应用蜜蜂繁殖进化型粒子群算法求解车辆路径问题

为了提高粒子群算法求解车辆路径问题时收敛速度和全局搜索能力,将蜜蜂繁殖进化机制与粒子群算法相结合,应用到CVRP问题的求解。该算法中,最优的个体作为蜂王与通过选择机制选择的雄蜂以随机概率进行交叉,增强了最优个体信息的应用能力;同时,随机产生一部分雄蜂种群,并将其与蜂王交叉增加了算法的多样性。实例分析表明该算法具有较好的全局搜索能力,验证了该算法的可行性。     

A dynamic programming-based particle swarm optimization algorithm for an inventory management problem under uncertainty

This article presents a dynamic programming-based particle swarm optimization (DP-based PSO) algorithm for solving an inventory management problem for large-scale construction projects under a fuzzy random environment. By taking into account the purchasing behaviour and strategy under rules of international bidding, a multi-objective fuzzy random dynamic programming model is constructed. To deal with the uncertainties, a hybrid crisp approach is used to transform fuzzy random parameters into fuzzy variables that are subsequently defuzzified by using an expected value operator with optimistic–pessimistic index. The iterative nature of the authors’ model motivates them to develop a DP-based PSO algorithm. More specifically, their approach treats the state variables as hidden parameters. This in turn eliminates many redundant feasibility checks during initialization and particle updates at each iteration. Results and sensitivity analysis are presented to highlight the performance of the authors’ optimization method, which is very effective as compared to the standard PSO algorithm.     

A particle swarm optimizer for constrained multi-objective engineering design problems

This article presents a particle swarm optimizer (PSO) capable of handling constrained multi-objective optimization problems. The latter occur frequently in engineering design, especially when cost and performance are simultaneously optimized. The proposed algorithm combines the swarm intelligence fundamentals with elements from bio-inspired algorithms. A distinctive feature of the algorithm is the utilization of an arithmetic recombination operator, which allows interaction between non-dominated particles. Furthermore, there is no utilization of an external archive to store optimal solutions. The PSO algorithm is applied to multi-objective optimization benchmark problems and also to constrained multi-objective engineering design problems. The algorithmic effectiveness is demonstrated through comparisons of the PSO results with those obtained from other evolutionary optimization algorithms. The proposed particle swarm optimizer was able to perform in a very satisfactory manner in problems with multiple constraints and/or high dimensionality. Promising results were also obtained for a multi-objective engineering design problem with mixed variables.     

具有时间窗的开放式车辆路径的改进微粒群算法

分析了车场开放的带时间窗的车辆路径问题,在完成配送服务的车辆数目不确定的条件下,建立了该问题的数学模型,同时运用改进的微粒群算法求解该问题,算法采用一种基于客户的序数编码方法构造初始种群,对微粒群算法的进化方程进行了改进,使改进微粒群算法的搜索过程具有自适应性。最后根据第三方物流配送的实际,基于问题的不同目标,运用数值检验了模型和算法的有效性。     

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.     

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。     

Guided particle swarm optimization method to solve general nonlinear optimization problems

The development of hybrid algorithms is becoming an important topic in the global optimization research area. This article proposes a new technique in hybridizing the particle swarm optimization (PSO) algorithm and the Nelder–Mead (NM) simplex search algorithm to solve general nonlinear unconstrained optimization problems. Unlike traditional hybrid methods, the proposed method hybridizes the NM algorithm inside the PSO to improve the velocities and positions of the particles iteratively. The new hybridization considers the PSO algorithm and NM algorithm as one heuristic, not in a sequential or hierarchical manner. The NM algorithm is applied to improve the initial random solution of the PSO algorithm and iteratively in every step to improve the overall performance of the method. The performance of the proposed method was tested over 20 optimization test functions with varying dimensions. Comprehensive comparisons with other methods in the literature indicate that the proposed solution method is promising and 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.     

粒子群优化算法综述

粒子群优化（PSO）算法是一种新兴的优化技术,其思想来源于人工生命和演化计算理论。PSO通过粒子追随自己找到的最好解和整个群的最好解来完成优化。该算法简单易实现,可调参数少,已得到广泛研究和应用。详细介绍了PSO的基本原理、各种改进技术及其应用等,并对其未来的研究提出了一些建议。     

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.     

改进粒子群算法在农产品物流配送路径管理中的应用

目的 为了更加合理地进行车辆路径调度管理,提高粒子群求解车辆路径优化问题的性能。方法 提出了一种动态猴子跳跃机制的粒子群优化算法,它借助群体的动态分组,采用不同的动态惯性权重来提高算法的速度,引入猴子跳跃机制来保证全局收敛性。最后把改进算法应用到物流配送路径优化的2个实例中,同一环境下,改进算法搜寻到最优路径适应值、平均运算时间,以及求得最优解的成功次数,均优于标准粒子群优化算法。结果 结果表明,改进的算法能快速有效地确定物流配送路径。结论 改进粒子群优化算法不仅具有较快的寻优速度,而且也提高了算法的收敛性,保证了寻优质量,因此具有很大的应用价值。     

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.     

基于改进粒子群算法的制造单元设施布局问题研究

为避免单元系统布局和单元内设施布局分开孤立研究所导致的问题解空间损失,利用并行工程的思想对单元布局的两个环节集成考虑,对单元系统布局、单元内设施布置、设施摆放方向进行同时描述,并建立多目标集成优化模型。针对模型的复杂性,设计了改进粒子群算法,算法吸收了遗传算法中的交叉操作算子,具有跳出局部最优解的能力。最后通过求解单元设施布置实例,验证模型和算法的有效性。     

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     

求解VRP问题的混沌模拟退火萤火虫算法

目的使萤火虫优化算法(GSO)能够适用于车辆路径问题(VRP)的求解,同时提高该算法的求解性能。方法通过对GSO算法的改进,提出求解VRP问题的混沌模拟退火萤火虫优化算法(CSAGSO)。首先,设计改进的GSO算法(IGSO)使IGSO算法能够适应VRP问题的求解;其次,在IGSO算法中引入模拟退火机制,提出模拟退火萤火虫优化算法(SAGSO),使IGSO算法可有效避免陷入局部极小并最终趋于全局最优。然后,在SAGSO算法中引入混沌机制,提出CSAGSO算法,对SAGSO算法的荧光素浓度值进行混沌初始化和混沌扰动;最后,对标准算例集进行仿真测试。结果与遗传算法、蚁群算法和粒子群算法相比,CSAGSO算法的全局寻优能力、收敛速度及稳定性均改善了50%以上。结论对GSO算法的改进是合理的,且CSAGSO算法的全局优化能力、收敛速度和稳定性均优于遗传算法、蚁群算法和粒子群算法。     

Decomposition-based multi-objective differential evolution particle swarm optimization for the design of a tubular permanent magnet linear synchronous motor

This article proposes a decomposition-based multi-objective differential evolution particle swarm optimization (DMDEPSO) algorithm for the design of a tubular permanent magnet linear synchronous motor (TPMLSM) which takes into account multiple conflicting objectives. In the optimization process, the objectives are evaluated by an artificial neural network response surface (ANNRS), which is trained by the samples of the TPMSLM whose performances are calculated by finite element analysis (FEA). DMDEPSO which hybridizes differential evolution (DE) and particle swarm optimization (PSO) together, first decomposes the multi-objective optimization problem into a number of single-objective optimization subproblems, each of which is associated with a Pareto optimal solution, and then optimizes these subproblems simultaneously. PSO updates the position of each particle (solution) according to the best information about itself and its neighbourhood. If any particle stagnates continuously, DE relocates its position by using two different particles randomly selected from the whole swarm. Finally, based on the DMDEPSO, optimization is gradually carried out to maximize the thrust of TPMLSM and minimize the ripple, permanent magnet volume, and winding volume simultaneously. The result shows that the optimized TPMLSM meets or exceeds the performance requirements. In addition, comparisons with chosen algorithms illustrate the effectiveness of DMDEPSO to find the Pareto optimal solutions for the TPMLSM optimization problem.     

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。     

Optimisation of the multi-depots pick-up and delivery problems with time windows and multi-vehicles using PSO algorithm

Many sectors in the transport industry are concerned about the vehicle routing problem (VRP), hence the growing interest of researchers for this type of problem and its variants. This is due essentially to its many real applications in logistics for the transport of goods. The originality and contribution of our work is that we have dealt a problem that combines several variants: multiple vehicles (m), multiple depots (MD), pickup and delivery problem (PDP) with time windows (TW). Hence the notation of our problem: m-MDPDPTW. In this paper, we present the m-MDPDPTW, which is an optimisation problem belonging to the category of NP Hard problems. This problem must meet requests for transport between customers and suppliers satisfying precedence, capacity and time constraints. The goal is to find the best solution, which is the best route minimising the total travelled distance. To solve and optimise our m-MDPDPTW, we have developed a new algorithm based on the particle swarm optimisation (PSO) method. The performance of this new approach is tested on data set instances of Li and Lim's benchmark problems in which we have added multiple depot locations. Comparing with prior works, our proposed approach gave better results by decreasing the distance for several studied instances.     

求解复杂优化问题的双层多种群粒子群优化算法

为解决粒子群优化算法存在的易早熟和精度低问题,提出了一种双层多种群粒子群优化算法.此算法采用上下两层,即下层N个基础种群和上层一个精英种群.各个基础种群相互独立进化,并从精英种群中得到优良信息指导自己的进化.上层精英种群首先通过接受各基础种群的当前最优粒子来更新自己的粒子集合,然后执行自适应变异操作,最后随机地向每一个基础种群输送出本次进化后的一个最优粒子来改进其下一轮搜索.该算法的并行双进化机制增加了群体的随机性和多样性,提高了全局搜索能力和收敛精度.实例仿真表明该算法具有较好的性能,尤其对于复杂多峰函数优化,成功率显著提高.     

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.