Enhanced Multi-Objective Grey Wolf Optimization using Adaptive Diversity Tuning and Levy Flights

Feature selection is a widely utilized technique in educational data mining that aims to simplify and reduce the computational burden associated with data analysis. However, previous studies have overlooked the high costs involved in acquiring certain types of educational data. In this study, we investigate the application of a multi-objective gray wolf optimizer (GWO) with cost-sensitive feature selection to predict students’ academic performance in college English, while minimizing both prediction error and feature cost. To improve the performance of the multi-objective binary GWO, a novel position update method and a selection mechanism for a, b, and d are proposed. Additionally, the adaptive mutation of Pareto optimal solutions improves convergence and avoids falling into local traps. The repairing technique of duplicate solutions expands population diversity and reduces feature cost. Experiments using UCI datasets demonstrate that the proposed algorithm outperforms existing state-of-the-art algorithms in hypervolume (HV), inverted generational distance (IGD), and Pareto optimal solutions. Finally, when predicting the academic performance of students in college English, the superiority of the proposed algorithm is again confirmed, as well as its acquisition of key features that impact cost-sensitive feature selection.

This paper introduces an improved multi-objective grey wolf optimizer (IMOGWO) and demonstrates its application to the aerodynamic optimization of an axial cooling fan. Building upon the traditional multi-objective grey wolf optimizer (MOGWO), several improvement strategies were adopted to enhance its performance. Firstly, the IMOGWO started population initialization based on the Bloch coordinates of qubits to ensure a high-quality initial population. Additionally, it employed a nonlinear convergence factor to facilitate global exploration and integrated the inspiration of Manta Ray Foraging to enhance the information exchange between populations. Finally, associative learning was leveraged for archive updating, allowing for perturbative mutation of solutions in crowded regions of the archive to increase solution diversity and improve the algorithm’s search capability. The proposed IMOGWO was applied to five multi-objective benchmark functions, comprising three two-objective and two three-objective problems, and experimental results were compared with three well-known multi-objective algorithms: the non-dominated sorting genetic algorithm II (NSGA II), MOGWO, and the multi-objective multi-verse optimizer (MOMVO). It is demonstrated that the proposed algorithm had advantages in convergence accuracy and diversity of solutions, which were quantified by the performance metrics (generational distance (GD), inverted generational distance (IGD), Spacing (SP), and Hypervolume (HV)). Furthermore, a multi-objective optimization process coupled with the IMOGWO algorithm and Computational Fluid Dynamics (CFD) was proposed. By optimizing the design parameters of an axial cooling fan, a set of non-dominated solutions was obtained within limited iteration steps. Consequently, the IMOGWO also presented an effective and practical approach for addressing multi-objective optimization challenges with respect to engineering problems.

Multi-objective Grey Wolf Optimizer for improved cervix lesion classification

Multi-objective scheduling of a single mobile robot based on the grey wolf optimization algorithm

With the rise of low-cost launches, miniaturized space technology, and commercialization, the cost of space missions has dropped, leading to a surge in flexible Earth observation satellites. This increased demand for complex and diverse imaging products requires addressing multi-objective optimization in practice. To this end, we propose a multi-objective agile Earth observation satellite scheduling problem (MOAEOSSP) model and introduce a reinforcement learning-based multi-objective grey wolf optimization (RLMOGWO) algorithm. It aims to maximize observation efficiency while minimizing energy consumption. During population initialization, the algorithm uses chaos mapping and opposition-based learning to enhance diversity and global search, reducing the risk of local optima. It integrates Q-learning into an improved multi-objective grey wolf optimization framework, designing state-action combinations that balance exploration and exploitation. Dynamic parameter adjustments guide position updates, boosting adaptability across different optimization stages. Moreover, the algorithm introduces a reward mechanism based on the crowding distance and inverted generational distance (IGD) to maintain Pareto front diversity and distribution, ensuring a strong multi-objective optimization performance. The experimental results show that the algorithm excels at solving the MOAEOSSP, outperforming competing algorithms across several metrics and demonstrating its effectiveness for complex optimization problems.

The initial Moth-Flame Optimization (MFO) algorithm is appropriately changed to deal with multi-objective optimization problems described as Multi-objective Moth-Flame Optimization (MMFO). The primary idea of this MFO is the navigating technique of moths in nature which fly in night time by keeping a fixed angle relative to the moon. Nevertheless, these elegant bugs are entrapped in a useless/deadly spiral route around fabricated lights. Normally principles like using fixed-sized external archive make the recommended technique vary from the initial single-objective MFO. The efficiency of recommended MMFO is tested on eight multi-objective engineering design problems concerning remarkable precision and uniformity compared to Multi-objective Particle Swarm Optimization (MOPSO), Multi-objective Gray Wolf Optimizer (MOGWO), and Multi-objective Ant Lion Optimizer (MOALO). According to the results of different performance metrics, such as Generational Distance (GD), Inverted Generational Distance (IGD), and Maximum Spread (MS), the proposed algorithm can provide quality Pareto fronts with very competitive results.

Multi-Objective Feature Selection Algorithm using Beluga Whale Optimization

Multiobjective forensic-based investigation algorithm for solving structural design problems

Feature selection or dimensionality reduction can be considered as a multi-objective minimization problem with two objectives: minimizing the number of features and minimizing the error rate simultaneously. Despite being a multi-objective problem, most existing approaches treat feature selection as a single-objective optimization problem. Recently, Multi-objective Grey Wolf optimizer (MOGWO) was proposed to solve multi-objective optimization problem. However, MOGWO was originally designed for continuous optimization problems and hence, it cannot be utilized directly to solve multi-objective feature selection problems which are inherently discrete in nature. Therefore, in this research, a binary version of MOGWO based on sigmoid transfer function called BMOGW-S is developed to optimize feature selection problems. A wrapper based Artificial Neural Network (ANN) is used to assess the classification performance of a subset of selected features. To validate the performance of the proposed method, 15 standard benchmark datasets from the UCI repository are employed. The proposed BMOGWO-S was compared with MOGWO with a tanh transfer function and Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-objective Particle Swarm Optimization (MOPSO). The results showed that the proposed BMOGWO-S can effectively determine a set of non-dominated solutions. The proposed method outperforms the existing multi-objective approaches in most cases in terms of features reduction as well as classification error rate while benefiting from a lower computational cost.

A multiple search strategies based grey wolf optimizer for solving multi-objective optimization problems

The goal of an optimization technique is to find the best solution to an optimization problem. In a single-objective problem, the best solution is the optimal value for the objective function, while in a multi-objective problem, the selection of solutions is not a straightforward task because there are several objective functions which are in conflict. There are many diverse applications such as image processing and data mining, which can be formulated as a multi-objective problem. This paper presents a new decomposition-based multi-objective optimization method using the grey wolf optimizer, which transforms the problem into several sub-problems and examines all the sub-problems simultaneously. Our proposed algorithm obtains the Pareto front using a neighborhood relation among the sub-problems. The levy flight distribution has also been used which increases the exploration and exploitation features in the algorithm in order to improve the search ability. The performance of our proposed algorithm is evaluated on UF family of benchmark functions in terms of different metric such as inverted generational distance (IGD), generational distance (GD), hyper-volume (HV), and spacing (SP). The experimental results indicate the superior performance of the proposed method.

With the advancement toward 6G technology, mobile data growth is estimated to increase many fold. There will also be an increase in the control plane load (IoT, IoE). Such problems call for the technologies that can efficiently utilize the resources to optimize the system performance, and the possible solution is cognitive radio technology. As the spectrum sensing is the key enabler of cognitive radio technology, in this paper, the multi-objective parameters defining the efficiency of spectrum sensing for a cognitive radio network (CRN), which are throughput, interference, and energy efficiency, defined in terms of sensing time, power allocation, and detection threshold are dealt. In this paper, a novel Multi-Objective Modified Grey Wolf Optimization (MOMGWO) algorithm is proposed to solve the multi-objective optimization problem in the field of spectrum sensing in a cognitive radio network which is an important paradigm in wireless communication technology. Modification in Grey Wolf Optimization (GWO) is applied to balance the trade-off between exploration and exploitation process in conventional GWO, to obtain global optima. Modification is introduced in terms of mutation in leader selection, discrimination weight, and mutation coefficient. The non-dominated solution set of the proposed algorithm is compared with the existing algorithms like Non-dominated Sorting Genetic Algorithm (NSGA-II), Multi-Objective Particle Swarm Optimization (MOPSO), Multi-Objective Cat Swarm Optimization (MOCSO), and conventional Multi-Objective Grey Wolf Optimization (MOGWO) algorithm. The simulation result shows that the proposed MOMGWO has outperformed the existing algorithms with respect to the quality of the Pareto front. Thus, the best solutions for the spectrum sensing parameters in optimizing multi-objective problems for cognitive radio network can be obtained via the proposed MOMGWO algorithm.

Building energy consumption accounts for a large proportion of the overall energy use in society, and energy-saving optimization scheduling is currently a research hotspot. However, traditional scheduling methods often struggle to achieve an effective balance between multiple objectives such as energy conservation, economy, and indoor comfort. To construct an energy-saving scheduling model that can consider multiple objectives, this paper puts forward a building energy scheduling model based on a Multi-Objective Grey Wolf Optimizer, taking total energy consumption, operating cost, and indoor comfort deviation as the optimization objectives. The model introduces a set of multi-energy collaborative constraints involving wind energy, photovoltaic systems, energy storage, and combined cooling, heating, and power systems. To improve algorithm performance, we innovatively integrated particle swarm optimization and simulated annealing to enhance the model's global search and local optimization capabilities, and introduced residual long short-term memory networks to improve load forecasting accuracy. Experimental results show that compared to similar models, the proposed algorithm improves the energy-saving rate by 13.3% in a typical household scenario. Its response time is 12 s, memory usage is 89 MB, and convergence speed is 42.86% faster than the slowest comparable model. The Multi-Objective Grey Wolf Optimizer effectively coordinates the multi-objective needs of building energy systems. It significantly improves energy savings and economic performance while ensuring indoor comfort. This algorithm provides strong support for intelligent building energy scheduling and offers practical value for promoting the carbon neutrality goals in the building sector.

The Multi-Objective Grey Wolf Optimizer (MOGWO) is a recent metaheuristic in solving multi-objective problems. This article implements two mechanisms for adjusting the control parameters of the MOGWO. The techniques are based on fuzzy logic and were originally proposed to improve the convergence of the single-objective version of the MOGWO. To evaluate the two fuzzy implementations, five multiobjective test problems were used, where each algorithm was submitted to a sequence of ten runs. The inverted generational distance was used as a metric for the comparison and evaluation of the algorithms. The results show that the two fuzzy mechanisms improve the convergence of the MOGWO.

This work introduces the Advanced Multi-Objective Salp Swarm Algorithm Exploration Technique (AMET), which is a novel optimization framework designed to enhance the efficiency and robustness of multi-robot exploration. AMET combines the deterministic structure of Coordinated Multi-Robot Exploration (CME) with the adaptive search capabilities of the Multi-Objective Salp Swarm Algorithm (MSSA) to achieve a balanced trade-off between exploration efficiency and mapping accuracy. To validate its effectiveness, AMET is compared to both multi-objective and single-objective exploration strategies, including CME combined with Multi-Objective Grey Wolf Optimizer (CME-MGWO), Multi-Objective Ant Colony Optimization (CME-MACO), Multi-Objective Dragonfly Algorithm (CME-MODA), and the single-objective CME with traditional Salp Swarm Algorithm (CME-SSA). The evaluation focuses on four critical performance metrics: runtime efficiency, exploration area coverage, mission completion resilience, and the reduction of redundant exploration. Experimental results across multiple case studies demonstrate that AMET consistently outperforms both single-objective and multi-objective counterparts, achieving superior area coverage, reduced computational overhead, and enhanced exploration coordination. These findings highlight the potential of AMET as a scalable and efficient approach for robotic exploration, providing a foundation for future advancements in multi-robot systems. The proposed method opens new possibilities for applications in search-and-rescue operations, planetary surface exploration, and large-scale environmental monitoring.