strategy. Experimental results on the IEEE CEC2020 and CEC2022 benchmark test suites demonstrate that MS-SBOA significantly outperforms nine comparative algorithms, including VPPSO, IAGWO, and QHSBOA, under both 10-dimensional and 20-dimensional settings. The proposed algorithm exhibits superior optimization accuracy, faster convergence speed, and stronger robustness. Statistical analyses using the Wilcoxon rank-sum test and the Friedman mean rank test further confirm that the observed performance improvements are statistically significant. Moreover, MS-SBOA is applied to three-dimensional wireless sensor network (3D WSN) deployment optimization problems, where the average coverage rates reach 76.22% and 82.32% for 30-node and 50-node deployment scenarios, respectively. The resulting node distributions are more uniform, and the computational efficiency is improved compared with competing algorithms.