An Improved Whale Optimization Algorithm Based on Nonlinear Parameters and Feedback Mechanism

Whale optimization algorithm (WOA) is a relatively novel swarm-based optimization algorithm that has the advantage of less control parameters, strong global optimization ability and easy of implementation. However, there is still an insufficiency of low accuracy, premature, and slow convergence speed in tackling large-scale global optimization (LSGO) problems. To address the issue, an enhanced whale optimization algorithm (EWOA), which combines the original WOA with opposition-based learning, chaotic map and dynamic inertia weight, is proposed for solving LSGO problems. Chaotic opposition-based learning initialization strategy by comparing the fitness of an individual to its opposite and retaining well-diversified solutions is employed to accelerate convergence speed and improve the exploration. In addition, in order to make full use of and balance the exploration and exploitation of the original WOA, a novel chaotic cooperative updating strategy of nonlinear control parameter and dynamic inertia weight is given. Moreover, optimal individual chaotic searching strategy is integrated with evolutionary population updating to avoid the possibility of being trapped into local optima. The experimental results on four classical benchmark functions with dimensions ranging from 100 to 1000 demonstrate the effectiveness and efficiency of the chaotic opposition-based learning initialization strategy, chaotic nonlinear control parameter updating strategy and optimal individual chaotic searching strategy. The comparisons show that the proposed EWOA significantly improves the performance of WOA and provides competitive results for LSGO problems compared with state-of-the-art algorithms.

In this paper, a multi-strategy enhanced chimpanzee optimization algorithm (MSEChOA) acting on path planning for delivery vehicles is proposed to achieve the goal of shortening global path lengths for the delivery unmanned vehicles and obtaining safer paths. In the initialization phase, the algorithm introduces a hybrid good point set and chaos initialization strategy, combining the advantages of both to enhance the randomness and homogeneity of the initial population. After that, it incorporates a benchmark weight strategy and Gaussian-modulated cosine factor to adaptively adjust algorithm parameters, thus balancing the global and local search capabilities and improving the search efficiency. In the end, the algorithm incorporates a global search enhancer (GEE) to further enhance the global search capability in the later phases, thereby avoiding local optima. Experiments on several benchmark test functions show that MSEChOA outperforms traditional ChOA and other optimization algorithms in optimization accuracy and convergence speed. In simulation experiments, MSEChOA shows stronger path planning ability and good computational efficiency in both simple and complex environments, proving its feasibility and superiority in the field of path planning.

Interference resource optimization is a prerequisite for air defense suppression mission planning, and the degree of optimization of interference resources directly determines the quality of the interference results. In this problem, this paper establishes an interference resource optimization model with radar detection probability, interference effectiveness, and interference bandwidth utilization as the objective functions. Then, in the solution process, to address the issues of the Whale Optimization Algorithm (WOA) easily falling into local optima and low convergence accuracy, the BIO-WOA (Bernoulli Chaotic mapping In-nonlinear Factors and Opposition-based Learning Improved Whale Optimization Algorithm, BIO-WOA) is proposed. First, the population initialization is completed using Bernoulli chaotic mapping based on the whale optimization algorithm, increasing the diversity and uniformity of solutions and enhancing the algorithm’s global search capability. Then, a nonlinear convergence factor is proposed to balance the local and global search capabilities of the algorithm. Subsequently, the centroid opposition-based learning is used to generate mutated whales, improving the algorithm’s ability to escape local optima. Finally, the effectiveness of the algorithm is verified through test functions and simulation experiments.

Mechanical interactions between the projectile and barrel during weapon system launch, such as projectile axis oscillation and the contact-collision between the bourrelet band and barrel, negatively impact strike accuracy and flight stability. To investigate the nonlinear behavior of the projectile under varying charge, projectile, and barrel parameters, this study proposes a coupled ballistic model based on the interior ballistic theory of gas–solid two-phase flow and launch dynamics. The model captures the multi-degree-of-freedom characteristics of in-bore projectile motion. Given the complexity of contact interactions involving objects with intricate geometries in small gaps, a rigid-body collision model is introduced to handle the contact-collision between the bourrelet band and barrel. By performing coupled calculations, the final coupled motion equations of the entire system are solved. Additionally, an improved non-dominated sorting whale optimization algorithm is employed to optimize key coupling parameters, reducing the number of collisions while maintaining high projectile velocity and low chamber pressure, thereby enhancing launch stability. The algorithm incorporates adaptive weighting and disturbance factors to balance global and local search capabilities. The results demonstrate that the coupled model effectively captures the translational and rotational characteristics of the projectile within the propulsion system, while the improved whale optimization algorithm successfully addresses the specific tri-objective optimization problem.

Optimal Feedback Strategy in The Game Variant of Generalized Travelling Salesman Problem

Particle swarm optimization (PSO) is a stochastic population-based algorithm which was originally introduced by Kennedy and Eberhart [1]. This optimization algorithm is motivated by intelligent collective behavior of some animals such as flocks of birds or schools of fish. As in most of the metaheuristic optimization algorithms, in PSO, a population of individuals, known as particles, are evolved through successive iterations. The most important advantages of PSO, compared to other optimization strategies, are its easy implementation and few parameters requiring adjustment. Since the initial development of PSO by Kennedy and Eberhart, several variants of this algorithm have been proposed by researchers. The first modification was introducing an inertia weight parameter in the velocity update equation of the initial PSO-a PSO model which is now accepted as the global best PSO algorithm [2]. The goal of the inertia weight parameter is to balance the exploration and exploitation characteristics of PSO. Generally, large inertia weight values are expected to increase the velocity of the particles and improve the long-range exploration of the PSO algorithm, while low inertia values increase the short-range exploration. Due to the strong effect of the inertia weight on the performance of PSO, many researchers have investigated different inertia weight control approaches during the past decades, and many different strategies have been proposed. Various inertia weighting strategies can be categorized into three main classes (Figure 7.1): (1) constant or random, (2) time-varying, and (3) adaptive inertia weights. The first class contains strategies in which the value of the inertia weight is constant during the search or is determined randomly. In the second class, the inertia weight is defined as a function of time (iteration number), and hence these strategies are referred to as time-varying inertia weight strategies. These methods are not considered adaptive since they do not monitor the situation of the particles in the search space, and the value of the inertia weight in each iteration is known before the execution of the algorithm. The third class of the inertia weight strategies consists of those methods which use a feedback parameter to monitor the state of the algorithm and adjust the value of the inertia weight based on the feedback parameter's value. This chapter presents the major existing inertia weight control strategies in the above three categories and discusses examples of each category in detail. The remainder of this chapter is organized as follows. The next section gives a short review of the PSO algorithm, and the role ofthe inertia weight parameter in the velocity update equation. Sections 7.2-7.4 review the three groups of inertia weight strategies, constant or random, time-varying, and adaptive models. Section 7.5 reports some experimental evaluations of different inertia weight models. Finally, Section 7.6 concludes this chapter. A short description of the symbols frequently used in this chapter is shown in Table 7.1.

To address the shortcomings of the whale optimization algorithm (WOA) in terms of insufficient global search ability and slow convergence speed, a differential evolution chaotic whale optimization algorithm (DECWOA) is proposed in this paper. Firstly, the initial population is generated by introducing the Sine chaos theory at the beginning of the algorithm to increase the population diversity. Secondly, new adaptive inertia weights are introduced into the individual whale position update formula to lay the foundation for the global search and improve the optimization performance of the algorithm. Finally, the differential variance algorithm is fused to improve the global search speed and accuracy of the whale optimization algorithm. The impact of various improvement strategies on the performance of the algorithm is analyzed using different kinds of test functions that are randomly selected. The particle swarm optimization algorithm (PSO), butterfly optimization algorithm (BOA), WOA, chaotic feedback adaptive whale optimization algorithm (CFAWOA), and DECWOA algorithm are compared for the optimal search performance. Experimental simulations are performed using MATLAB software, and the results show that the improved whale optimization algorithm has a better global optimization-seeking capability. The improved whale optimization algorithm is applied to the distribution network fault location of IEEE-33 nodes, and the effectiveness and accuracy of the distribution network fault zone location based on the multistrategy improved whale optimization algorithm is verified.

Structural Damage Identification Based on Improved Fruit Fly Optimization Algorithm

Clustering as an unsupervised learning method is a process of dividing a data object or observation object into a subset, that is to classify the data through observation learning instead of example learning without the guidance of the prior class label information. Bat algorithm (BA) is a swarm intelligence optimization algorithm inspired by bat’s ultrasonic echo localization foraging behavior, but it has the disadvantages of being easily trapped into local minima and not being highly accurate. So an improved bat algorithm was proposed. In the global search, a Gaussian-like convergence factor is added, and five different convergence factors are proposed to improve the global optimization ability of the algorithm. In the local search, the hunting mechanism of the whale optimization algorithm (WOA) and the sine position updating strategy are adopted to improve the local optimization ability of the algorithm. This paper compares the clustering effect of the improved bat algorithm with bat algorithm, flower pollination algorithm (FPA), harmony search (HS) algorithm, whale optimization algorithm and particle swarm optimization (PSO) algorithm on seven real data sets under six different convergence factors. The simulation results show that the clustering effect of the improved bat algorithm is superior to other intelligent optimization algorithms.

For Particle Swarm Algorithm uses fixed inertia weights, weaken too slow and extremely easy to fall into local optimum so I propose an adaptive inertia weight method, this inertia weight has a larger weight in the early stage, can increase the global search capability and avoid algorithm falling into local optimum, in late period, this inertia weight has a smaller weight and can increase algorithm local search ability and overall increase convergence rate. But during the optimization process, There are some more complicated functions that will still fall into the local minimum even using this adaptive inertia weight. In order to avoid the occurrence of premature phenomenon so use reverse escape strategy, apply new optimization methods to the basic particle swarm algorithm, the application of several basic functions proves that the proposed optimization method has higher precision and convergence speed.

This paper tackles network losses and voltage stability issues in grid-connected wind farms by proposing a reactive power allocation method for wind power distribution networks using an improved grey wolf algorithm. The study analyzes the distribution system incorporating wind farms and establishes an optimization model for reactive power. This model aims to minimize active power loss within the wind farm and ensures a rational distribution of reactive power output for each unit. This method integrates Tent chaotic mapping, an improved nonlinear control parameter strategy, and the particle swarm algorithm concept, effectively enhancing the solution accuracy, convergence speed, and global search capability of the standard grey wolf algorithm. A specific wind farm is used as a case study to simulate the reactive power optimization model and evaluate the proposed enhanced algorithm against other algorithms. The findings show that the proposed algorithm outperforms others by significantly reducing system active power losses and improving voltage quality. It also effectively addresses issues related to local convergence and limited global search capability in optimization algorithms, demonstrating its feasibility and superiority.

Firefly algorithm is a new heuristic intelligent optimization algorithm and has excellent performance in many optimization problems. However, like other intelligent algorithms, the firefly algorithm still has some shortcomings, such as the algorithm is easy to fall into the local optimal, and the convergence speed is slow in the later period. Therefore, this paper proposes a new firefly algorithm with dynamic step change strategy (DsFA) to balance the global and local search capabilities. Thirteen well-known benchmark functions are used to verify the performance of our proposed method, the computational results show that DsFA is more efficient than many other FA algorithms.KeywordsFirefly algorithmHeuristic intelligent optimization algorithmDynamic step change strategy

The rapid advancement of unmanned aerial vehicle (UAV) technology has enabled the coordinated operation of multi-UAV systems, offering significant applications in agriculture, logistics, environmental monitoring, and disaster relief. In agriculture, UAVs are widely utilized for tasks such as ecological restoration, crop monitoring, and fertilization, providing efficient and cost-effective solutions for improved productivity and sustainability. This study addresses the collaborative task allocation problem for multi-UAV systems, using ecological grassland restoration as a case study. A multi-objective, multi-constraint collaborative task allocation problem (MOMCCTAP) model was developed, incorporating constraints such as UAV collaboration, task completion priorities, and maximum range restrictions. The optimization objectives include minimizing the maximum task completion time for any UAV and minimizing the total time for all UAVs. To solve this model, a deep reinforcement learning-based seagull optimization algorithm (DRL-SOA) is proposed, which integrates deep reinforcement learning with the seagull optimization algorithm (SOA) for adaptive optimization. The algorithm improves both global and local search capabilities by optimizing key phases of seagull migration, attack, and post-attack refinement. Evaluation against five advanced swarm intelligence algorithms demonstrates that the DRL-SOA outperforms the alternatives in convergence speed and solution diversity, validating its efficacy for solving the MOMCCTAP.

An improved slime mold algorithm (IMSMA) is presented in this paper for a multiprocessor multitask fair scheduling problem, which aims to reduce the average processing time. An initial population strategy based on Bernoulli mapping reverse learning is proposed for the slime mold algorithm. A Cauchy mutation strategy is employed to escape local optima, and the boundary-check mechanism of the slime mold swarm is optimized. The boundary conditions of the slime mold population are transformed into nonlinear, dynamically changing boundaries. This adjustment strengthens the slime mold algorithm’s global search capabilities in early iterations and strengthens its local search capability in later iterations, which accelerates the algorithm’s convergence speed. Two unimodal and two multimodal test functions from the CEC2019 benchmark are chosen for comparative experiments. The experiment results show the algorithm’s robust convergence and its capacity to escape local optima. The improved slime mold algorithm is applied to the multiprocessor fair scheduling problem to reduce the average execution time on each processor. Numerical experiments showed that the IMSMA performs better than other algorithms in terms of precision and convergence effectiveness.

Parameter self-tuning of servo control systems is crucial for optimizing automation processes, especially in complex systems such as permanent magnet synchronous motors. In this paper, a nonlinear adaptive whale optimization algorithm (NAWOA) is proposed and applied to parameter self-tuning, which improves the traditional whale optimization algorithm (WOA) by nonlinearly adaptively adjusting two parameters during optimization to enhance fast convergence and global search capabilities. A servo control system with three parameters to be tuned is constructed using both simulation and physical methods. Simulation and experimental results show that the NAWOA outperforms the genetic algorithm, particle swarm optimization, and WOA in parameter self-tuning of the servo control system with lower error indicators and fast convergence speed. Although it still faces the challenge of initial condition dependency, the proposed NAWOA provides a powerful solution for real-time industrial applications.