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A Branch-and-Bound Based Heuristic Algorithm for Minimizing Makespan in Machining-Assembly Flowshop Scheduling 被引量:1
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作者 Kazuko Morizawa 《Engineering(科研)》 2014年第13期877-885,共9页
This paper proposes a heuristic algorithm, called list-based squeezing branch and bound algorithm, for solving a machine-fixed, machining-assembly flowshop scheduling problem to minimize makespan. The machine-fixed, m... This paper proposes a heuristic algorithm, called list-based squeezing branch and bound algorithm, for solving a machine-fixed, machining-assembly flowshop scheduling problem to minimize makespan. The machine-fixed, machining-assembly flowshop consists of some parallel two-machine flow lines at a machining stage and one robot at an assembly stage. Since an optimal schedule for this problem is not always a permutation schedule, the proposed algorithm first finds a promising permutation schedule, and then searches better non-permutation schedules near the promising permutation schedule in an enumerative manner by elaborating a branching procedure in a branch and bound algorithm. The results of numerical experiments show that the proposed algorithm can efficiently provide an optimal or a near-optimal schedule with high accuracy such as mean relative error being less than 0.2% and the maximum relative error being at most 3%. 展开更多
关键词 Scheduling HEURISTIC branch and bound algorithm Machining-Assembly FLOWSHOP MAKESPAN
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Lower Bounds and a Nearly Fastest General Parallel Branch-and-Bound Algorithm 被引量:2
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作者 Wu, Jigang Xie, Xing +1 位作者 Wan, Yingyu Chen, Guoliang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2000年第3期65-73,共9页
In this paper, it is supposed that the B&B algorithm finds the first optimal solution after h nodes have been expanded and m active nodes have been created in the state-space tree. Then the lower bound Ω(m+h log ... In this paper, it is supposed that the B&B algorithm finds the first optimal solution after h nodes have been expanded and m active nodes have been created in the state-space tree. Then the lower bound Ω(m+h log h) of the running time for the general sequential B&B algorithm and the lower bound Ω(m/p+h log p) for the general parallel best-first B&B algorithm in PRAM-CREW are proposed, where p is the number of processors available. Moreover, the lower bound Ω(M/p+H+(H/p) log (H/p)) is presented for the parallel algorithms on distributed memory system, where M and H represent total number of the active nodes and that of the expanded nodes processed by p processors, respectively. In addition, a nearly fastest general parallel best-first B&B algorithm is put forward. The parallel algorithm is the fastest one as p = max{hε, r}, where ε = 1/ rootlogh, and r is the largest branch number of the nodes in the state-space tree. 展开更多
关键词 branch-AND-bound State-space tree Active list Parallel algorithm Combinatorial search.
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Relaxation-strategy-based Modification Branch-and-Bound Algorithm for Solving a Class of Transportation-production Problems
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作者 DU Ting-song FEI Pu-sheng JIAN Ji-gui 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第1期52-59,共8页
In this paper,a new algorithm relaxation-strategy-based modification branchand-bound algorithm is developed for a type of solving the minimum cost transportationproduction problem with concave production costs.The maj... In this paper,a new algorithm relaxation-strategy-based modification branchand-bound algorithm is developed for a type of solving the minimum cost transportationproduction problem with concave production costs.The major improvement of the proposed new method is that modification algorithm reinforces the bounding operation using a Lagrangian relaxation,which is a concave minimization but obtains a tighter bound than the usual linear programming relaxation.Some computational results are included.Computation results indicate that the algorithm can solve fairly large scale problems. 展开更多
关键词 branch-and-bound algorithm transportation-production problem Lagrangian relaxation
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On the “Onion Husk” Algorithm for Approximate Solution of the Traveling Salesman Problem
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作者 Mikhail E. Abramyan Nikolai I. Krainiukov Boris F. Melnikov 《Journal of Applied Mathematics and Physics》 2024年第4期1557-1570,共14页
The paper describes some implementation aspects of an algorithm for approximate solution of the traveling salesman problem based on the construction of convex closed contours on the initial set of points (“cities”) ... The paper describes some implementation aspects of an algorithm for approximate solution of the traveling salesman problem based on the construction of convex closed contours on the initial set of points (“cities”) and their subsequent combination into a closed path (the so-called contour algorithm or “onion husk” algorithm). A number of heuristics related to the different stages of the algorithm are considered, and various variants of the algorithm based on these heuristics are analyzed. Sets of randomly generated points of different sizes (from 4 to 90 and from 500 to 10,000) were used to test the algorithms. The numerical results obtained are compared with the results of two well-known combinatorial optimization algorithms, namely the algorithm based on the branch and bound method and the simulated annealing algorithm. . 展开更多
关键词 branch and bound Method Contour algorithm “Onion Husk” algorithm Simulated Annealing Method Traveling Salesman Problem
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Algorithms for Multicriteria Scheduling Problems to Minimize Maximum Late Work, Tardy, and Early
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作者 Karrar Alshaikhli Aws Alshaikhli 《Journal of Applied Mathematics and Physics》 2024年第2期661-682,共22页
This study examines the multicriteria scheduling problem on a single machine to minimize three criteria: the maximum cost function, denoted by maximum late work (V<sub>max</sub>), maximum tardy job, denote... This study examines the multicriteria scheduling problem on a single machine to minimize three criteria: the maximum cost function, denoted by maximum late work (V<sub>max</sub>), maximum tardy job, denoted by (T<sub>max</sub>), and maximum earliness (E<sub>max</sub>). We propose several algorithms based on types of objectives function to be optimized when dealing with simultaneous minimization problems with and without weight and hierarchical minimization problems. The proposed Algorithm (3) is to find the set of efficient solutions for 1//F (V<sub>max</sub>, T<sub>max</sub>, E<sub>max</sub>) and 1//(V<sub>max</sub> + T<sub>max</sub> + E<sub>max</sub>). The Local Search Heuristic Methods (Descent Method (DM), Simulated Annealing (SA), Genetic Algorithm (GA), and the Tree Type Heuristics Method (TTHM) are applied to solve all suggested problems. Finally, the experimental results of Algorithm (3) are compared with the results of the Branch and Bound (BAB) method for optimal and Pareto optimal solutions for smaller instance sizes and compared to the Local Search Heuristic Methods for large instance sizes. These results ensure the efficiency of Algorithm (3) in a reasonable time. 展开更多
关键词 Scheduling Single Machine Hierarchical Simultaneous Minimization algorithmS branch and bound Local Search Heuristic Methods
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基于Branch & Bound方法MIQP问题的求解及应用 被引量:6
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作者 张聚 李平 王万良 《系统仿真学报》 CAS CSCD 2003年第4期488-491,共4页
研究基于 Branch & Bound (B&B) 方法的混合整数二次规划(Mixed Integer Quadratic Programming, MIQP)问题的求解,以及在一类混杂系统优化控制中的应用。B & B算法求解MIQP问题的过程,可视为对于一个二叉树的搜索。影响B &... 研究基于 Branch & Bound (B&B) 方法的混合整数二次规划(Mixed Integer Quadratic Programming, MIQP)问题的求解,以及在一类混杂系统优化控制中的应用。B & B算法求解MIQP问题的过程,可视为对于一个二叉树的搜索。影响B & B算法寻优效率的两个主要方面是:分支变量的选择规则,以及树搜索策略。通过设定控制变量QPmax, 用以限制寻优过程求解QP问题的最大数目,可以在较短的时间内获得MIQP问题的满足整数约束条件次优解。利用MATLAB编制MIQP问题的求解程序,并在混杂系统优化控制中的应用,做了仿真计算。 展开更多
关键词 混合整数二次规划 MIQP问题 branch&bound方法 二叉树
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Job-shop问题的Branch-bound方法
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作者 傅少川 曹建胜 张福祥 《山东工业大学学报》 1996年第A09期396-399,共4页
本文给出了Job-shop问题的一种Branch-bound方法。
关键词 分枝定界算法 关键路法 JOB-SHOP问题
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基于BB-递归核函数SVR算法的U型折弯件模型参数优化研究
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作者 徐承亮 胡梓枫 +1 位作者 曹志勇 张详林 《湖北大学学报(自然科学版)》 CAS 2024年第1期115-121,共7页
影响U型折弯件回弹的因素众多,工件尺寸、力学性能、负载条件、材料各向异性等相互耦合,表现出高度复杂的非线性,从而导致回弹预测结果的不确定性。本研究以板料折弯件回弹后的张开角(α)为目标函数,构建一个递归核函数支持向量回归(SVR... 影响U型折弯件回弹的因素众多,工件尺寸、力学性能、负载条件、材料各向异性等相互耦合,表现出高度复杂的非线性,从而导致回弹预测结果的不确定性。本研究以板料折弯件回弹后的张开角(α)为目标函数,构建一个递归核函数支持向量回归(SVR)模型,并部署到分支界限法(BB)中,从而筛选出维度为4的最优的特征变量参数子集,其决定系数(R^(2))为0.982147,均方误差(MSE)为0.00433,模型预测精度相对较高。算法优化得到的折弯件参数为:厚度(t)为12 mm,上模宽度(d)为90 mm,上模圆角半径(r)为9 mm,载荷速度(v)为10 mm/s。BB递归核函数SVR算法、有限元模拟和实际测量的α分别为16.3°、17.5°和18.2°,尽管有限元结果更接近于实际值,但是BB递归核函数SVR算法可以为有限元模拟提供筛选出的参数(t,d,r,v)的数据,以快速进行模拟并预测张开角α,并实现回弹补偿装置的高效设计。 展开更多
关键词 U型折弯件 支持向量机 分支界限法 SVR算法
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一类加工需要额外资源的平行机调度问题的算法设计
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作者 江明月 简苏平 +2 位作者 崔晓龙 万龙 董建明 《浙江大学学报(理学版)》 CAS CSCD 北大核心 2024年第3期321-327,335,共8页
给出了一类加工需要额外资源的平行机调度问题的精确算法。针对在平行机上加工的工件,除需要机器资源外,还需要一个单位额外资源的问题,考虑额外资源的种类和数量有限,以给出问题的最优调度使工件的完工时间最小为目标。该问题源于地球... 给出了一类加工需要额外资源的平行机调度问题的精确算法。针对在平行机上加工的工件,除需要机器资源外,还需要一个单位额外资源的问题,考虑额外资源的种类和数量有限,以给出问题的最优调度使工件的完工时间最小为目标。该问题源于地球观测卫星的数据下载,在智能制造和信息处理等领域亦有广泛应用。给出了该问题的整数规划模型、最优解下界和分支定界算法;给出了一种有效的分支策略以避免重复分支,设计了相应的定界方法以提高算法的收敛速度。通过小规模实例和大量的数值仿真实验,验证了算法的正确性和在不同参数配置下的有效性。 展开更多
关键词 平行机调度问题 额外资源 整数规划模型 分支定界算法
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基于图卷积和注意力神经网络的旅行商问题新解法
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作者 韦念念 韩曙光 《计算机科学》 CSCD 北大核心 2024年第S01期210-217,共8页
旅行商问题是一个经典的组合优化问题。为快速求解旅行商问题,设计了由图嵌入网络、图卷积神经网络、注意力神经网络和多层感知机组合而成的深度学习模型的学习分支规则,通过改进传统的分支定界算法提高算法性能。对15个城市的旅行商问... 旅行商问题是一个经典的组合优化问题。为快速求解旅行商问题,设计了由图嵌入网络、图卷积神经网络、注意力神经网络和多层感知机组合而成的深度学习模型的学习分支规则,通过改进传统的分支定界算法提高算法性能。对15个城市的旅行商问题实例进行监督训练,并在SCIP求解器上分别测试10,15,20,25和30个城市的旅行商问题实例。发现:基于学习分支规则的分支定界算法的求解时间比基于传统分支规则的分支定界算法的求解时间分别快-0.0022 s,0.0178 s,1.7643 s,2.3074 s和2.0538 s。因此,基于图神经网络的分支变量选择对传统分支规则的改进是有效的,可以较好地泛化到训练规模更大的旅行商问题实例中。 展开更多
关键词 旅行商问题 图卷积神经网络 注意力网络 分支定界算法 监督学习
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基于最小权覆盖的医药电商配送中心选址及区域覆盖优化研究
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作者 李建红 丁秀好 +1 位作者 雷鸣颢 罗晓萌 《运筹与管理》 CSCD 北大核心 2024年第4期7-13,共7页
配送中心选址及区域划分是物流配送过程中的关键环节,直接决定了配送时效及配送成本,在当今电子商务领域显得尤为重要。本文针对国内医药电商企业,提出了一种考虑药品配送时效的配送中心选址策略;随后建立该问题的整数规划模型,采用最... 配送中心选址及区域划分是物流配送过程中的关键环节,直接决定了配送时效及配送成本,在当今电子商务领域显得尤为重要。本文针对国内医药电商企业,提出了一种考虑药品配送时效的配送中心选址策略;随后建立该问题的整数规划模型,采用最小权顶点覆盖方法描述问题,并通过优先队列分支限界算法对此模型进行求解,得出最优选址结果;最后按最小运费原则将被重复覆盖区域进行再划分,得到配送中心选址及区域划分最终方案。本文基于上述策略为国内某头部医药电商企业提供了两种选址方案:保留企业原有配送中心并确定新配送中心选址点(改进选址方案)和从企业所有需求节点中重新为配送中心选址(重选址方案),并使用企业真实销量和物流数据进行算例分析。 展开更多
关键词 配送中心选址 区域划分 最小权顶点覆盖 优先队列分支限界算法
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Discrete differential evolution algorithm for integer linear bilevel programming problems 被引量:1
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作者 Hong Li Li Zhang Yongchang Jiao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2016年第4期912-919,共8页
A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forc... A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods. 展开更多
关键词 discrete linear bilevel programming problem discrete differential evolution constraint handling method branch and bound algorithm
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Weekly Fleet Assignment Model and Algorithm 被引量:1
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作者 朱星辉 朱金福 巩在武 《Journal of Southwest Jiaotong University(English Edition)》 2007年第3期231-235,共5页
A 0-1 integer programming model for weekly fleet assignment was put forward based on linear network and weekly flight scheduling in China. In this model, the objective function is to maximize the total profit of fleet... A 0-1 integer programming model for weekly fleet assignment was put forward based on linear network and weekly flight scheduling in China. In this model, the objective function is to maximize the total profit of fleet assignment, subject to the constraints of coverage, aircraft flow balance, fleet size, aircraft availability, aircraft usage, flight restriction, aircraft seat capacity, and stopover. Then the branch-and-bound algorithm based on special ordered set was applied to solve the model. At last, a real- wofld case study on an airline with 5 fleets, 48 aircrafts and 1 786 flight legs indicated that the profit increase was ¥ 1 591276 one week and the running time was no more than 4 rain, which shows that the model and algorithm are fairly good for domestic airline. 展开更多
关键词 Flight scheduling Fleet assignment problem 0-1 Integer programming model branch-and-bound algorithm
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Algorithmic Optimization of BDDs and Performance Evaluation for Multi-level Logic Circuits with Area and Power Trade-offs 被引量:2
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作者 Saurabh Chaudhury Anirban Dutta 《Circuits and Systems》 2011年第3期217-224,共8页
Binary Decision Diagrams (BDDs) can be graphically manipulated to reduce the number of nodes and hence the area. In this context, ordering of BDDs play a major role. Most of the algorithms for input variable ordering ... Binary Decision Diagrams (BDDs) can be graphically manipulated to reduce the number of nodes and hence the area. In this context, ordering of BDDs play a major role. Most of the algorithms for input variable ordering of OBDD focus primarily on area minimization. However, suitable input variable ordering helps in minimizing the power consumption also. In this particular work, we have proposed two algorithms namely, a genetic algorithm based technique and a branch and bound algorithm to find an optimal input variable order. Of course, the node reordering is taken care of by the standard BDD package buddy-2.4. Moreover, we have evaluated the performances of the proposed algorithms by running an exhaustive search program. Experi-mental results show a substantial saving in area and power. We have also compared our techniques with other state-of-art techniques of variable ordering for OBDDs and found to give superior results. 展开更多
关键词 algorithmic OPTIMIZATION BDDS Genetic algorithm branch & bound Variable ORDERING Area-Power Trade-offs
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AN INTERVAL ALGORITHM FOR CONSTRAINED GLOBAL OPTIMIZATION
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作者 张连生 朱文兴 田蔚文 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1995年第1期63-74,共12页
In order to solve the constrained global optimization problem,we use penalty functions not only on constraints but also on objective function. Then within the framework of interval analysis,an interval Branch-and-Boun... In order to solve the constrained global optimization problem,we use penalty functions not only on constraints but also on objective function. Then within the framework of interval analysis,an interval Branch-and-Bound algorithm is given,which does not need to solve a sequence of unconstrained problems. Global convergence is proved. Numerical examples show that this algorithm is efficient. 展开更多
关键词 CONSTRAINED golbal optimization INTERVAL analysis penally FUNCTION branch -and-bound algorithm.
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基于规则集定向搜索算法的装船翻箱问题 被引量:2
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作者 杨小明 周云鹏 +1 位作者 耿志康 徐子奇 《计算机集成制造系统》 EI CSCD 北大核心 2023年第3期1040-1054,共15页
集装箱码头的自动化与智能化是港口物流发展新趋势,其中箱区自动化与智能化是其中的重点。自动化集装箱码头纵向大箱区布局模式使其翻箱问题成为制约码头效率提升的一个重要因素。针对自动化码头大箱区的贝内装船翻箱问题,提出基于规则... 集装箱码头的自动化与智能化是港口物流发展新趋势,其中箱区自动化与智能化是其中的重点。自动化集装箱码头纵向大箱区布局模式使其翻箱问题成为制约码头效率提升的一个重要因素。针对自动化码头大箱区的贝内装船翻箱问题,提出基于规则集快速求解方法,并基于该方法构建相应的分支定界算法和定向搜索算法,同时分析了3种算法的时间复杂度。分支定界算法可求得该问题理论最优解,定向搜索算法能在短时内获得接近理论最优解。算例分析表明,基于规则集定向搜索算法和分支定界算法在小规模算例中都能高效求解该问题。在大规模算例中,基于规则集定向搜索算法仍然具有很高计算效率,同时优化结果接近理论最优解。通过与现有文献的数据对比分析,表明本文提出的基于规则集定向搜索算法在求解集装箱装船翻箱问题时具有更好的优化效果和更高的计算效率。 展开更多
关键词 装船翻箱问题 定向搜索算法 分支定界算法 自动化集装箱码头
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An Algorithm for Global Optimization Using Formula Manupulation
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作者 Tsutomu Shohdohji Fumihiko Yano 《Applied Mathematics》 2012年第11期1601-1606,共6页
Constrained nonlinear optimization problems are well known as very difficult problems. In this paper, we present a new algorithm for solving such problems. Our proposed algorithm combines the Branch-and-Bound algorith... Constrained nonlinear optimization problems are well known as very difficult problems. In this paper, we present a new algorithm for solving such problems. Our proposed algorithm combines the Branch-and-Bound algorithm and Lipschitz constant to limit the search area effectively;this is essential for solving constrained nonlinear optimization problems. We obtain a more appropriate Lipschitz constant by applying the formula manipulation system of each divided area. Therefore, we obtain a better approximate solution without using a lot of searching points. The efficiency of our proposed algorithm has been shown by the results of some numerical experiments. 展开更多
关键词 Global Optimization LIPSCHITZ CONSTANT LIPSCHITZ Condition branch-AND-bound algorithm FORMULA MANIPULATION
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Safe Bounds in Semidefinite Programming by Using Interval Arithmetic
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作者 Orkia Derkaoui Ahmed Lehireche 《American Journal of Operations Research》 2014年第5期293-300,共8页
Efficient solvers for optimization problems are based on linear and semidefinite relaxations that use floating point arithmetic. However, due to the rounding errors, relaxation thus may overestimate, or worst, underes... Efficient solvers for optimization problems are based on linear and semidefinite relaxations that use floating point arithmetic. However, due to the rounding errors, relaxation thus may overestimate, or worst, underestimate the very global optima. The purpose of this article is to introduce an efficient and safe procedure to rigorously bound the global optima of semidefinite program. This work shows how, using interval arithmetic, rigorous error bounds for the optimal value can be computed by carefully post processing the output of a semidefinite programming solver. A lower bound is computed on a semidefinite relaxation of the constraint system and the objective function. Numerical results are presented using the SDPA (SemiDefinite Programming Algorithm), solver to compute the solution of semidefinite programs. This rigorous bound is injected in a branch and bound algorithm to solve the optimisation problem. 展开更多
关键词 SEMIDEFINITE Programming INTERVAL ARITHMETIC Rigorous Error boundS SDPA SOLVER branch and bound algorithm
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Combined Algorithms of Optimal Resource Allocation
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作者 Valery I. Struchenkov 《Applied Mathematics》 2012年第1期78-85,共8页
Under study is the problem of optimum allocation of a resource. The following is proposed: the algorithm of dynamic programming in which on each step we only use the set of Pareto-optimal points, from which unpromisin... Under study is the problem of optimum allocation of a resource. The following is proposed: the algorithm of dynamic programming in which on each step we only use the set of Pareto-optimal points, from which unpromising points are in addition excluded. For this purpose, initial approximations and bilateral prognostic evaluations of optimum are used. These evaluations are obtained by the method of branch and bound. A new algorithm “descent-ascent” is proposed to find upper and lower limits of the optimum. It repeatedly allows to increase the efficiency of the algorithm in the comparison with the well known methods. The results of calculations are included. 展开更多
关键词 Dynamic PROGRAMMING The PARETO Set branch and bound Method The CURSE of Dimensionality algorithm “Descent-Ascent”
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基于分布式分支界限算法的产消者联盟电能交易策略 被引量:3
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作者 杨国桢 李晓露 +1 位作者 柳劲松 林顺富 《智慧电力》 北大核心 2023年第3期9-16,共8页
随着分布式能源在配电网中的高比例渗透,产消者作为新型主体参与市场竞争日益受到关注。基于合作博弈的产消者联盟电能交易可增加产消者的整体收益,产消者采用动态联盟结构可提升对环境变化的适应协调能力。为此,提出基于多代理系统(MAS... 随着分布式能源在配电网中的高比例渗透,产消者作为新型主体参与市场竞争日益受到关注。基于合作博弈的产消者联盟电能交易可增加产消者的整体收益,产消者采用动态联盟结构可提升对环境变化的适应协调能力。为此,提出基于多代理系统(MAS)的产消者联盟运行框架,以及在此框架下产消者联盟电能交易的双层优化模型。上层模型使用分布式分支界限算法求解最优联盟结构下的产消者电能交易策略;下层模型根据更新的交易电价调整产消者购售电计划。最后通过仿真算例验证了所提方法的合理性、有效性及模型的可扩展性。 展开更多
关键词 产消者 合作博弈 动态联盟结构 分布式分支界限算法 多代理系统
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