Hybrid simplex search and particle swarm optimization for the global optimization of multimodal functions

This article proposes the hybrid Nelder–Mead (NM)–Particle Swarm Optimization (PSO) algorithm based on the NM simplex search method and PSO for the optimization of multimodal functions. The hybrid NM–PSO algorithm is very easy to implement, in practice, since it does not require gradient computation. This hybrid procedure performed the exploration with PSO and the exploitation with the NM simplex search method. In a suite of 17 multi-optima test functions taken from the literature, the computational results via various experimental studies showed that the hybrid NM–PSO approach is superior to the two original search techniques (i.e. NM and PSO) in terms of solution quality and convergence rate. In addition, the presented algorithm is also compared with eight other published methods, such as hybrid genetic algorithm (GA), continuous GA, simulated annealing (SA), and tabu search (TS) by means of a smaller set of test functions. On the whole, the new algorithm is demonstrated to be extremely effective and efficient at locating best-practice optimal solutions for multimodal functions.     

An improved hybrid self-inertia weight adaptive particle swarm optimization algorithm with local search

As an evolutionary computing technique, particle swarm optimization (PSO) has good global search ability, but the swarm can easily lose its diversity, leading to premature convergence. To solve this problem, an improved self-inertia weight adaptive particle swarm optimization algorithm with a gradient-based local search strategy (SIW-APSO-LS) is proposed. This new algorithm balances the exploration capabilities of the improved inertia weight adaptive particle swarm optimization and the exploitation of the gradient-based local search strategy. The self-inertia weight adaptive particle swarm optimization (SIW-APSO) is used to search the solution. The SIW-APSO is updated with an evolutionary process in such a way that each particle iteratively improves its velocities and positions. The gradient-based local search focuses on the exploitation ability because it performs an accurate search following SIW-APSO. Experimental results verified that the proposed algorithm performed well compared with other PSO variants on a suite of benchmark optimization functions.     

Probabilistic optimal design of laminates using improved particle swarm optimization

A new approach to the particle swarm optimization (PSO) is proposed for the solution of non-linear optimization problems with constraints, and is applied to the reliability-based optimum design of laminated composites. Special mutation-interference operators are introduced to increase swarm variety and improve the convergence performance of the algorithm. The reliability-based optimum design of laminated composites is modelled and solved using the improved PSO. The maximization of structural reliability and the minimization of total weight of laminates are analysed. The stacking sequence optimization is implemented in the improved PSO by using a special coding technique. Examples show that the improved PSO has high convergence and good stability and is efficient in dealing with the probabilistic optimal design of composite structures.     

Drilling path optimization by the particle swarm optimization algorithm with global convergence characteristics

Drilling path optimization is one of the key problems in holes-machining. This paper presents a new approach to solve the drilling path optimization problem belonging to discrete space, based on the particle swarm optimization (PSO) algorithm. Since the standard PSO algorithm is not guaranteed to be global convergent or local convergent, based on the mathematical model, the algorithm is improved by adopting the method to generate the stop evolution particle once again to obtain the ability of convergence on the global optimization solution. Also, the operators are proposed by establishing the Order Exchange Unit (OEU) and the Order Exchange List (OEL) to satisfy the need of integer coding in drilling path optimization. The experimentations indicate that the improved algorithm has the characteristics of easy realization, fast convergence speed, and better global convergence capability. Hence the new PSO can play a role in solving the problem of drilling path optimization.     

A new images segmentation method based on modified particle swarm optimization algorithm

The partitioning of an image into several constituent components is called image segmentation. Many approaches have been developed; one of them is the particle swarm optimization (PSO) algorithm, which is widely used. PSO algorithm is one of the most recent stochastic optimization strategies. In this article, a new efficient technique for the magnetic resonance imaging (MRI) brain images segmentation thematic based on PSO is proposed. The proposed algorithm presents an improved variant of PSO, which is particularly designed for optimal segmentation and it is called modified particle swarm optimization. The fitness function is used to evaluate all the particle swarm in order to arrange them in a descending order. The algorithm is evaluated by performance measures such as run time execution and the quality of the image after segmentation. The performance of the segmentation process is demonstrated by using a defined set of benchmark images and compared against conventional PSO, genetic algorithm, and PSO with Mahalanobis distance based segmentation methods. Then we applied our method on MRI brain image to determinate normal and pathological tissues. © 2013 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 23, 265–271, 2013     

Multi-objective optimization of engineering systems using game theory and particle swarm optimization

This study proposes particle swarm optimization (PSO) based algorithms to solve multi-objective engineering optimization problems involving continuous, discrete and/or mixed design variables. The original PSO algorithm is modified to include dynamic maximum velocity function and bounce method to enhance the computational efficiency and solution accuracy. The algorithm uses a closest discrete approach (CDA) to solve optimization problems with discrete design variables. A modified game theory (MGT) approach, coupled with the modified PSO, is used to solve multi-objective optimization problems. A dynamic penalty function is used to handle constraints in the optimization problem. The methodologies proposed are illustrated by several engineering applications and the results obtained are compared with those reported in the literature.     

Stability assessment of earth slope using modified particle swarm optimization

This paper has proposed an effective method to determine the minimum factor of safety (FS) and associated critical failure surface in slope stability analysis. The search for the minimum FS based on limit equilibrium methods is a complex optimization problem as the objective function is non-smooth and non-convex. Recently, particle swarm optimization (PSO) as a meta-heuristic optimization algorithm has been developed with success in treating various types of problems. In the current study, a new approach of PSO is proposed to calculate the safety factor of earth slopes. The safety factors of the general slip surfaces are calculated using Spencer method of slices, and each new slip surface is randomly generated by straight line technique. The reliability and efficiency of the proposed algorithm are examined by considering a number of published cases. The results indicate that the new method can predict a more critical failure mechanism with a lower FS and can outperform the other methods in the literature as well as standard PSO. Finally, the proposed method will be validated by considering an existing slope failure in Ulu Klang, Malaysia.     

Evolutionary computation of unconstrained and constrained problems using a novel momentum-type particle swarm optimization

This study proposes a novel momentum-type particle swarm optimization (PSO) method, which will find good solutions of unconstrained and constrained problems using a delta momentum rule to update the particle velocity. The algorithm modifies Shi and Eberhart's PSO to enhance the computational efficiency and solution accuracy. This study also presents a continuous non-stationary penalty function, to force design variables to satisfy all constrained functions. Several well-known and widely used benchmark problems were employed to compare the performance of the proposed PSO with Kennedy and Eberhart's PSO and Shi and Eberhart's modified PSO. Additionally, an engineering optimization task for designing a pressure vessel was applied to test the three PSO algorithms. The optimal solutions are presented and compared with the data from other works using different evolutionary algorithms. To show that the proposed momentum-type PSO algorithm is robust, its convergence rate, solution accuracy, mean absolute error, standard deviation, and CPU time were compared with those of both the other PSO algorithms. The experimental results reveal that the proposed momentum-type PSO algorithm can efficiently solve unconstrained and constrained engineering optimization problems.     

Hybridizing the harmony search algorithm with a spreadsheet ‘Solver’ for solving continuous engineering optimization problems

In this article, a hybrid global–local optimization algorithm is proposed to solve continuous engineering optimization problems. In the proposed algorithm, the harmony search (HS) algorithm is used as a global-search method and hybridized with a spreadsheet ‘Solver’ to improve the results of the HS algorithm. With this purpose, the hybrid HS–Solver algorithm has been proposed. In order to test the performance of the proposed hybrid HS–Solver algorithm, several unconstrained, constrained, and structural-engineering optimization problems have been solved and their results are compared with other deterministic and stochastic solution methods. Also, an empirical study has been carried out to test the performance of the proposed hybrid HS–Solver algorithm for different sets of HS solution parameters. Identified results showed that the hybrid HS–Solver algorithm requires fewer iterations and gives more effective results than other deterministic and stochastic solution algorithms.     

A surrogate-assisted particle swarm optimization algorithm based on efficient global optimization for expensive black-box problems

Evolutionary algorithms cannot effectively handle computationally expensive problems because of the unaffordable computational cost brought by a large number of fitness evaluations. Therefore, surrogates are widely used to assist evolutionary algorithms in solving these problems. This article proposes an improved surrogate-assisted particle swarm optimization (ISAPSO) algorithm, in which a hybrid particle swarm optimization (PSO) is combined with global and local surrogates. The global surrogate is not only used to predict fitness values for reducing computational burden but also regarded as a global searcher to speed up the global search process of PSO by using an efficient global optimization algorithm, while the local one is constructed for a local search in the neighbourhood of the current optimal solution by finding the predicted optimal solution of the local surrogate. Empirical studies on 10 widely used benchmark problems and a real-world structural design optimization problem of a driving axle show that the ISAPSO algorithm is effective and highly competitive.     

Biogeography-based particle swarm optimization with fuzzy elitism and its applications to constrained engineering problems

In evolutionary algorithms, elites are crucial to maintain good features in solutions. However, too many elites can make the evolutionary process stagnate and cannot enhance the performance. This article employs particle swarm optimization (PSO) and biogeography-based optimization (BBO) to propose a hybrid algorithm termed biogeography-based particle swarm optimization (BPSO) which could make a large number of elites effective in searching optima. In this algorithm, the whole population is split into several subgroups; BBO is employed to search within each subgroup and PSO for the global search. Since not all the population is used in PSO, this structure overcomes the premature convergence in the original PSO. Time complexity analysis shows that the novel algorithm does not increase the time consumption. Fourteen numerical benchmarks and four engineering problems with constraints are used to test the BPSO. To better deal with constraints, a fuzzy strategy for the number of elites is investigated. The simulation results validate the feasibility and effectiveness of the proposed algorithm.     

On the optimal control of steel annealing processes via various versions of genetic and particle swarm optimization algorithms

7 This paper elucidates the computation of optimal controls for steel annealing processes as hybrid systems which comprise of one or more furnaces integrated with plant-wide planning and scheduling operations. A class of hybrid system is considered to capture the trade-off between metallurgical quality requirement and timely product delivery. Various optimization algorithms including particle swarm optimization algorithm (PSO) with time varying inertia weight methods, PSO with globally and locally tuned parameters (GLBest PSO), parameter free PSO (pf-PSO) and PSO like algorithm via extrapolation (ePSO), real coded genetic algorithm (RCGA) and two-phase hybrid real coded genetic algorithm (HRCGA) are considered to solve the optimal control problems for the steel annealing processes (SAP). The optimal solutions including optimal line speed, optimal cost, and job completion time and convergence rate obtained through all these optimization algorithms are compared with each other and also those obtained via the existing method, forward algorithm (FA). Various statistical analyses and analysis of variance (ANOVA) test and hypothesis t-test are carried out in order to compare the performance of each method in solving the optimal control problems of SAP. The comparative study of the performance of the various algorithms indicates that the PSO like algorithms, pf-PSO and ePSO are equally good and are also better than all the other optimization methods considered in this chapter.     

Experiments with hybrid Bernstein global optimization algorithm for the OPF problem in power systems

This article presents an algorithm based on the Bernstein form of polynomials for solving the optimal power flow (OPF) problem in electrical power networks. The proposed algorithm combines local and global optimization methods and is therefore referred to as a ‘hybrid’ Bernstein algorithm in the context of this work. The proposed algorithm is a branch-and-bound procedure wherein a local search method is used to obtain a good upper bound on the global minimum at each branching node. Subsequently, the Bernstein form of polynomials is used to obtain a lower bound on the global minimum. The performance of the proposed algorithm is compared with the previously reported Bernstein algorithm to demonstrate its efficacy in terms of the chosen performance metrics. Furthermore, the proposed algorithm is tested on the OPF problem for several benchmark IEEE power system examples and its performance is compared with generic global optimization solvers such as BARON and COUENNE. The test results demonstrate that the hybrid Bernstein global optimization algorithm delivers satisfactory performance in terms of solution optimality.     

包装物回收物流中的车辆路径优化问题

目的提高遗传算法(GA)求解包装物回收车辆路径优化问题的性能。方法通过对传统GA算法的改进,提出混合蜂群遗传算法(HBGA)。首先改进传统GA算法的初始种群生成方式,设计初始种群混合生成算子;其次,提出最大保留交叉算子,对优秀子路径进行保护;然后,在上述改进的基础上引入蜜蜂进化机制,用以保证种群多样性和优秀个体特征信息的利用程度;最后,对标准算例集进行仿真测试。结果与传统GA算法相比,HBGA算法在全局寻优能力、算法稳定性和运行速度方面均有所改善。HBGA算法的全局寻优能力和算法稳定性均优于粒子群算法(PSO)、蚁群算法(ACO)和禁忌搜索算法(TS),但运行速度稍慢于TS算法。结论对传统GA算法的改进是合理的,且HBGA算法整体求解性能优于PSO算法、ACO算法和TS算法。     

A new optimization algorithm based on a combination of particle swarm optimization,convergence and divergence operators for single-objective and multi-objective problems

Particle swarm optimization (PSO) is a randomized and population-based optimization method that was inspired by the flocking behaviour of birds and human social interactions. In this work, multi-objective PSO is modified in two stages. In the first stage, PSO is combined with convergence and divergence operators. Here, this method is named CDPSO. In the second stage, to produce a set of Pareto optimal solutions which has good convergence, diversity and distribution, two mechanisms are used. In the first mechanism, a new leader selection method is defined, which uses the periodic iteration and the concept of the particle's neighbour number. This method is named periodic multi-objective algorithm. In the second mechanism, an adaptive elimination method is employed to limit the number of non-dominated solutions in the archive, which has influences on computational time, convergence and diversity of solution. Single-objective results show that CDPSO performs very well on the complex test functions in terms of solution accuracy and convergence speed. Furthermore, some benchmark functions are used to evaluate the performance of periodic multi-objective CDPSO. This analysis demonstrates that the proposed algorithm operates better in three metrics through comparison with three well-known elitist multi-objective evolutionary algorithms. Finally, the algorithm is used for Pareto optimal design of a two-degree of freedom vehicle vibration model. The conflicting objective functions are sprung mass acceleration and relative displacement between sprung mass and tyre. The feasibility and efficiency of periodic multi-objective CDPSO are assessed in comparison with multi-objective modified NSGAII.     

混合粒子群算法在混流装配线优化调度中的应用

应用粒子群算法求解混流装配线的优化调度问题,给出粒子的构造方法,并针对算法中存在过早收敛的问题,提出了一种与局部优化和粒子微变异方法相结合的混合粒子群算法.给出了一个实例,实例应用粒子群算法和混合粒子群算法分别进行求解,与其他一些方法比较表明,混合粒子群算法可以有效、快速地求得混流装配线优化调度问题的解.     

Swarm algorithms for single- and multi-objective optimization problems incorporating sensitivity analysis

Swarm algorithms such as particle swarm optimization (PSO) are non-gradient probabilistic optimization algorithms that have been successfully applied for global searches in complex problems such as multi-peak problems. However, application of these algorithms to structural and mechanical optimization problems still remains a complex matter since local optimization capability is still inferior to general numerical optimization methods. This article discusses new swarm metaphors that incorporate design sensitivities concerning objective and constraint functions and are applicable to structural and mechanical design optimization problems. Single- and multi-objective optimization techniques using swarm algorithms are combined with a gradient-based method. In the proposed techniques, swarm optimization algorithms and a sequential linear programming (SLP) method are conducted simultaneously. Finally, truss structure design optimization problems are solved by the proposed hybrid method to verify the optimization efficiency.     

A cloud theory-based particle swarm optimization for multiple decision maker vehicle routing problems with fuzzy random time windows

This article puts forward a cloud theory-based particle swarm optimization (CTPSO) algorithm for solving a variant of the vehicle routing problem, namely a multiple decision maker vehicle routing problem with fuzzy random time windows (MDVRPFRTW). A new mathematical model is developed for the proposed problem in which fuzzy random theory is used to describe the time windows and bi-level programming is applied to describe the relationship between the multiple decision makers. To solve the problem, a cloud theory-based particle swarm optimization (CTPSO) is proposed. More specifically, this approach makes improvements in initialization, inertia weight and particle updates to overcome the shortcomings of the basic particle swarm optimization (PSO). Parameter tests and results analysis are presented to highlight the performance of the optimization method, and comparison of the algorithm with the basic PSO and the genetic algorithm demonstrates its efficiency.     

基于粒子群优化聚类的汽轮机组振动故障诊断

针对模糊C-均值聚类算法(FCM)容易陷入局部极值和对初始值敏感的不足,提出了一种新的模糊聚类算法(PFCM),新算法利用粒子群优化算法(PSO)全局寻优、快速收敛的特点,代替了FCM算法的基于梯度下降的迭代过程,使算法具有很强的全局搜索能力,很大程度上避免了FCM算法易陷入局部极值的缺陷,同时也降低了FCM算法对初始值的敏感度。将该算法应用于汽轮机组振动故障诊断中,与电厂运行实际故障状态对照,仿真结果表明该算法提高了故障诊断的正确率。为汽轮机振动故障诊断方法的研究提供了一种新的思路。     

改进的混合粒子群优化算法

针对粒子群算法后期收敛速度较慢,易陷入局部最优的缺点,提出了改进的混合粒子群算法.通过更改现有的速度更新公式,加入扰动项,以及引入交叉和变异算子等措施,改进了粒子群算法的性能.数值试验表明,改进后的粒子群算法在全局寻优和局部寻优能力上均得到提高,是一种有效的优化算法.