Improved Driving Training-Based Optimization Algorithm Using Levy Flight and Crowding Distance Techniques

This article’s innovation and novelty are introducing a new metaheuristic method called mother optimization algorithm (MOA) that mimics the human interaction between a mother and her children. The real inspiration of MOA is to simulate the mother’s care of children in three phases education, advice, and upbringing. The mathematical model of MOA used in the search process and exploration is presented. The performance of MOA is assessed on a set of 52 benchmark functions, including unimodal and high-dimensional multimodal functions, fixed-dimensional multimodal functions, and the CEC 2017 test suite. The findings of optimizing unimodal functions indicate MOA’s high ability in local search and exploitation. The findings of optimization of high-dimensional multimodal functions indicate the high ability of MOA in global search and exploration. The findings of optimization of fixed-dimension multi-model functions and the CEC 2017 test suite show that MOA with a high ability to balance exploration and exploitation effectively supports the search process and can generate appropriate solutions for optimization problems. The outcomes quality obtained from MOA has been compared with the performance of 12 often-used metaheuristic algorithms. Upon analysis and comparison of the simulation results, it was found that the proposed MOA outperforms competing algorithms with superior and significantly more competitive performance. Precisely, the proposed MOA delivers better results in most objective functions. Furthermore, the application of MOA on four engineering design problems demonstrates the efficacy of the proposed approach in solving real-world optimization problems. The findings of the statistical analysis from the Wilcoxon signed-rank test show that MOA has a significant statistical superiority compared to the twelve well-known metaheuristic algorithms in managing the optimization problems studied in this paper.

A good exploration ability can ensure that the method jumps out of local optimum in multimodal problems and a good exploitation can ensure an algorithm converge faster to global optimum values. So, this paper proposes a new hybrid sperm swarm optimization and genetic algorithm to obtain global optimal solutions termed HSSOGA which is developed based on the concept of balancing the exploration and exploitation capability by merging Sperm Swarm Optimization (SSO), which has a fast convergence rate, and a Genetic Algorithm (GA) that can explore a search domain efficiently. To ensure that the proposed method delivers good performance, it is evaluated with 11 standard test function problems consisting of 5 unimodal and 6 multimodal functions. The proposed HSSOGA set is compared with conventional GA and SSO methods, as well as with several hybrid methods such as Hybrid Firefly and Particle Swarm Optimization (HFPSO), hybrid Simulated Annealing and Genetic Algorithm (SAGA), Hybrid Particle Swarm Optimization and Genetic Algorithm (HFPSO), hybrid Particle Swarm Optimization and Grey Wolf Optimization (PSOGWO), and closely related Hybrid Sperm Swarm Optimization and Gravitational Search Algorithm (HSSOGSA). The results are evaluated in terms of each method’s best fitness, mean, standard deviation, and convergence rates. The numerical experiment results show that HSSOGA has better convergence towards the true global optimum values as compared to the conventional and existing hybrid methods in most unimodal and multimodal test function problems.

Autonomous groups of particles swarm optimization (AGPSO), inspired by individual diversity in biological swarms such as insects or birds, is a modified particle swarm optimization (PSO) variant. The AGPSO method is simple to understand and easy to implement on a computer. It has achieved an impressive performance on high-dimensional optimization tasks. However, AGPSO also struggles with premature convergence, low solution accuracy and easily falls into local optimum solutions. To overcome these drawbacks, random-walk autonomous group particle swarm optimization (RW-AGPSO) is proposed. In the RW-AGPSO algorithm, Levy flights and dynamically changing weight strategies are introduced to balance exploration and exploitation. The search accuracy and optimization performance of the RW-AGPSO algorithm are verified on 23 well-known benchmark test functions. The experimental results reveal that, for almost all low- and high-dimensional unimodal and multimodal functions, the RW-AGPSO technique has superior optimization performance when compared with three AGPSO variants, four PSO approaches and other recently proposed algorithms. In addition, the performance of the RW-AGPSO has also been tested on the CEC’14 test suite and three real-world engineering problems. The results show that the RW-AGPSO is effective for solving high complexity problems.

<p>In last decade, numerous meta-heuristic algorithms have been proposed for dealing the complexity and difficulty of numerical optimization problems in the realworld which is growing continuously recently, but only a few algorithms have caught researchers’ attention. In this study, a new swarm-based meta-heuristic algorithm called Rhizostoma optimization algorithm (ROA) is proposed for solving the optimization problems based on simulating the social movement of Rhizostoma octopus (barrel jellyfish) in the ocean. ROA is intended to mitigate the two optimization problems of trapping in local optima and slow convergence. ROA is proposed with three different movement strategies (simulated annealing (SA), fast simulated annealing (FSA), and Levy walk (LW)) and tested with 23 standard mathematical benchmark functions, two classical engineering problems, and various real-world datasets including three widely used datasets to predict the students’ performance. Comparing the ROA algorithm with the latest meta-heuristic optimization algorithms and a recent published research proves that ROA is a very competitive algorithm with a high ability in optimization performance with respect to local optima avoidance, the speed of convergence and the exploration/exploitation balance rate, as it is effectively applicable for performing optimization tasks.</p>

The Sailfish Optimizer: A novel nature-inspired metaheuristic algorithm for solving constrained engineering optimization problems

The goal was to address the problems of slow convergence speed, low solution accuracy and insufficient performance in solving complex functions in the search process of an arithmetic optimization algorithm (AOA). A multi-strategy improved arithmetic optimization algorithm (SSCAAOA) is suggested in this study. By enhancing the population’s initial distribution, optimizing the control parameters, integrating the positive cosine algorithm with improved parameters, and adding inertia weight coefficients and a population history information sharing mechanism to the PSO algorithm, the optimization accuracy and convergence speed of the AOA algorithm are improved. This increases the algorithm’s ability to perform a global search and prevents it from hitting a local optimum. Simulations of SSCAAOA using other optimization algorithms are used to examine their efficacy on benchmark test functions and engineering challenges. The analysis of the experimental data reveals that, when compared to other comparative algorithms, the improved algorithm presented in this paper has a convergence speed and accuracy that are tens of orders of magnitude faster for the unimodal function and significantly better for the multimodal function. Practical engineering tests also demonstrate that the revised approach performs better.

ABSTRACTThree‐dimensional path planning for UAV in complex terrains and obstacle‐limited areas is one of the major challenges faced during mission execution, requiring a simple yet effective algorithm. To solve such problems, an improved Sand Cat Swarm Optimization (SCSO) is proposed, addressing the issue where traditional SCSO is prone to getting stuck in local optima. In this improved approach, a nonlinear adjustment mechanism based on a dynamic factor k is introduced to better balance the exploration and exploitation phases. Additionally, the predatory attack strategy of Harris's Hawks was introduced to improve the position update formula during the exploration phase of the SCSO, thus enhancing the algorithm's convergence speed. A new variant of the SCSO, named HKSCSO, is proposed and applied to UAV path planning. Cost functions are introduced to evaluate path length, flight altitude, and angle comprehensively. HKSCSO's performance was tested in three 3D urban environments, showing faster convergence and safer paths compared to SCSO, Harris's Hawks Optimization (HHO), Particle Swarm Optimization (PSO), Seagull Optimization Algorithm (SOA), Whale Optimization Algorithm (WOA), Parrot Optimizer (PO), and Mantis Search Algorithm (MSA). These results indicate HKSCSO's potential as an effective solution for UAV three‐dimensional path planning.

Collaborative beamforming in wireless sensor networks using a novel particle swarm optimization algorithm variant

Real-world optimization problems in engineering, logistics, and resource allocation are often constrained and multi-modal, posing a challenge for traditional optimization algorithms. Metaheuristic algorithms inspired by natural and artificial phenomena have shown promise, but many fail to balance exploration and exploitation effectively, especially under stringent constraints. Existing algorithms such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and Differential Evolution (DE) face issues in convergence speed and constraint handling, particularly in high-dimensional spaces or when constraints are dynamic or complex. We propose an Adaptive Pattern-Driven Optimization (APDO) algorithm, a novel tailor-inspired metaheuristic that mimics the adaptive decision-making process of a tailor designing garments. APDO integrates three primary operators—Pattern Selection, Fabric Adjustment, and Stitch Reinforcement—to handle constraints adaptively. The algorithm combines pattern memory (historical bests), probabilistic pattern mutation, and a constraint-domination principle to ensure feasibility and diversity. The core idea is to iteratively “cut and stitch” solutions to adapt the search process, enabling dynamic constraint satisfaction and global optimization. We benchmarked APDO against five popular methods (GA, PSO, DE, Firefly Algorithm, and Whale Optimization Algorithm) on a suite of 10 real-world constrained problems, including mechanical component design and energy scheduling tasks. APDO outperformed all baselines in terms of convergence speed, constraint satisfaction rate, and solution quality. In particular, APDO achieved an average feasibility rate of 97.6% and an improvement of 4.2–11.8% in best fitness across problems.

An active learning brain storm optimization (ALBSO) algorithm with a dynamically changing cluster cycle is proposed to enhance the performance of BSO algorithm. In the original BSO, a new individual is generated only by simply choosing one individual or two individuals from one cluster or two clusters with a certain probability. Although the diversity of the population is well maintained, owing to this way of random selection, it seriously affects the performance of BSO. In machine learning, instead of learning from random samples, a learner with active learning has the ability to select its own training data, such as the data of best value or mean value. Referring to the idea of active learning, the active learning strategy with intra-cluster learning and inter-cluster learning is integrated into BSO to elevate the solution accuracy and the convergence speed. In addition, to reduce the time burden of clustering operation, a dynamically changing cluster cycle with one-step clustering is adopted in the proposed ALBSO. Through experimental analysis by utilizing the active learning strategy with the dynamically changing cluster cycle, on the basis of the original diversity maintenance framework, the proposed ALBSO can balance the relationship of diversification and intensification, meanwhile, the time complexity is remarkably reduced. The experimental study on a set of 38 test functions and two real-world problems shows that the performance of BSO is significantly improved, and ALBSO is an effective method to optimize complex unimodal and multimodal functions in comparison with several other well-known algorithms.

Glowworm Swarm Optimization (GSO) is one of the common swarm intelligence algorithms, where GSO has the ability to optimize multimodal functions efficiently. In this paper, a parallel MapReduce-based GSO algorithm is proposed to speedup the GSO optimization process. The authors argue that GSO can be formulated based on the MapReduce parallel programming model quite naturally. In addition, they use higher dimensional multimodal benchmark functions for evaluating the proposed algorithm. The experimental results show that the proposed algorithm is appropriate for optimizing difficult multimodal functions with higher dimensions and achieving high peak capture rates. Furthermore, a scalability analysis shows that the proposed algorithm scales very well with increasing swarm sizes. In addition, an overhead of the Hadoop infrastructure is investigated to find if there is any relationship between the overhead, the swarm size, and number of nodes used.

With the rapid development of unmanned aerial vehicle (UAV) technology, its applications in military and civilian fields are becoming increasingly widespread. However, realizing autonomous navigation of UAVs in complex environments still faces numerous challenges, especially the three-dimensional path planning problem. This paper proposes an improved parrot optimization algorithm (IPO) by introducing SPM chaotic mapping, adaptive switching factor, and hybrid Cauchy and Gaussian mutation strategies to enhance the algorithm's global search capability and convergence speed. The improved IPO is combined with the MATLAB simulation platform to construct a complete three-dimensional path-planning solution framework. Extensive simulation experiments demonstrate that, compared with the standard parrot optimization and other optimization algorithms, this algorithm significantly improves optimization accuracy, convergence speed, and path smoothness, showing good potential for engineering applications. The experimental results indicate that under the complex three-dimensional environment modeling of the Beijing International Studies University (BISU) campus, the improved IPO algorithm can quickly and accurately find the optimal collision-free path with minimal flight cost, which demonstrates excellent prospects for engineering applications.

With the continuous increasing of system modeling accuracy and control performance requirements, the fractional‐order models are applied to describe the dynamic characteristics of the real systems more accurately over traditional integer‐order models. Traditional identification algorithms for fractional‐order system require stringent information on the derivatives of the objective function and initial values of the parameters, which is difficult in practical applications. The differential evolution (DE) algorithm has the advantage of simple implementation and superior performance for solving multi‐dimensional complex optimization problems which is suitable for the identification of fractional‐order systems. Aiming at improving the solution accuracy and convergence speed, an improved DE (IDE) algorithm for fractional‐order system identification is proposed. The movement strategy of the marine predator algorithm (MPA) and the mutation strategy of randomly selecting one from the optimal individual population as the basis vector are both adopted in this proposed IDE algorithm. The parameter information of the successfully mutated individual is archived during the iteration process. The scaling factor and crossover probability factor are adaptively adjusted according to the archived information to enhance the best solution accuracy obtained in the search process. By testing 13 sets of unimodal and multimodal functions with high‐performance optimization algorithms, the accuracy performance of the proposed IDE solution is verified. The IDE algorithm is applied to identify the parameters of the fractional‐order system of permanent magnet synchronous motor with simulation and experiment. The identification results clearly show the effectiveness of the proposed methodology.

Social foraging behavior of Escherichia coli bacteria has recently been explored to develop a novel algorithm for distributed optimization and control. The Bacterial Foraging Optimization Algorithm (BFOA), as it is called now, is currently gaining popularity in the community of researchers, for its effectiveness in solving certain difficult real-world optimization problems. Until now, very little research work has been undertaken to improve the convergence speed and accuracy of the basic BFOA over multi-modal fitness landscapes. This article comes up with a hybrid approach involving Particle Swarm Optimization (PSO) and BFOA algorithm for optimizing multi-modal and high dimensional functions. The proposed hybrid algorithm has been extensively compared with the original BFOA algorithm, the classical g_best PSO algorithm and a state of the art version of the PSO. The new method is shown to be statistically significantly better on a five-function test-bed and one difficult engineering optimization problem of spread spectrum radar poly-phase code design.KeywordsBacterial Foraginghybrid optimizationparticle swarm optimizationRadar poly-phase code design

Abstract. With the advancement of urbanization, urban-rural public transport issues have become one of the most critical issues in urban development. The paper makes a detailed study on the optimization of urban-rural bus routes in Erqi District of Zhengzhou, China. The factors of bus stop selection are analyzed, and the three categories, including traffic road condition factors, economic benefit factors and waiting number factors, are mainly considered. The analytic hierarchy process is used to determine 35 specific objectives of urban-rural bus stop optimization, 20 of which are selected for simulation experiment with large weight. Then the ant colony optimization (ACO) algorithm in path optimization is analyzed, which has the following two advantages. First, the global pheromone update is combined with the local pheromone update to enhance the algorithm's optimization ability and convergence speed. Second, through the method of spatial contraction transformation, the ant constructs a solution to reduce the number of construction steps and speed up the operation. Based on the actual analysis of urban-rural public transportation in the Erqi District of Zhengzhou, a simulation experiment is executed to show that the ACO algorithm is able to find out the optimal path, which is 15.1% shorter than the ant colony system (ACS) algorithm. The ACO algorithm improved path planning has good time effectiveness and path practicability.