Solving pressure vessel design problems by an effective global harmony search algorithm

Harmony Search (HS) algorithm is a new meta-heuristic global search algorithm. To solve the algorithm easily fall into the local optimal problem, this paper proposes an adaptive novel global harmony search (ANGHS) algorithm based on NGHS algorithm. First, a new location update strategy is given using the adjustment parameter F. Then, the mutation operation is introduced in the case of excluding the small probability Pm. In order to avoid blind adjustment of the step size in the late search and effectively adjust the structure of the solution, the definition of the norm is introduced to adjust parameter bw dynamically. In this paper, 7 standard Benchmark functions are used to simulate the experiment. The results show that the algorithm avoids the premature problem of the algorithm and enhances the global search ability of the algorithm, with obvious improvement in convergence speed and stability, and has good optimize performance.

Shunt capacitors are broadly applied in distribution systems to scale down power losses, improve voltage profile and boost system capacity. The amount of capacitors added and location of deployment in the system highly determine the advantage of compensation. A novel global harmony search (GHS) algorithm in parallel with the backward/ forward sweep power flow technique and radial harmonic power flow was used to investigate the optimal placement and sizing of capacitors in radial distribution networks for minimizing power loss and total cost by taking account load unbalancing, mutual coupling and harmonics. The optimal capacitor placement outcomes show that the GHS algorithm can reduce total power losses up to 60 kW and leads to more than 18% of cost saving. The results also demonstrate that the GHS algorithm is more effective in minimization of power loss and total costs compared with genetic algorithm (GA), particle swarm optimization (PSO) and harmony search (HS) algorithm. Moreover, the proposed algorithm converges within 800 iterations and is faster in terms of computational time and gives better performance in finding optimal capacitor location and size compared with other optimization techniques.

Particle swarm optimization (PSO) algorithm is generally improved by adaptively adjusting the inertia weight or combining with other evolution algorithms. However, in most modified PSO algorithms, the random values are always generated by uniform distribution in the range of [0, 1]. In this study, the random values, which are generated by uniform distribution in the ranges of [0, 1] and [−1, 1], and Gauss distribution with mean 0 and variance 1 ( U [ 0 , 1 ] , U [ − 1 , 1 ] and G ( 0 , 1 ) ), are respectively used in the standard PSO and linear decreasing inertia weight (LDIW) PSO algorithms. For comparison, the deterministic PSO algorithm, in which the random values are set as 0.5, is also investigated in this study. Some benchmark functions and the pressure vessel design problem are selected to test these algorithms with different types of random values in three space dimensions (10, 30, and 100). The experimental results show that the standard PSO and LDIW-PSO algorithms with random values generated by U [ − 1 , 1 ] or G ( 0 , 1 ) are more likely to avoid falling into local optima and quickly obtain the global optima. This is because the large-scale random values can expand the range of particle velocity to make the particle more likely to escape from local optima and obtain the global optima. Although the random values generated by U [ − 1 , 1 ] or G ( 0 , 1 ) are beneficial to improve the global searching ability, the local searching ability for a low dimensional practical optimization problem may be decreased due to the finite particles.

This paper describes an improved global harmony search (IGHS) algorithm for identifying the nonlinear discrete-time systems based on second-order Volterra model. The IGHS is an improved version of the novel global harmony search (NGHS) algorithm, and it makes two significant improvements on the NGHS. First, the genetic mutation operation is modified by combining normal distribution and Cauchy distribution, which enables the IGHS to fully explore and exploit the solution space. Second, an opposition-based learning (OBL) is introduced and modified to improve the quality of harmony vectors. The IGHS algorithm is implemented on two numerical examples, and they are nonlinear discrete-time rational system and the real heat exchanger, respectively. The results of the IGHS are compared with those of the other three methods, and it has been verified to be more effective than the other three methods on solving the above two problems with different input signals and system memory sizes.

A dynamic adaptive particle swarm optimization and genetic algorithm is presented to solve constrained engineering optimization problems. A dynamic adaptive inertia factor is introduced in the basic particle swarm optimization algorithm to balance the convergence rate and global optima search ability by adaptively adjusting searching velocity during search process. Genetic algorithm–related operators including a selection operator with time-varying selection probability, crossover operator, and n-point random mutation operator are incorporated in the particle swarm optimization algorithm to further exploit optimal solutions generated by the particle swarm optimization algorithm. These operators are used to diversify the swarm and prevent premature convergence. Tests on nine constrained mechanical engineering design optimization problems with different kinds of objective functions, constraints, and design variables in nature demonstrate the superiority of the dynamic adaptive particle swarm optimization and genetic algorithm against several other meta-heuristic algorithms in terms of solution quality, robustness, and convergence rate in most cases.

Harmony search (HS) algorithm is an emerging population oriented stochastic metaheuristic algorithm, which is inspired by the music improvisation process. This paper introduces an Amended harmony search (AHS) algorithm for solving optimization problems. In AHS, an enhanced approach is employed for generating better solution that improves accuracy and convergence speed of harmony search (HS). The effects of various parameters on harmony search algorithm are analyzed in this paper. The proposed approach performs fine tuning of two parameters bandwidth and pitch adjustment rate. The proposed algorithm is demonstrated on complex benchmark functions and results are compared with two recent variants of HS optimization algorithms, improved harmony search (IHS) and highly reliable harmony search (HRHS). Results suggested that the AHS method has strong convergence and has better balance capacity of exploration and exploitation.

Genetic algorithm for non-linear mixed integer programming problems and its applications

The particle swarm optimization (PSO) algorithm presents a new way for finding optimal solutions of complex optimization problems. In this paper a modified particle swarm optimization algorithm is presented. We modify the PSO algorithm in some aspects. Firstly, a contractive factor is introduced to the position update equation, and the particles are limited in search region. A new strategy for updating velocity is then adopted, in which the velocity is weakened linearly. Thirdly, using an idea of intersecting two modified PSO algorithms. Finally, adding an item of integral control in the modified algorithm can improve its global search ability. Based on these strategies, we proposed a new PSO algorithm named crossed PSO algorithm. Simulation results show that the crossed PSO is superior to the original PSO algorithm and can get overall promising performance over a wide range of problems.

The performances of Particle Swarm Optimization and Genetic Algorithm have been compared to develop a methodology for concurrent and integrated design of mechanical structure and controller of a 2-dof robotic manipulator solving tracking problems. The proposed design scheme optimizes various parameters belonging to different domains (that is, link geometry, mass distribution, moment of inertia, control gains) concurrently to design manipulator, which can track some given paths accurately with a minimum power consumption. The main strength of this study lies with the design of an integrated scheme to solve the above problem. Both real-coded Genetic Algorithm and Particle Swarm Optimization are used to solve this complex optimization problem. Four approaches have been developed and their performances are compared. Particle Swarm Optimization is found to perform better than the Genetic Algorithm, as the former carries out both global and local searches simultaneously, whereas the latter concentrates mainly on the global search. Controllers with adaptive gain values have shown better performance compared to the conventional ones, as expected.

Particle swarm optimization algorithm is a new evolutionary computation method, which is applicable to complex optimization problems that are nonlinear, nondifferentiable and multimodal. A method for identification of time-varying delay systems using particle swarm optimization is proposed. The basic idea of the method is that the identification problems are cast as mixed-integer nonlinear programming problems, and then particle swarm optimization algorithm is used to find the optimal estimation of the time-varying parameters. Simulation results reveal that the suggested identification scheme possesses a good tracking ability to the time-varying delay systems.

In this paper, a new meta-heuristic algorithm, called beetle swarm optimization (BSO) algorithm, is proposed by enhancing the performance of swarm optimization through beetle foraging principles. The performance of 23 benchmark functions is tested and compared with widely used algorithms, including particle swarm optimization (PSO) algorithm, genetic algorithm (GA) and grasshopper optimization algorithm (GOA). Numerical experiments show that the BSO algorithm outperforms its counterparts. Besides, to demonstrate the practical impact of the proposed algorithm, two classic engineering design problems, namely, pressure vessel design problem and himmelblau?s optimization problem, are also considered and the proposed BSO algorithm is shown to be competitive in those applications.

An improved harmony search algorithm for power economic load dispatch

According to the features of order-type vulcanization workshop scheduling, deficiencies of PSO, as well as the excellent characteristics of the chaos principle, target mutations, and cooperation particles, a new particle swarm optimization algorithm, that is, chaos double-mutations cooperation particles swarm optimization was proposed. This can maintain the diversity of particles, avoid results falling into local optimum and improve the algorithm's global search ability. Four optimization algorithm convergences were compared and the change orders of vulcanization workshop scheduling were stimulated by testing. Results show that it is very effective and the chaos double-mutations cooperation particles swarm optimization in solving the order-type vulcanization workshop scheduling was verified.

Non-convex optimization problems are prevalent in scientific and engineering applications, often characterized by multiple local minima that challenge standard optimization techniques. Global optimization methods, such as Genetic Algorithms (GA) (1992) [4] and Particle Swarm Optimization (PSO) (1995) [6], provide robust global exploration but tend to converge slowly. Conversely, local search methods, such as Newton’s method (2004) [1], (2006) [7], and the Conjugate Gradient (CG) (1964) [3] method, offer rapid convergence but are susceptible to local minima. In this paper, we present four hybrid optimization algorithms that integrate the exploratory strength of global algorithms with the refinement ability of local methods. The proposed hybrids, Genetic Algorithms (GA) + Newton, GA + CG, PSO + Newton, and PSO + CG, are evaluated against their standalone counterparts on standard benchmark functions (2013) [5], including Rosenbrock, Rastrigin, Ackley, and Himmelblau. This work builds upon our previous research on the hybridization of two global search algorithms, the Nelder–Mead (simplex) algorithm and the Bat algorithm, which resulted in the Hybrid Simplex Bat Algorithm (HSBA) [2], recently Published. Results demonstrate that the hybrid approaches consistently outperform traditional methods in terms of accuracy, convergence rate, and computational efficiency.

Federated learning (FL) over wireless networks has become a key enabler for privacy-preserving distributed artificial intelligence (AI). However, high learning latency remains a critical bottleneck due to the presence of stragglers, limited wireless resources, and frequent model uploads. While model quantization can mitigate this issue by reducing communication overhead, its effectiveness is sensitive to device heterogeneity and time-varying channel conditions. To address this issue, we propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FedDamQu</i>, a communication-efficient FL framework with doubly-adaptive model quantization, which dynamically adjusts quantization bit-widths across devices and communication rounds to balance latency and accuracy. Our objective is to maximize the model performance under learning latency constraints. The main contributions are summarized as follows. 1) Convergence Analysis under Unreliable Channels: We derive a novel convergence error upper bound for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FedDamQu</i>, which explicitly quantifies the impact of device selection, unreliable transmission, and quantization error on the global model performance, under both fixed and dynamic quantization gain settings. 2) Joint Optimization Framework: Based on the knowledge from the proposed theoretical bound, we formulate a joint mixed integer nonlinear programming (MINLP) problem that integrates device selection, quantization bit-width configuration, and bandwidth allocation to minimize the convergence error under latency constraints. 3) Efficient Solution Design: The MINLP problem is decomposed into three subproblems, where closed-form solutions for quantization bit-width configuration and bandwidth allocation subproblems are derived, and a lightweight yet effective iterative algorithm is developed to obtain a suboptimal solution for the device selection subproblem. Extensive experiment results validate the theoretical analysis and demonstrate that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FedDamQu</i> consistently outperforms existing methods in terms of convergence rate and model accuracy, while significantly reducing the overall learning latency.