Improved Arithmetic Optimization Algorithm Based on Curriculum Education for Numerical Optimization and Practical Problems

Marine Predators Algorithm (MPA) is a recent efficient metaheuristic algorithm that is enlightened by the biological behavior of ocean predators and prey. This algorithm simulates the Levy and Brownian movements of prevalent foraging strategy and has been applied to many complex optimization problems. However, the algorithm has defects such as a low diversity of the solutions, ease into the local optimal solutions, and decreasing convergence speed in dealing with complex problems. A modified version of this algorithm called ODMPA is proposed based on the tent map, the outpost mechanism, and the differential evolution mutation with simulated annealing (DE-SA) mechanism. The tent map and DE-SA mechanism are added to enhance the exploration capability of MPA by increasing the diversity of the search agents, and the outpost mechanism is mainly used to improve the convergence speed of MPA. To validate the outstanding performance of the ODMPA, a series of global optimization problems are selected as the test sets, including the standard IEEE CEC2014 benchmark functions, which are the authoritative test set, three well-known engineering problems, and photovoltaic model parameters tasks. Compared with some famous algorithms, the results reveal that ODMPA has achieved better performance than its counterparts in CEC2014 benchmark functions. And in solving real-world optimization problems, ODMPA could get higher accuracy than other metaheuristic algorithms. These practical results demonstrate that the mechanisms introduced positively affect the original MPA, and the proposed ODMPA can be a widely effective tool in tackling many optimization problems.

Particle swarm optimization (PSO) algorithm has shown promising performances on various benchmark functions and engineering optimization problems. However, it is still difficult to achieve a satisfying trade-off between exploration and exploitation for all the optimization problems and different evolving stages. Furthermore, control parameters of some related mechanisms need pre-experience by the requirement of trial-and-error scheme. This paper presents a novel PSO algorithm, which adaptively adopts various search strategies, called Self-adapting Hybrid Strategy PSO (SaHSPS). Unlike some other peer PSO variants, this method dynamically changes the probabilities of different strategies according to their previous successful searching memories, without any additional control parameters. The probabilities of different strategies would be re-initialized according to a proposed dynamic probabilistic model to diverse the population. Besides, particles are updated by probabilistically selected strategies after niching PSO with Ring topology. Moreover, a dynamic updating mechanism by niching PSO is proposed to guarantee the parallel searching capability during the whole evolution process. Thus, this proposed algorithm might be problem-independent and search-stage-independent, yielding more satisfying solutions on various optimization problems. A comprehensive experimental study is conducted on 28 benchmark functions of CEC 2013 special session on real-parameter optimization, including shifted, rotated, multi-modal, high conditioned, expanded and composition problems, compared with several state-of-the-art variants of PSO and differential evolution (DE) algorithms. Comparison results show that SaHSPS obtains outstanding performances on the majority of the test problems. Moreover, a practical engineering problem, real power loss minimization of IEEE 30-bus power system, is used to further evaluate SaHSPS. The numerical results, compared with other stochastic search algorithms, show that SaHSPS could find high-quality solutions with higher probability.

Several evolutionary algorithms (EAs) are proposed in the literature to solve continuous optimisation problems. In this paper we present a new search startegy to improve the efficiency of the Shuffled Frog Leaping Algorithm (SFLA). The shuffled frog leaping algorithm is a population-based approach for a heuristic search in optimization problems. The algorithm consists of a set of virtual frogs partitioned into several groups called “memeplexes”. However, After some optimization runs frogs position's become closer in each memeplex. Indeed, this problem leads to a premature convergence. For getting better effiency we propose a novel search strategy by infecting not only the worst indvidual but also the best indvidual idea's. To further improve the speed of convergence of the algorithm, we have introduced two acceleration factors in the search strategy formulation. The proposed algorithm has been evaluated on five mathematical benchmark functions. Compared with a the orginal SFLA and the particle swarm optimization algorithm, the experimental results in terms of optimization performance and the speed of convergence shows that the proposed algorithm can be an effective tool for solving combinatorial optimization problems.

With the increasing complexity and difficulty of numerical optimization problems in the real world, many efficient meta-heuristic optimization methods have been proposed to solve these problems. An improved Fireworks Algorithm (FWA) with elitism-based selection and optimal particle guidance strategies (EO-FWA) was proposed to address the limitations of the traditional FWA in terms of optimization accuracy and convergence speed, which not only improves the efficiency of the searching agent but also accelerates its convergence speed. In addition, by adopting boundary-based mapping rules, EO-FWA eliminates the randomness of traditional modulo operation mapping rules, which improves its stability and reliability. Twelve benchmark functions in CEC-BC-2022 are used to test the performance of EO-FWA, and the welded beam design problem is optimized at the end. The results show that EO-FWA exhibits stronger competitiveness than other algorithms in dealing with high-dimensional optimization problems and engineering optimization problem, and it can balance exploitation and exploration effectively so as to prevent the algorithm from falling into local optimal solutions.

The aim of this paper is to present a design of a metaheuristic search called improved monkey algorithm (MA+) that provides a suitable solution for the optimization problems. The proposed algorithm has been renewed by a new method using random perturbation (RP) into two control parameters (p1 and p2) to solve a wide variety of optimization problems. A novel RP is defined to improve the control parameters and is constructed off the proposed algorithm. The main advantage of the control parameters is that they more generally prevented the proposed algorithm from getting stuck in optimal solutions. Many optimization problems at the maximum allowable number of iterations can sometimes lead to an inferior local optimum. However, the search strategy in the proposed algorithm has proven to have a successful global optimal solution, convergence optimal solution, and much better performance on many optimization problems for the lowest number of iterations against the original monkey algorithm. All details in the improved monkey algorithm have been represented in this study. The performance of the proposed algorithm was first evaluated using 12 benchmark functions on different dimensions. These different dimensions can be classified into three different types: low-dimensional (30), medium-dimensional (60), and high-dimensional (90). In addition, the performance of the proposed algorithm was compared with the performance of several metaheuristic algorithms using these benchmark functions on many different types of dimensions. Experimental results show that the improved monkey algorithm is clearly superior to the original monkey algorithm, as well as to other well-known metaheuristic algorithms, in terms of obtaining the best optimal value and accelerating convergence solution.

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.

Proper planning of charging infrastructure can significantly facilitate the popularization of electric vehicles and alleviate users’ mileage anxiety. Charging station siting and sizing are two key challenges in the planning with each of them being a complex optimization problem. In this paper, a multi-objective optimization approach is proposed to solve them together. First, considering that accurate charging demand estimation is crucial for planning, a traffic road network is established for this purpose. A Monte Carlo method is used to estimate the spatiotemporal distribution of charging demand in a region based on the probabilistic characteristics of user trips. Since uncoordinated charging not only increases the load but also leads to unstable operation of the local power system, a heuristic algorithm is proposed to coordinate charging scheduling. Then, based on the scheduled demand, this paper proposes a framework for the siting and sizing of charging stations to optimize the benefits for both operators and users by minimizing the construction, operation and maintenance costs, and the user’s detour time. As the given problem is a complex multi-objective combinatorial optimization problem, it is easy to fall into local optimum if traditional evolutionary algorithms are employed. Therefore, a multi-objective dynamic binary particle swarm optimization method is designed to solve this problem effectively. Finally, experimental simulations show that the proposed method outperforms the other comparative algorithms in terms of solution quality. A case study is presented to demonstrate the applicability and effectiveness of the proposed method in optimizing the location and capacity of charging stations.

Tree–seed algorithm is a stochastic search algorithm with superior performance suitable for solving continuous optimization problems. However, it is also prone to fall into local optimum and slow in convergence. Therefore, this paper proposes an improved tree–seed algorithm based on pattern search, dimension permutation, and elimination update mechanism (PDSTSA). Firstly, a global optimization strategy based on pattern search is used to promote detection ability. Secondly, in order to maintain the diversity of the population, a random mutation strategy of individual dimension replacement is introduced. Finally, the elimination and update mechanism based on inferior trees is introduced in the middle and later stages of the iteration. Subsequently, PDSTSA is compared with seven representative algorithms on the IEEE CEC2015 test function for simulation experiments and convergence curve analysis. The experimental results indicate that PDSTSA has better optimization accuracy and convergence speed than other comparison algorithms. Then, the Wilcoxon rank sum test demonstrates that there is a significant difference between the optimization results of PDSTSA and each comparison algorithm. In addition, the results of eight algorithms for solving engineering constrained optimization problems further prove the feasibility, practicability, and superiority of PDSTSA.

In this work, a method to control the parameters of Differential Evolution (DE) algorithm is proposed. Here the control parameters of DE are co-evolved by Particle Swarm Optimization (PSO) algorithm. The classical DE algorithm has two main control parameters: Scale Factor (F) and Cross-over Rate (CR). These are selected on trial-and-error basis for solving optimization problems. Several optimization problems lead to optimal or sub-optimal solution by proper selection of control parameters of the DE algorithm. In this proposed method, PSO algorithm is used to tune the scale factor and cross-over rate in DE algorithm. Basically PSO algorithm is used as a meta-optimizer for DE algorithm. The proposed method is termed as mPSO-DE in this paper. The mPSO-DE algorithm is applied on 12 benchmark unconstrained optimization problems. The obtained results are compared with that of classical DE algorithm. From the experimental studies, it has been found that the proposed mPSO-DE algorithm performed better than DE algorithm.

An improved multi-population ensemble differential evolution

The idea of network protocol design based on optimization theory has been proposed and used practically in Internet for about 15 years. However, for large-scale wireless ad hoc network, although protocol could be viewed as a recursive solving of a global optimization problem, protocol design is still facing huge challenge because an effective distributed algorithm for solving global optimization problem is still lacking. We solve the problem by putting forward a systematic design method based on optimization decomposition. The systematic method includes primal decomposition method and dual decomposition method, with which a complex optimization problem can be decomposed into several smaller and independent optimization subproblems. By using subgradient method, each of these subproblems can be solved distributively. Further, the above two methods can be combined in different sequences or used recursively to solve more complex optimization problems. Two examples of wireless protocol design, the transmission control protocol and the joint congestion control and power control protocol, are given to demonstrate its validity.

This study proposes a Hybrid Strategy Improved Dingo Optimization Algorithm (HSIDOA), designed to address the limitations of the standard DOA in complex optimization tasks, including its tendency to fall into local optima, slow convergence speed, and inefficient boundary search. The HSIDOA integrates a quadratic interpolation search strategy, a horizontal crossover search strategy, and a centroid-based opposition learning boundary-handling mechanism. By enhancing local exploitation, global exploration, and out-of-bounds correction, the algorithm forms an optimization framework that excels in convergence accuracy, speed, and stability. On the CEC2017 (30-dimensional) and CEC2022 (10/20-dimensional) benchmark suites, the HSIDOA achieves significantly superior performance in terms of average fitness, standard deviation, convergence rate, and Friedman test rankings, outperforming seven mainstream algorithms including MLPSO, MELGWO, MHWOA, ALA, HO, RIME, and DOA. The results demonstrate strong robustness and scalability across different dimensional settings. Furthermore, HSIDOA is applied to multi-level threshold image segmentation, where Otsu's maximum between-class variance is used as the objective function, and PSNR, SSIM, and FSIM serve as evaluation metrics. Experimental results show that HSIDOA consistently achieves the best segmentation quality across four threshold levels (4, 6, 8, and 10 levels). Its convergence curves exhibit rapid decline and early stabilization, with stability surpassing all comparison algorithms. In summary, HSIDOA delivers comprehensive improvements in global exploration capability, local exploitation precision, convergence speed, and high-dimensional robustness. It provides an efficient, stable, and versatile optimization method suitable for both complex numerical optimization and image segmentation tasks.

Throughout the past few decades, a variant of differential evolution (DE) algorithms have been introduced with a competitive performance on complex optimization problems. However, the DE superiority is highly dependent on its control parameters and the search operators (i.e., mutation and crossover schemes). Therefore, to obtain the optimal performance, tuning the parameters is essential. In this paper, the DE algorithm is proposed that uses a new designed mutation scaling factor to dynamically adapt the movement of the individuals in the search space toward the optimal value during the evolutionary process. The numerical experiments are conducted on thirty CEC 2014 benchmark functions on four different dimensions; 10, 30, 50, and 100. The obtained results demonstrate that the proposed algorithm is highly competitive and shows better performance than the classical DE algorithm.

Genetic algorithms (GAs) are a stochastic search method for optimization problems based on the mechanics of natural selection and natural genetics (i.e., survival of the fittest). GAs have demonstrated considerable success in providing good solutions to many complex optimization problems and received more and more attentions during the past three decades. When the objective functions to be optimized in the optimization problems are multimodal or the search spaces are particularly irregular, algorithms need to be highly robust in order to avoid getting stuck at a local optimal solution. The advantage of GAs is just able to obtain the global optimal solution fairly. In addition, GAs do not require the specific mathematical analysis of optimization problems, which makes GAs themselves easily coded by users who are not necessarily good at mathematics and algorithms.KeywordsGenetic AlgorithmNash EquilibriumGenetic OperatorSoft ConstraintRoulette WheelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Evaluating center-seeking and initialization bias: The case of particle swarm and gravitational search algorithms