粒子群优化算法在0/1背包问题的应用

对于背包问题现有许多不同的求解方法.文中给出基于PSO的背包问题的一种新的求解方法.首先将背包问题对应到PSO算法中位置和速度的表示,建立了解决资源分配问题的随机粒子群算法,同时利用建立的算法与遗传算法比较,可见PSO得到了满意的计算结果.     

基于离散微粒群算法求解背包问题研究

微粒群算法(PSO)是一种新的演化算法,主要用于求解数值优化问题.基于离散微粒群算法(DPSO)分别与处理约束问题的罚函数法和贪心变换方法相结合,提出了求解背包问题的两个算法:基于罚函数策略的离散微粒群算法(PFDPSO)和基于贪心变换策略的离散微粒群算法(GDPSO).通过将这两个算法与文献[7]中的混合微粒群算法(Hybrid_PSO)进行数值计算比较发现:对于求解大规模的背包问题,GDPSO非常优秀,其求解能力优于Hybrid_PSO和PFDPSO,是求解背包问题的一种非常有效的方法.     

一种具有双重进化空间的扩展粒子群优化算法

为了使粒子群优化(PSO)适于求解更多类问题,提出一种由动力空间和制导空间共同进化的改进粒子群优化算法-具有双重进化空间的扩展粒子群优化算法(简记EPSO).在EPSO中,在演化转换映射的作用下,首先将动力空间中对粒子辅助位置的进化转换为制导空间中对主导位置的进化,然后基于对主导位置的择优选择操作实现算法的进化过程.EPSO克服了PSO仅适于求解连续域最优化问题的缺陷,也非常适于求解离散组合优化问题.对于随机3-SAT问题、背包问题和TSP问题,通过与PSO、ACO和GA等算法的计算对比表明:EPSO是一种继承了PSO优点的高效、扩展演化算法.     

解0-1背包问题的二进制差异演化算法

针对传统差异演化算法(DE)无法求解采用二进制编码问题的缺点,通过采用新的变异方法,提出了一种用于求解0-1背包问题的二进制差异演化算法,阐明了该算法求解背包问题的具体实现过程.通过多个0-1背包问题的仿真试验,表明了该算法在求解0-1背包问题时不仅能达到最优解,而且收敛速度快,同时也验证了算法在解决二进制编码问题上的可行性和有效性.     

PSO算法在含一阶导数变分问题中的应用

变分问题是一个研究泛函极值的经典数学问题,寻求变分问题的直接解法具有重要的理论和现实意义.鉴于PSO算法在极值问题中的广泛应用,利用分段Hermite插值.建立了求解含一阶导数的变分问题优化模型,构造出了适应度函数,从而使得PSO算法成功应用到变分问题的求解当中.数值实验结果表明了方法的可行性,同时也拓展了PSO算法的应用领域.     

基于改进PSO算法的任务分配研究

为了解决虚拟企业中的任务分配问题,建立了任务分配的多目标决策优化模型。分析了传统的PSO算法,通过设置算法中速度惯性权重和加速度系数的自动调整,以及引入遗传算法中的变异操作,实现了对该算法的改进。基于改进的PSO算法求解任务分配模型,研究了求解问题与粒子的映射以及采用TOPSIS计算粒子位置适应度的方法,进而设计了一种基于改进PSO算法的任务分配算法。通过应用实例及仿真实验,证明了改进的PSO算法应用于任务分配的可行性和有效性。     

一种求解背包问题的改进遗传算法

背包问题是计算机算法研究中NP完备类的一个困难问题．使用传统的优化方法在求解较大规模的背包问题时．都存在计算量大、迭代时间长的缺陷。为了克服传统优化方法的不足,提高求解的速度和精度,将人类繁育方式引入遗传算法中,形成一种求解背包问题的改进遗传算法（IGA）。介绍算法的基本思想以及使用该算法求解背包问题的方法．并通过实例证明该方法的可行性和有效性。     

求解广义背包问题的贪心DS_BPSO算法

首先针对演化算法求解背包问题定义了贪心变换的概念,并给出了该变换的一种有效实现算法;然后将此算法与文献[5]中提出的具有双重结构编码的二进制粒子群优化算法(DS_BPSO)相结合,提出了一种解决广义背包问题GKP(General Knapsack Problem)的快速算法:基于贪心变换的DS_BPSO算法(GDS_BPSO).利用该算法求解文献[3,6]中的著名背包实例,给出了该背包实例的目前最好结果.此外,对于随机生成的大规模背包实例,通过与文献[3]中的HGA算法对比计算表明:GDS_BPSO算法是求解广义背包问题的一种高效方法.     

折扣{0-1}背包问题粒子群算法的贪婪修复策略探究

群智能启发式算法求解折扣{0-1}背包问题（D{0-1}KP）时,为提升求解效率和求解质量,需采用某种修复与优化策略将非正常编码个体转换为符合解约束条件的编码个体。在引入项集价值密度概念基础上,以粒子群算法（PSO）为例,提出一组基于项集的贪婪修复与优化方法（group greedy repair and optimization algorithm,GGROA）,并进一步构造PSO-GGRDKP算法（PSO based GGROA for solving D{0-1}KP）以探究GGROA方法的可行性和性能。PSO-NGROADKP（PSO based NGROA for solving D{0-1}KP）和PSO-GRDKP（PSO based GROA for solving D{0-1}KP）是基于项贪心修复与优化方法的粒子群算法。在D{0-1}KP标准数据集的实验结果表明：与PSO-NGROADKP和PSO-GRDKP相比,PSO-GGRDKP算法的解误差率略高,但算法时间性能分别提升了13.8%、12.9%。     

基于蚁群系统的多选择背包问题优化算法

提出了一种用蚁群系统求解多选择背包问题的优化算法。该方法利用蚂蚁算法所具有的正反馈特性，再结合变异参数，使算法既有较快的求解速度又有较高的求解精度。实验结果表明，采用此算法能快速有效地解决背包问题。     

微粒群算法求解背包问题综述

微粒群算法是一种群体智能优化算法,它具有个体数目少、计算简单、鲁棒性好等优点;其缺点是容易陷入局部极值点,进化后期收敛速度慢且精度较差。本文对微粒群算法的基本原理、参数设置及优化进行了介绍,并对0-1背包问题的模型及目前的解决方法进行了简介。     

微粒群算法求解背包问题综述

微粒群算法是一种群体智能优化算法,它具有个体数目少、计算简单、鲁棒性好等优点;其缺点是容易陷入局部极值点,进化后期收敛速度慢且精度较差.本文对微粒群算法的基本原理、参数设置及优化进行了介绍,并对0-1背包问题的模型及目前的解决方法进行了简介.     

基于群体智能的0/1背包问题求解研究进展

0/1背包问题是运筹学中一个经典组合优化NP问题。在简要介绍0/1背包问题基础上,分析展望了0/1背包问题的应用前景。结合已有研究成果,总结并详细分析了蚁群算法、微粒群算法等群体智能算法在0/1背包问题求解方面具有的较好收敛速度、健壮性、稳定性、算法简单等优点。最后,针对群体智能算法在求解0/1背包问题过程中所出现的缺陷,提出了群体智能算法在0/1背包问题求解需要进一步解决的几个问题。     

Essential Particle Swarm Optimization queen with Tabu Search for MKP resolution

The Particle Swarm Optimization (PSO) algorithm is an innovative and promising optimization technique in evolutionary computation. The Essential Particle Swarm Optimization queen (EPSOq) is one of the recent discrete PSO versions that further simplifies the PSO principles and improves its optimization ability. Hybridization is a principle of combining two (or more) approaches in a wise way such that the resulting algorithm includes the positive features of both (or all) the algorithms. This paper proposes a new heuristic approach such that various features inspired from the Tabu Search are incorporated in the EPSOq algorithm in order to obtain another improved discrete PSO version. The implementation of this idea is identified with the acronym TEPSOq (Tabu Essential Particle Swarm Optimization queen). Experimentally, this approach is able to solve optimally large-scale strongly correlated 0–1 Multidimensional Knapsack Problem (MKP) instances. Computational results show that TEPSOq has outperforms not only the EPSOq, but also other existing PSO-based approaches and some other meta-heuristics in solving the 0–1 MKP. It was discovered also that this algorithm is able to locate solutions extremely close and even equal to the best known results available in the literature.     

蚁群算法求解多维0／1背包问题

0／1背包问题是一类典型的组合优化问题，并且是NP-完全的问题，研究它具有很重要的意义。本文针对多维0／1背包问题的特点，设计了二进制编码的有向图，使得蚁群算法可以应用到背包问题上。仿真结果表明，该蚁群算法在求解多维0／1背包问题上的是相当出色的。     

Solving the Multidimensional Multiple-choice Knapsack Problem by constructing convex hulls

This paper presents a heuristic to solve the Multidimensional Multiple-choice Knapsack Problem (MMKP), a variant of the classical 0–1 Knapsack Problem. We apply a transformation technique to map the multidimensional resource consumption to single dimension. Convex hulls are constructed to reduce the search space to find the near-optimal solution of the MMKP. We present the computational complexity of solving the MMKP using this approach. A comparative analysis of different heuristics for solving the MMKP has been presented based on the experimental results.     

A cross entropy algorithm for the Knapsack problem with setups

In this article we propose a new metaheuristic-based algorithm for the Integer Knapsack Problem with Setups. This problem is a generalization of the standard Integer Knapsack Problem, complicated by the presence of setup costs in the objective function as well as in the constraints. We propose a cross entropy based algorithm, where the metaheuristic scheme allows to relax the original problem to a series of well chosen standard Knapsack problems, solved through a dynamic programming algorithm. To increase the computational effectiveness of the proposed algorithm, we use a turnpike theorem, which sensibly reduces the number of iterations of the dynamic algorithm. Finally, to testify the robustness of the proposed scheme, we present extensive computational results. First, we illustrate the step-by-step behavior of the algorithm on a smaller, yet difficult, problem. Subsequently, to test the solution quality of the algorithm, we compare the results obtained on very large scale instances with the output of a branch and bound scheme. We conclude that the proposed algorithm is effective in terms of solution quality as well as computational time.     

Approximation for knapsack problems with multiple constraints

1IntroductionTheknapsackproblemisawelLknowncombinatorialoptimizationproblemthatfindsapplicationstocapitalbudgeting,loadingproblems,solutionoflargeoptimizationproblems,andcomputersystems.Anextensiveliteratureexistsonapproximationalgorithmsforvariousformsofknapsackproblems['--'l.Inthispaper,westudytheapproximationforfourkindsofknapsackproblemswithmultipleconstraints:0/1MultipleConstraintKnapsackProblem(0/1MCKP),IntegerMultipleConstraintKnapsackProblem(IntegerMCKP),0/1k-ConstraintKnapsack…     

Generalized quadratic multiple knapsack problem and two solution approaches

The Quadratic Knapsack Problem (QKP) is one of the well-known combinatorial optimization problems. If more than one knapsack exists, then the problem is called a Quadratic Multiple Knapsack Problem (QMKP). Recently, knapsack problems with setups have been considered in the literature. In these studies, when an item is assigned to a knapsack, its setup cost for the class also has to be accounted for in the knapsack. In this study, the QMKP with setups is generalized taking into account the setup constraint, assignment conditions and the knapsack preferences of the items. The developed model is called Generalized Quadratic Multiple Knapsack Problem (G-QMKP). Since the G-QMKP is an NP-hard problem, two different meta-heuristic solution approaches are offered for solving the G-QMKP. The first is a genetic algorithm (GA), and the second is a hybrid solution approach which combines a feasible value based modified subgradient (F-MSG) algorithm and GA. The performances of the proposed solution approaches are shown by using randomly generated test instances. In addition, a case study is realized in a plastic injection molding manufacturing company. It is shown that the proposed hybrid solution approach can be successfully used for assigning jobs to machines in production with plastic injection, and good solutions can be obtained in a reasonable time for a large scale real-life problem.     

Dynamic programming algorithms for the Zero-One Knapsack Problem

New dynamic programming algorithms for the solution of the Zero-One Knapsack Problem are developed. Original recursive procedures for the computation of the Knapsack Function are presented and the utilization of bounds to eliminate states not leading to optimal solutions is analyzed. The proposed algorithms, according to the nature of the problem to be solved, automatically determine the most suitable procedure to be employed. Extensive computational results showing the efficiency of the new and the most commonly utilized algorithms are given. The results indicate that, for difficult problems, the algorithms proposed are superior to the best branch and bound and dynamic programming methods.