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1.
折扣{0-1}背包问题(D{0-1}KP)是0-1背包问题(0-1KP)的一种更复杂的扩展形式。为了利用离散差分演化高效求解D{0-1}KP,首先提出了一个新V型转换函数(NV),通过NV将个体的实向量映射为一个二进制向量,与已有的S型和V型转换函数相比,NV计算复杂度更低,求解效率更高。然后,基于新V型转换函数给出了一种新的离散差分演化算法(NDDE),并利用NDDE提出了求解D{0-1}KP的一个新的高效方法。最后,为了验证NDDE求解D{0-1}KP的性能,利用它求解四类大规模D{0-1}KP实例,并与基于群论的优化算法(GTOA)、基于环理论的演化算法(RTEA)、混合教学优化算法(HTLBO)和鲸鱼优化算法(WOA)等已有算法的最好计算结果进行比较,比较结果表明,NDDE不仅求解精度更高,而且算法的稳定性佳,非常适于求解大规模D{0-1}KP实例。  相似文献   

2.
求解背包问题的贪心遗传算法及其应用   总被引:12,自引:0,他引:12  
分析了文献[2]中求解背包问题(KP)的混合遗传算法(HGA)所采用的贪心变换方法缺陷;重新定义了贪心变换的概念,并给出了一种新的且更高效的贪心变换方法,将此方法与遗传算法相结合得到一种新的混合遗传算法,称之贪心遗传算法(简记GGA).利用GGA得出了文献[2,4]中一个著名KP问题实例的目前最好结果;同时,对于文献[7]中的KP问题实例和一个随机生成的KP问题实例,将GGA算法与求解KP问题的最有效算法HGA算法进行对比计算,结果表明GGA算法远远优于HGA算法.  相似文献   

3.
一种求解背包问题的混合遗传微粒群算法   总被引:1,自引:0,他引:1  
背包问题是计算科学理论中一个著名的NP-hard问题,也是典型的组合优化问题,在物流系统的库存分配和货物装载等方面都有非常重要的应用.采用借鉴遗传算法的编码、交叉和变异的遗传微粒群算法对背包问题进行求解.为了增强遗传微粒群算法的搜索性能,将基于自学习规则的启发式算法与遗传微粒群算法相结合得到混合遗传算法用于求解背包问题.对多个标准测试实例的仿真计算表明,该算法能有效求解KP问题.  相似文献   

4.
针对折扣{0-1}背包问题(D{0-1}KP),当问题规模较大时,精确算法求解比较困难。基于此,将贪心核加速算子与猴群算法融合提出一种混合猴群算法(MMA)用于求解D{0-1}KP问题。同时在MMA算法的爬过程中引入诱导因子,避免爬过程陷入局部最优,再利用修复策略对不可行解进行修复。通过仿真实验,结果表明MMA算法求解大规模D{0-1}KP问题的计算性能有效,求解结果可行。  相似文献   

5.
随机时变背包问题(RTVKP)是一种新的动态背包问题,也是一种新的动态组合优化问题,目前它的求解算法主要是动态规划的精确算法、近似算法和遗传算法.本文首先利用动态规划提出了一个求解RTVKP问题的新精确算法,对算法时间复杂度的比较结果表明:它比已有的精确算法更适于求解背包载重较大的一类RTVKP实例.然后,分别基于差分演化和粒子群优化与贪心修正策略相结合,提出了求解RTVKP问题的两个进化算法.对5个RTVKP实例的数值计算结果比较表明: 精确算法一般不宜求解大规模的RTVKP实例,而基于差分演化、粒子群优化和遗传算法与贪心修正策略相结合的进化算法却不受实例规模与数据大小的影响,对于振荡频率大且具有较大数据的大规模RTVKP实例均能求得的一个极好的近似解.  相似文献   

6.
为利用混合蛙跳算法(SFLA)求解具有二进制编码特点的组合优化问题,基于双重编码机制,提出了一种二进制混合蛙跳算法(记为BSFLA)。基于罚函数法和贪心变换策略,探讨了利用BSFLA求解背包问题(KP)的可行性与有效性。计算结果表明BSFLA与贪心策略相结合是求解KP问题的一种有效的新方法。  相似文献   

7.
为了利用演化算法求解离散域上的组合优化问题,借鉴遗传算法(GA)、二进制粒子群优化(BPSO)和二进制差分演化(HBDE)中的映射方法,提出了一种基于映射变换思想设计离散演化算法的实用方法——编码转换法(ETM),并利用一个简单有效的编码转化函数给出了求解组合优化问题的离散演化算法一般算法框架A-DisEA.为了说明ETM的实用性与有效性,首先基于A-DisEA给出了一个离散粒子群优化算法(DisPSO),然后分别利用BPSO、HBDE和DisPSO等求解集合联盟背包问题和折扣{0-1}背包问题,通过对计算结果的比较表明:BPSO、HBDE和DisPSO的求解性能均优于GA,这不仅说明基于ETM的离散演化算法在求解KP问题方面具有良好的性能,同时也说明利用ETM方法设计离散演化算法是一种简单且有效的实用方法.  相似文献   

8.
为了利用多宇宙算法(MVO)求解折扣{0-1}背包问题(D{0-1}KP),基于模运算建立了离散型隧道模型和离散虫洞模型,引入具有反向搜索与突变特性的局部搜索策略,提出了第一个具有四进制编码的离散混合多宇宙算法DHMVO。在利用修复与优化算法消除不可行解的基础上,基于DHMVO提出了求解D{0-1}KP的一个新方法。为了检验DHMVO求解D{0-1}KP的性能,利用Kruskal-walli检验确定了其参数的最佳取值;将DHMVO求解四类大规模D{0-1}KP实例的计算结果与已有最好算法的计算结果进行比较,比较结果表明:DHMVO比其他算法的求解精度更高、稳定性更强,非常适合高效求解大规模D{0-1}KP实例。  相似文献   

9.
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.  相似文献   

10.
GA是一类基于自然选择和遗传学原理的有效搜索方法,它从一个种群开始,利用选择、交叉、变异等遗传算子对种群进行不断进化,最后得到全局最优解.但随着求解问题的复杂性及难度的增加,提高GA的运行速度便显得尤为突出,采用并行遗传算法(PGA)是提高搜索效率的方法之一.本文分析了并行遗传算法的四种模型,最后应用于0-1背包问题的求解.实验结果表明,该算法在具有较高搜索效率的同时,仍能维持很高的种群多样性.  相似文献   

11.
We formulate the time-constrained backpacker problem as an extension of the classical knapsack problem (KP), where a ‘backpacker’ travels from a origin to a destination on a directed acyclic graph, and collects items en route within the capacity of his knapsack and within a fixed time limit. We present a dynamic programming (DP) algorithm to solve this problem to optimality, and a ‘shift-and-merge’ DP algorithm to solve larger instances. The latter is an extension of the list-type DP, which has been successful for one-dimensional KPs, to the two-dimensional case. Computational experiments on a series of instances demonstrate advantage of the shift-and-merge technique over commercial MIP solvers.  相似文献   

12.
The 0–1 knapsack problem (KP) is a well-known intractable optimization problem with wide range of applications. Harmony Search (HS) is one of the most popular metaheuristic algorithms to successfully solve 0–1 KPs. Nevertheless, metaheuristic algorithms are generally compute intensive and slow when implemented in software. In this paper, we present an FPGA-based pipelined hardware accelerator to reduce computation time for solving large dimension 0–1 KPs using Binary Harmony Search algorithm. The proposed architecture exploits the intrinsic parallelism of population based metaheuristic algorithm and the flexibility and parallel processing capabilities of FPGAs to perform the computation concurrently thus enhancing performance. To validate the efficiency of the proposed hardware accelerator, experiments were conducted using a large number of 0–1 KPs. Comparative analysis on experimental results reveals that the proposed approach offers promising speedups of 51× – 111× as compared with a software implementation and 2× – 5× as compared with a hardware implementation of Binary Particle Swarm Optimization algorithm.  相似文献   

13.
This study proposes a fuzzy approach for solving the multiobjective and multilevel knapsack problems (KPs). The problem was first formulated as a multilevel programming problem with multiple decision makers (DMs). Then the degree of satisfaction of each DM was established and represented by their individual membership functions. The recursive formulation of dynamic programming was used to solve the decisions of the interrelated stages. The overall satisfaction of the decision was obtained through this stage-wise operation on the hierarchical structure. Capacity allocation was developed and a step-by-step solution procedure was illustrated. A detailed comparison between multiobjective and multilevel KPs was also carried out. Finally, the possible use of turnpike theorem in KPs was scrutinized in the fuzzy domain.  相似文献   

14.
We introduce a kernel learning algorithm, called kernel propagation (KP), to learn a nonparametric kernel from a mixture of a few pairwise constraints and plentiful unlabeled samples. Specifically, KP consists of two stages: the first is to learn a small-sized sub-kernel matrix just restricted to the samples with constrains, and the second is to propagate this learned sub-kernel matrix into a large-sized full-kernel matrix over all samples. As an interesting fact, our approach exposes a natural connection between KP and label propagation (LP), that is, one LP can naturally induce its KP counterpart. Thus, we develop three KPs from the three typical LPs correspondingly. Following the idea in KP, we also naturally develop an out-of-sample extension to directly capture a kernel matrix for outside-training data without the need of relearning. The final experiments verify that our developments are more efficient, more error-tolerant and also comparably effective in comparison with the state-of-the-art algorithm.  相似文献   

15.
用演化算法求解抛物型方程扩散系数的识别问题   总被引:4,自引:1,他引:3  
基于演化算法给出了一类求解参数识别反问题的一般方法,该方法表明只要找到好的、求解相应的正问题的数值方法,演化算法就可以用于求解此类反问题。设计有效的求解反问题的演化算法的关键是寻找一种适合反问题的解空间的编码表示形式、适当的适应值函数形式以及有效的计算正问题的数值方法。该文结合算法、传统的求解反问题的工方法和正则化技术,设计了一类求解参数识别反问题的方法。为验证此类方法,将其用于求解一维扩散方程的  相似文献   

16.
针对确定性算法难于求解的各项的重量系数和价值系数在大范围内取值的折扣{0-1}背包问题(D{0-1}KP),提出了基于差分演化策略的混沌乌鸦算法(DECCSA)。首先,采用混沌映射生成初始乌鸦种群;然后,采用混合编码方式和贪心修复与优化策略(GROS)解决了D{0-1}KP的编码问题;最后,引入差分演化策略提高算法的收敛速度。对4类大规模D{0-1}KP实例的计算结果表明:DECCSA比遗传算法、细菌觅食算法和变异蝙蝠算法求得的最好值和平均值更优,能得到最优解或更好的近似解,非常适于求解D{0-1}KP。  相似文献   

17.
Nonlinear equations systems (NESs) are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots. Evolutionary algorithms (EAs) are one of the methods for solving NESs, given their global search capabilities and ability to locate multiple roots of a NES simultaneously within one run. Currently, the majority of research on using EAs to solve NESs focuses on transformation techniques and improving the performance of the used EAs. By contrast, problem domain knowledge of NESs is investigated in this study, where we propose the incorporation of a variable reduction strategy (VRS) into EAs to solve NESs. The VRS makes full use of the systems of expressing a NES and uses some variables (i.e., core variable) to represent other variables (i.e., reduced variables) through variable relationships that exist in the equation systems. It enables the reduction of partial variables and equations and shrinks the decision space, thereby reducing the complexity of the problem and improving the search efficiency of the EAs. To test the effectiveness of VRS in dealing with NESs, this paper mainly integrates the VRS into two existing state-of-the-art EA methods (i.e., MONES and DR-JADE) according to the integration framework of the VRS and EA, respectively. Experimental results show that, with the assistance of the VRS, the EA methods can produce better results than the original methods and other compared methods. Furthermore, extensive experiments regarding the influence of different reduction schemes and EAs substantiate that a better EA for solving a NES with more reduced variables tends to provide better performance.   相似文献   

18.
当前折扣{0-1}背包问题(D{0-1}KP)模型将折扣关系作为一个新的个体,导致求解过程必需采取修复法对个体编码进行修复,求解方式较少。针对求解方法单一的问题,通过改变模型中二进制的编码表达方式,提出折扣关系不在个体编码中的表达方法。首先,设定对任意折扣关系,当且仅当所涉及个体编码值同时为1(即其乘积为1)时,折扣关系成立,据此建立简化折扣{0-1}背包问题(SD{0-1}KP)模型;然后,针对SD{0-1}KP模型,基于杰出者保留策略(EGA),结合贪心策略(GRE),提出改进遗传算法——第一遗传算法(FG);最后,再结合罚函数法,提出求解SD{0-1}KP高精度罚函数法——第二遗传算法(SG)。结果表明,SD{0-1}KP能够完全覆盖D{0-1}KP问题领域,与FirEGA相比,所提出的两类算法在求解速度方面优势明显,且SG算法首次引入罚函数法,有效地丰富了该问题的求解算法。  相似文献   

19.
In this paper, we propose a new view for designing an evolutionary algorithm by using algebraic theory to solve the combinatorial optimization problem. Using the addition, multiplication and inverse operation of the direct product of rings, we first propose two evolution operators: the global exploration operator (R-GEO) and the local development operator (R-LDO). Then, by utilizing the R-GEO and R-LDO to generate individuals and applying the greedy selection strategy to generate a new population, we propose a new algorithm – the Ring Theory-Based Evolutionary Algorithm (RTEA) – for the combinatorial optimization problem. Moreover, we give a new method for solving the discounted {0-1} knapsack problem (D{0–} KP) by using the RTEA. To verify the performance of the RTEA, we use it and existing algorithms to solve four kinds of large-scale instances of the D{0-1} KP. The computational results show that the RTEA performs better than the others, and it is more suitable for solving the D{0-1} KP problem. Moreover, it indicates that using algebraic theory to design evolutionary algorithms is feasible and effective.  相似文献   

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