A modified particle swarm optimization for aggregate production planning

Particle swarm optimization (PSO) originated from bird flocking models. It has become a popular research field with many successful applications. In this paper, we present a scheme of an aggregate production planning (APP) from a manufacturer of gardening equipment. It is formulated as an integer linear programming model and optimized by PSO. During the course of optimizing the problem, we discovered that PSO had limited ability and unsatisfactory performance, especially a large constrained integral APP problem with plenty of equality constraints. In order to enhance its performance and alleviate the deficiencies to the problem solving, a modified PSO (MPSO) is proposed, which introduces the idea of sub-particles, a particular coding principle, and a modified operation procedure of particles to the update rules to regulate the search processes for a particle swarm. In the computational study, some instances of the APP problems are experimented and analyzed to evaluate the performance of the MPSO with standard PSO (SPSO) and genetic algorithm (GA). The experimental results demonstrate that the MPSO variant provides particular qualities in the aspects of accuracy, reliability, and convergence speed than SPSO and GA.     

广义粒子群优化模型

粒子群优化算法提出至今一直未能有效解决的离散及组合优化问题．针对这个问题,文中首先回顾了粒子群优化算法在整数规划问题的应用以及该算法的二进制离散优化模型,并分析了其缺陷．然后,基于传统算法的速度一位移更新操作,在分析粒子群优化机理的基础上提出了广义粒子群优化模型（GPSO）,使其适用于解决离散及组合优化问题．GPSO模型本质仍然符合粒子群优化机理,但是其粒子更新策略既可根据优化问题的特点设计,也可实现与已有方法的融合．该文以旅行商问题（TSP）为例,针对遗传算法（GA）解决该问题的成功经验,使用遗传操作作为GPSO模型中的更新算子,进一步提出基于遗传操作的粒子群优化模型,并以Inverover算子作为模型中具体的遗传操作设计了基于GPSO模型的TSP算法．与采用相同遗传操作的GA比较,基于GPSO模型的算法解的质量与收敛稳定性提高,同时计算费用显著降低．     

The impact of particular components of the PSO-based algorithm solving the Dynamic Vehicle Routing Problem

This paper presents and analyzes a Two-Phase Multi-Swarm Particle Swarm Optimizer (2MPSO) solving the Dynamic Vehicle Routing Problem (DVRP). The research presented in this paper focuses on finding a configuration of several optimization improvement techniques, dedicated to solving dynamic optimization problems, within the 2MPSO framework. Techniques, whose impact on results achieved for DVRP is analyzed, include: solving the current state of a problem with a capacitated clustering and routing heuristic algorithms, solving requests-to-vehicles assignment by the PSO algorithm, route optimization by a separate instance of the PSO algorithm, and knowledge transfer between subsequent states of the problem. The results obtained by the best chosen configuration of the 2MPSO are compared with the state-of-the-art literature results on a popular set of benchmark instances.Our study shows that strong results achieved by 2MPSO should be attributed to three factors: generating initial solutions with a clustering heuristic, optimizing the requests-to-vehicle assignment with a metaheuristic approach, direct passing of solutions obtained in the previous stage (times step) of the problem solving procedure to the next stage. Additionally, 2MPSO outperforms the average results obtained by other algorithms presented in the literature, both in the time limited experiments, as well as those restricted by the number of fitness function evaluations.     

A modified particle swarm optimization for economic dispatch with non-smooth cost functions

This paper presents a new approach to economic dispatch (ED) problems with non-smooth cost functions using a particle swarm optimization (PSO) technique. The practical ED problems have non-smooth cost functions with equality and inequality constraints, which makes the problem of finding the global optimum difficult when using any mathematical approaches. Since, standard PSO may converge at the early stage, in this paper, a modified PSO (MPSO) mechanism is suggested to deal with the equality and inequality constraints in the ED problems. To validate the results obtained by MPSO, standard particle swarm optimization (PSO) and guaranteed convergence particle swarm optimization (GCPSO) are applied for comparison. Also, the results obtained by MPSO, PSO and GCPSO are compared with the previous approaches reported in the literature. The results show that the MPSO produces optimal or nearly optimal solutions for the study systems.     

全变异粒子群优化算法

针对粒子群优化算法容易早熟、收敛精度低等缺点,通过采用全变异策略、最大搜索速度自适应调整等策略得到了一种全变异粒子群优化算法,其中的全变异策略是在陷入早熟的条件下全体粒子参加变异,并且当把粒子看成染色体时,每一个基因等概率地参加变异,可以克服算法的早熟而继续优化,提高了算法的收敛精度。对Shubert函数进行实验的结果表明了算法的有效性。     

水火电力系统短期优化调度的一种改进粒子群算法

针对水火联调问题,建立满足电量平衡、水量平衡、机组特性及综合利用要求的短期优化调度模型,提出了一种改进粒子群算法(MPSO).MPSO针对粒子群算法易早熟收敛的弊端,引入了变异操作,使粒子以一定的概率向其他粒子个体最好解学习;针对粒子群算法在进化后期多样性受损易陷入局部最优的缺陷,引入了迁徙操作,在种群聚集程度不能容忍时重新生成解空间内均匀分布的粒子.对某典型水火电力系统优化问题的求解结果表明,MPSO比其他方法更有效.     

引入多级扰动的混合型粒子群优化算法

为解决粒子群优化算法易陷入局部最优值的问题,提出一种引入多级扰动的混合型粒子群优化算法.该算法结合两种经典改进粒子群优化算法的优点,即带惯性参数的标准粒子群优化算法和带收缩因子的粒子群优化算法,在此基础上,引入多级扰动机制：在更新粒子位置时,引入一级扰动,使粒子对解空间的遍历能力得到加强;若优化过程陷入“局部最优”的情况,则引入二级扰动,使得优化过程继续,从而摆脱局部最优值.使用了6个测试函数——Sphere函数、Ackley函数、Rastrigin函数、Styblinski-Tang函数、Duadric函数及Rosenbrock函数来对所提出的混合型粒子群优化算法进行仿真运算和对比验证.模拟运算的结果表明：所提出的混合型粒子群优化算法在对测试函数进行仿真时,其收敛精度和收敛速度都优于另外两种经典的改进粒子群优化算法;另外,在处理多峰函数时,本算法不易被局部最优值所限制.     

A revised ant algorithm for solving location–allocation problem with risky demand in a multi-echelon supply chain network

This study addresses a capacitated facility location and task allocation problem of a multi-echelon supply chain against risky demands. Two and three-echelon networks are considered to maximize profit. The study represents the problem by a bi-level stochastic programming model. The revised ant algorithm proposed in the study improves the existing ant algorithm by using new design of heuristic desirability and efficient greedy heuristics to solve the problem. A set of computational experiments is reported to not only allow to fine-tune the parameters of the algorithm but also to evaluate its performance for solving the problem proposed. Experiments reveal that the proposed solution algorithm can reach 95–99% of the optimal solution against risky demands while consuming only 1000th of the computational time for large-sized problems as compared to an optimization-based tool.     

A DSS for production planning focused on customer service and technological aspects

Production planning and control in manufacturing systems cover several aspects, at different hierarchical levels, including decisions on production and inventory quantities, resource acquisition, production allocation and sequencing. We consider a problem that is typical of companies that manufacture products in production plants placed in different production areas worldwide. A solution framework for the production allocation and balancing problems based on mathematical programming is proposed. Its computational efficiency is improved using techniques from constraint programming, in order to make it possible to solve real world instances of the problems. An industrial test case is used as a benchmark to prove the effectiveness of the proposed approach.     

基于Toy模型蛋白质折叠预测的多种群微粒群优化算法研究

基于Toy模型的蛋白质折叠结构预测问题是一个典型的NP问题.提出了多种群微粒群优化算法用于计算蛋白质能量最小值.该算法采用了一种新的算法结构,在该结构中,每一代的种群被分为精英子种群、开采子种群和勘探子种群三部分,通过改善种群的局部开采能力和全局勘探能力来提高算法的性能.分别采用Fibonacci蛋白质测试序列和真实蛋白质序列进行了折叠结构预测的仿真实验.实验结果表明该算法能够更精确地进行蛋白质折叠结构预测,为生物科学研究提供了一条有效途径.     

多策略粒子群优化算法

为了克服粒子群优化算法易早熟、局部搜索能力弱的问题,提出了一种改进的粒子群优化算法--多策略粒子群优化算法。在群体寻优过程中,各粒子根据搜索到的最优位置的变动情况,从几种备选的策略中抉择出当代的最优搜索策略。其中,最优粒子有最速下降策略、矫正下降策略和随机移动策略可以选择,非最优粒子有聚集策略和扩散策略可以选择。四个典型测试函数的数值实验结果表明,新提出的算法比标准粒子群优化算法具有更强和更稳定的全局搜索能力。     

A novel hybrid PSO–GWO approach for unit commitment problem

Particle swarm optimization algorithm is a inhabitant-based stochastic search procedure, which provides a populace-based search practice for getting the best solution from the problem by taking particles and moving them around in the search space and efficient for global search. Grey Wolf Optimizer is a recently developed meta-heuristic search algorithm inspired by Canis-lupus. This research paper presents solution to single-area unit commitment problem for 14-bus system, 30-bus system and 10-generating unit model using swarm-intelligence-based particle swarm optimization algorithm and a hybrid PSO–GWO algorithm. The effectiveness of proposed algorithms is compared with classical PSO, PSOLR, HPSO, hybrid PSOSQP, MPSO, IBPSO, LCA–PSO and various other evolutionary algorithms, and it is found that performance of NPSO is faster than classical PSO. However, generation cost of hybrid PSO–GWO is better than classical and novel PSO, but convergence of hybrid PSO–GWO is much slower than NPSO due to sequential computation of PSO and GWO.     

基于DSmT的专家推荐模型

为解释和修正信任管理系统中第二手信任评价与第一手信任评价之间的差异,提出一种基于DSmT的专家推荐模型——扰动模型。在该模型中,为求扰动评价,引出DSmT反问题。并介绍一种修正的粒子群优化算法,为求DSmT反问题的近似解,选取3个测试函数测试其性能,证明其能提高收敛速度。实验表明,扰动模型可以较好地解释第二手信任评价与第一手信任评价之间的差异,通过修正第二手信任评价可使其与第一手信任评价更一致。     

A two-stage discrete particle swarm optimization for the problem of multiple multi-level redundancy allocation in series systems

Nowadays, the redundancy allocation problem (RAP) is increasingly becoming an important tool in the initial stages of or prior to planning, designing, and control of systems. The multiple multi-level redundancy allocation problem (MMRAP) is an extension of the traditional RAP such that all available items for redundancy (system, module and component) can be simultaneously chosen. In this paper, a novel particle swarm optimization algorithm (PSO) called the two-stage discrete PSO (2DPSO) is presented to solve MMRAP in series systems such that some subsystems or modules consist of different components in series. To the best of our knowledge, this is the first attempt to use a PSO to MMRAP. The proposed PSO used a totally new, very simple, effective and efficient mechanism to move to the next position without velocity. The result obtained by 2DPSO has been compared with those obtained by genetic algorithm (GA) and binary PSO (BPSO). Computational results show that the proposed 2DPSO is very competitive and performs well in the number of times it finds the best solutions, the average numbers of the earliest finding of the best solutions, and computation times.     

Modified particle swarm optimization structure approach to direction of arrival estimation

This study considers the problem of estimating the direction-of-arrival (DOA) for code-division multiple access (CDMA) signals. In this type of problem, the associated cost function of the DOA estimation is generally a computationally-expensive and highly-nonlinear optimization problem. A fast convergence of the global optimization algorithm is therefore required to attain results within a short amount of time. In this paper, we propose a new application of the modify particle swarm optimization (MPSO) structure to achieve a global optimal solution with a fast convergence rate for this type of DOA estimation problem.The MPSO uses a first-order Taylor series expansion of the objective function to address the issue of enhanced PSO search capacity for finding the global optimum leads to increased performance. The first-order Taylor series approximates the spatial scanning vector in terms of estimating deviation results in and reducing to a simple one-dimensional optimization problem and the estimating deviation has the tendency to fly toward a better search area. Thus, the estimating deviation can be used to update the velocity of the PSO. Finally, several numerical examples are presented to illustrate the design procedure and to confirm the performance of the proposed method.     

多UCAV协同任务分配模型及粒子群算法求解

任务分配是多无人作战飞机(UCAV)协同控制的基础.对此,分析了影响任务分配的关键战技指标,建立了针对攻击任务的多UCAV协同任务分配模型.应用连续粒子群算法对问题进行求解,建立了粒子与实际问题间的映射,通过位置饱和策略构造粒子的搜索空间,采用自适应惯性权重提高粒子群算法的收敛速度和全局寻优能力.考虑到单机的任务载荷限制,引入了买卖合同机制以实现多机任务协调.仿真结果表明,所提出模型和算法可以较好地解决多UCAV协同任务分配问题.     

基于海图和改进粒子群优化算法的AUV全局路径规划

针对AUV（自主水下机器人）在复杂条件海域做全局路径规划时面临的环境信息缺少,环境建模困难和常规算法复杂、求解能力弱等问题,提出一种基于海图和改进粒子群优化算法的全局路径规划方法．首先利用电子海图的先验知识建立3维静态环境模型,并构造路径航程、危险度和平滑函数;在粒子群优化算法中引入搜索因子和同性因子自适应地调整参数,并结合鱼群算法的“跳跃”过程提升算法的求解能力．同时建立安全违背度和选优规则以提高所规划路径的安全性．仿真实验结果表明,本文方法与传统粒子群算法和蚁群算法相比,规划出短航程、安全性高的全局路径的能力更强,可满足AUV在复杂海域航行时的全局路径规划需求．     

A hybrid Lagrangian-simulated annealing-based heuristic for the parallel-machine capacitated lot-sizing and scheduling problem with sequence-dependent setup times

This paper examines the parallel-machine capacitated lot-sizing and scheduling problem with sequence-dependent setup times, time windows, machine eligibility and preference constraints. Such problems are quite common in the semiconductor manufacturing industry. In particular, this paper pays special attention to the chipset production in the semiconductor Assembly and Test Manufacturing (ATM) factory and constructs a Mixed Integer Programming (MIP) model for the problem. The primal problem is decomposed into a lot-sizing subproblem and a set of single-machine scheduling subproblems by Lagrangian decomposition. A Lagrangian-based heuristic algorithm, which incorporates the simulated annealing algorithm aimed at searching for a better solution during the feasibility construction stage, is proposed. Computational experiments show that the proposed hybrid algorithm outperforms other heuristic algorithms and meets the practical requirement for the tested ATM factory.     

An enhanced ant colony optimization (EACO) applied to capacitated vehicle routing problem

In this paper, an enhanced ant colony optimization (EACO) is proposed for capacitated vehicle routing problem. The capacitated vehicle routing problem is to service customers with known demands by a homogeneous fleet of fixed capacity vehicles starting from a depot. It plays a major role in the field of logistics and belongs to NP-hard problems. Therefore, it is difficult to solve the capacitated vehicle routing problem directly when solutions increase exponentially with the number of serviced customers. The framework of this paper is to develop an enhanced ant colony optimization for the capacitated vehicle routing problem. It takes the advantages of simulated annealing and ant colony optimization for solving the capacitated vehicle routing problem. In the proposed algorithm, simulated annealing provides a good initial solution for ant colony optimization. Furthermore, an information gain based ant colony optimization is used to ameliorate the search performance. Computational results show that the proposed algorithm is superior to original ant colony optimization and simulated annealing separately reported on fourteen small-scale instances and twenty large-scale instances.     

A Cross Entropy-based heuristic for the capacitated multi-source Weber problem with facility fixed cost

This paper investigates a capacitated planar location–allocation problem with facility fixed cost. A zone-based fixed cost which consists of production and installation costs is considered. A nonlinear and mixed integer formulation is first presented. A powerful three stage Cross Entropy meta-heuristic with novel density functions is proposed. In the first stage a covering location problem providing a multivariate normal density function for the associated stochastic problem is solved. The allocation values considering a multinomial density function are obtained in the second stage. In the third stage, single facility continuous location problems are solved. Several instances of various sizes are used to assess the performance of the proposed meta-heuristic. Our approach performs well when compared with the optimizer GAMS which is used to provide the optimal solution for small size instances and lower/upper bounds for some of the larger ones.