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The Whale Optimization Algorithm (WOA) is a swarm intelligence algorithm based on natural heuristics, which has gained considerable attention from researchers and engineers. However, WOA still has some limitations, including limited global search efficiency and a slow convergence rate. To address these issues, this paper presents an improved whale optimization algorithm with multiple strategies, called Dynamic Gain-Sharing Whale Optimization Algorithm (DGSWOA). Specifically, a Sine–Tent–Cosine map is first adopted to more effectively initialize the population, ensuring a more uniform distribution of individuals across the search space. Then, a gaining–sharing knowledge based algorithm is used to enhance global search capability and avoid falling into a local optimum. Finally, to increase the diversity of solutions, Dynamic Opposition-Based Learning is incorporated for population updating. The effectiveness of our approach is evaluated through comparative experiments on blackbox optimization benchmarking and two engineering application problems. The experimental results suggest that the proposed method is competitive in terms of solution quality and convergence speed in most cases.

Heuristic optimization algorithms have been proved to be powerful in solving nonlinear and complex optimization problems; therefore, many effective optimization algorithms have been applied to solve optimization problems in real-world scenarios. This paper presents a modification of the recently proposed Gaining–Sharing Knowledge (GSK)-based algorithm and applies it to optimize resource scheduling in the Internet of Vehicles (IoV). The GSK algorithm simulates different phases of human life in gaining and sharing knowledge, which is mainly divided into the senior phase and the junior phase. The individual is initially in the junior phase in all dimensions and gradually moves into the senior phase as the individual interacts with the surrounding environment. The main idea used to improve the GSK algorithm is to divide the initial population into different groups, each searching independently and communicating according to two main strategies. Opposite-based learning is introduced to correct the direction of convergence and improve the speed of convergence. This paper proposes an improved algorithm, named parallel opposition-based Gaining–Sharing Knowledge-based algorithm (POGSK). The improved algorithm is tested with the original algorithm and several classical algorithms under the CEC2017 test suite. The results show that the improved algorithm significantly improves the performance of the original algorithm. When POGSK was applied to optimize resource scheduling in IoV, the results also showed that POGSK is more competitive.

Recently, many-objective optimization problems (MaOPs) have become a hot issue of interest in academia and industry, and many more many-objective evolutionary algorithms (MaOEAs) have been proposed. NSGA-II/SDR (NSGA-II with a strengthened dominance relation) is an improved NSGA-II, created by replacing the traditional Pareto dominance relation with a new dominance relation, termed SDR, which is better than the original algorithm in solving small-scale MaOPs with few decision variables, but performs poorly in large-scale MaOPs. To address these problems, we added the following improvements to the NSGA-II/SDR to obtain NSGA-II/SDR-OLS, which enables it to better achieve a balance between population convergence and diversity when solving large-scale MaOPs: (1) The opposition-based learning (OBL) strategy is introduced in the initial population initialization stage, and the final initial population is formed by the initial population and the opposition-based population, which optimizes the quality and convergence of the population; (2) the local search (LS) strategy is introduced to expand the diversity of populations by finding neighborhood solutions, in order to avoid solutions falling into local optima too early. NSGA-II/SDR-OLS is compared with the original algorithm on nine benchmark problems to verify the effectiveness of its improvement. Then, we compare our algorithm with six existing algorithms, which are promising region-based multi-objective evolutionary algorithms (PREA), a scalable small subpopulation-based covariance matrix adaptation evolution strategy (S3-CMA-ES), a decomposition-based multi-objective evolutionary algorithm guided by growing neural gas (DEA-GNG), a reference vector-guided evolutionary algorithm (RVEA), NSGA-II with conflict-based partitioning strategy (NSGA-II-conflict), and a genetic algorithm using reference-point-based non-dominated sorting (NSGA-III).The proposed algorithm has achieved the best results in the vast majority of test cases, indicating that our algorithm has strong competitiveness.

The jellyfish search (JS) algorithm impersonates the foraging behavior of jellyfish in the ocean. It is a newly developed metaheuristic algorithm that solves complex and real-world optimization problems. The global exploration capability and robustness of the JS algorithm are strong, but the JS algorithm still has significant development space for solving complex optimization problems with high dimensions and multiple local optima. Therefore, in this study, an enhanced jellyfish search (EJS) algorithm is developed, and three improvements are made: (i) By adding a sine and cosine learning factors strategy, the jellyfish can learn from both random individuals and the best individual during Type B motion in the swarm to enhance optimization capability and accelerate convergence speed. (ii) By adding a local escape operator, the algorithm can skip the trap of local optimization, and thereby, can enhance the exploitation ability of the JS algorithm. (iii) By applying an opposition-based learning and quasi-opposition learning strategy, the population distribution is increased, strengthened, and more diversified, and better individuals are selected from the present and the new opposition solution to participate in the next iteration, which can enhance the solution’s quality, meanwhile, convergence speed is faster and the algorithm’s precision is increased. In addition, the performance of the developed EJS algorithm was compared with those of the incomplete improved algorithms, and some previously outstanding and advanced methods were evaluated on the CEC2019 test set as well as six examples of real engineering cases. The results demonstrate that the EJS algorithm can skip the trap of local optimization, can enhance the solution’s quality, and can increase the calculation speed. In addition, the practical engineering applications of the EJS algorithm also verify its superiority and effectiveness in solving both constrained and unconstrained optimization problems, and therefore, suggests future possible applications for solving such optimization problems.

The spherical search algorithm is an effective optimizer to solve bound-constrained non-linear global optimization problems. Nevertheless, it may fall into the local optima when handling combination optimization problems. This paper proposes an enhanced self-adapting spherical search algorithm with differential evolution (SSDE), which is characterized by an opposition-based learning strategy, a staged search mechanism, a non-linear self-adapting parameter, and a mutation-crossover approach. To demonstrate the outstanding performance of the SSDE, eight optimizers on the CEC2017 benchmark problems are compared. In addition, two practical constrained engineering problems (the welded beam design problem and the pressure vessel design problem) are solved by the SSDE. Experimental results show that the proposed algorithm is highly competitive compared with state-of-the-art algorithms.

The seagull optimization algorithm (SOA), a well-known illustration of intelligent algorithms, has recently drawn a lot of academic interest. However, it has a variety of issues including slower convergence, poorer search accuracy, the single path for pursuing optimization, and the simple propensity to slip into local optimality. This paper suggests a multi-mechanism seagull optimization algorithm (GEN−SOA) that incorporates the generalized opposition-based, adaptive nonlinear weights, and evolutionary boundary constraints to address these demerits further. These methods are balanced and promoted the population variety and the capability to conduct global and local search. Compared with SOA, PSO, SCA, SSA, and BOA on 12 well-known test functions, the experimental results demonstrate that GEN-SOA has a higher accuracy and faster convergence than the other five algorithms, and it can find the global optimal solution beyond the local optimum. Furthermore, to verify the capability of GEN−SOA to solve practical problems, this paper applied GEN−SOA to solve two standard engineering optimization design problems including a welding optimization and a pressure vessel optimization, and the experimental results showed that it has significant advantages over SOA.

The manta ray foraging optimizer (MRFO) is a novel nature-inspired optimization algorithm that simulates the foraging strategy and behavior of manta ray groups, i.e., chain, spiral, and somersault foraging. Although the native MRFO has revealed good competitive capability with popular meta-heuristic algorithms, it still falls into local optima and slows the convergence rate in dealing with some complex problems. In order to ameliorate these deficiencies of the MRFO, a new elite chaotic MRFO, termed the CMRFO algorithm, integrated with chaotic initialization of population and an opposition-based learning strategy, is developed in this paper. Fourteen kinds of chaotic maps with different properties are used to initialize the population. Thereby, the chaotic map with the best effect is selected; meanwhile, the sensitivity analysis of an elite selection ratio in an elite chaotic searching strategy to the CMRFO is discussed. These strategies collaborate to enhance the MRFO in accelerating overall performance. In addition, the superiority of the presented CMRFO is comprehensively demonstrated by comparing it with a native MRFO, a modified MRFO, and several state-of-the-art algorithms using (1) 23 benchmark test functions, (2) the well-known IEEE CEC 2020 test suite, and (3) three optimization problems in the engineering field, respectively. Furthermore, the practicability of the CMRFO is illustrated by solving a real-world application of shape optimization of cubic generalized Ball (CG-Ball) curves. By minimizing the curvature variation in these curves, the shape optimization model of CG-Ball ones is established. Then, the CMRFO algorithm is applied to handle the established model compared with some advanced meta-heuristic algorithms. The experimental results demonstrate that the CMRFO is a powerful and attractive alternative for solving engineering optimization problems.

The main component of a cryptographic system that allows us to ensure its strength against attacks, is the substitution box. The strength of this component can be validated by various metrics, one of them being the nonlinearity. To this end, it is essential to develop a design for substitution boxes that allows us to guarantee compliance with this metric. In this work, we implemented a hybrid between the stochastic fractal search algorithm in conjunction with opposition-based learning. This design is supported by sequential model algorithm configuration for the proper parameters configuration. We obtained substitution boxes of high nonlinearity in comparison with other works based on metaheuristics and chaotic schemes. The proposed substitution box is evaluated using bijectivity, the strict avalanche criterion, nonlinearity, linear probability, differential probability and bit-independence criterion, which demonstrate the excellent performance of the proposed approach.

A slime mould algorithm (SMA) is a new meta-heuristic algorithm, which can be widely used in practical engineering problems. In this paper, an improved slime mould algorithm (ESMA) is proposed to estimate the water demand of Nanchang City. Firstly, the opposition-based learning strategy and elite chaotic searching strategy are used to improve the SMA. By comparing the ESMA with other intelligent optimization algorithms in 23 benchmark test functions, it is verified that the ESMA has the advantages of fast convergence, high convergence precision, and strong robustness. Secondly, based on the data of historical water consumption and local economic structure of Nanchang, four estimation models, including linear, exponential, logarithmic, and hybrid, are established. The experiment takes the water consumption of Nanchang City from 2004 to 2019 as an example to analyze, and the estimation models are optimized using the ESMA to determine the model parameters, then the estimation models are tested. The simulation results show that all four models can obtain better prediction accuracy, and the proposed ESMA has the best effect on the hybrid prediction model, and the prediction accuracy is up to 97.705%. Finally, the water consumption of Nanchang in 2020–2024 is forecasted.

In the era of big data, the size and complexity of the data are increasing especially for those stored in remote locations, and whose difficulty is further increased by the ongoing rapid accumulation of data scale. Real-world optimization problems present new challenges to traditional intelligent optimization algorithms since the traditional serial optimization algorithm has a high computational cost or even cannot deal with it when faced with large-scale distributed data. Responding to these challenges, a distributed cooperative evolutionary algorithm framework using Spark (SDCEA) is first proposed. The SDCEA can be applied to address the challenge due to insufficient computing resources. Second, a distributed quantum-behaved particle swarm optimization algorithm (SDQPSO) based on the SDCEA is proposed, where the opposition-based learning scheme is incorporated to initialize the population, and a parallel search is conducted on distributed spaces. Finally, the performance of the proposed SDQPSO is tested. In comparison with SPSO, SCLPSO, and SALCPSO, SDQPSO can not only improve the search efficiency but also search for a better optimum with almost the same computational cost for the large-scale distributed optimization problem. In conclusion, the proposed SDQPSO based on the SDCEA framework has high scalability, which can be applied to solve the large-scale optimization problem.

Opposition-based learning (OBL) has been widely used to improve many swarm intelligent optimization (SI) algorithms for continuous problems during the past few decades. When the SI optimization algorithms apply OBL to solve discrete problems, the construction and utilization of the opposite solution is the key issue. Ant colony optimization (ACO) generally used to solve combinatorial optimization problems is a kind of classical SI optimization algorithm. Opposition-based ACO which is combined in OBL is proposed to solve the symmetric traveling salesman problem (TSP) in this paper. Two strategies for constructing opposite path by OBL based on solution characteristics of TSP are also proposed. Then, in order to use information of opposite path to improve the performance of ACO, three different strategies, direction, indirection, and random methods, mentioned for pheromone update rules are discussed individually. According to the construction of the inverse solution and the way of using it in pheromone updating, three kinds of improved ant colony algorithms are proposed. To verify the feasibility and effectiveness of strategies, two kinds of ACO algorithms are employed to solve TSP instances. The results demonstrate that the performance of opposition-based ACO is better than that of ACO without OBL.