求解约束优化问题的退火遗传算法

针对基于罚函数遗传算法求解实际约束优化问题的困难与缺点,提出了求解约束优化问题的退火遗传算法。对种群中的个体定义了不可行度,并设计退火遗传选择操作。算法分三阶段进行,首先用退火算法搜索产生初始种群体,随后利用遗传算法使搜索逐渐收敛于可行的全局最优解或较优解,最后用退火优化算法对解进行局部优化。两个典型的仿真例子计算结果证明该算法能极大地提高计算稳定性和精度。     

优化的板材排料问题算法分析

研究了板材排料的问题，提出了一种板材排料问题的新方法，并在此基础上建立了实现该方法相应的板材排料的优化算法，解决了在板材排料中矩形件析材的排料问题。     

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。     

基于SA-QPSO算法的多层制造单元内部布局方法

针对多层制造单元内部的设备布局优化问题,本文建立考虑单元尺寸、物料搬运量、损失时间以及单元稳定性的多目标优化数学模型。为更快速、高效地求解该问题,使用模拟退火算法（Simulated Annealing,SA）确定单元内设备所在平面以及层面,使用量子粒子群算法（Quantum Particle Swarm Optimization,QPSO）确定设备具体坐标值和所在高度。以某汽车零件加工车间为实例,运用SA-QPSO算法生成直线形、“U”形和环形3种最优空间布局方案,验证了SA-QPSO算法在多层制造单元内部布局方法设计方面的可行性。     

基于序列模型的三维矩形布局算法

针对三维矩形布局问题进行了研究。在三元序列的基础上,结合布局物体的几何可行域,提出了三元序列结合几何可行域的布局算法。并且利用遗传算法对布局算法进行优化,得到了三元序列结合可行域布局遗传算法。分析和实例证明,三元序列结合几何可行域的改进算法有效地提高了布局效率。     

基于蒙特卡罗方法的矩形布局问题研究

根据蒙特卡罗方法产生的随机步长,控制矩形在布局空间中移动。矩形移动时,自动满足边界约束条件,简化了矩形可行域边界的计算过程。结合定位函数,得到的可行域可用于完成矩形的布局。测试结果表明,使用该方法求解矩形布局问题,布局空间90%以上被矩形占据。     

基于改进最低水平线方法与遗传算法的矩形件排样优化算法

传统的最低水平线方法用于矩形件排样时可能产生较多未被利用的空白区域,造成不必要的材料浪费.针对此缺陷,在搜索过程中引入启发式判断,实现空白区域的填充处理,提高板材利用率.在应用遗传算法优化矩形件排样顺序时,在进化过程中采用分阶段设置遗传算子的方法,改善算法的搜索性能与效果.通过改进最低水平线方法与基于分阶段遗传算子的遗传算法相结合,共同求解矩形件排样问题.排样测试数据表明,所提出的矩形件排样优化算法能够有效改善排样效果,提高材料利用率.     

船体曲表面敷设矩形块生成算法研究

以船体外表面敷设矩形块为背景,针对原有在船体外板展开图上进行平面布置设计的不足,提出进行矩形块三维布置设计,并相应提出3种较为可行的曲面矩形块生成算法,同时通过对3种算法从计算量、形状误差和交互响应速度3个方面进行对比,并综合3个方面的优缺点进行选优,在以设计误差和交互响应速度为优先考虑的前提下,认为按第3种算法生成矩形块来进行三维布置设计是最佳的选择.     

一个求解多边形最小面积外接矩形的算法

多边形最小面积外接矩形是地理信息系统和图形学领域一个极其有用的工具,但是其精确求解过程比较困难.首先证明了一个多边形的最小面积外接矩形必定过该多边形凸包的一条边,然后基于该思想提出了一个计算多边形最小面积外接矩形的算法,并对算法的效率进行了分析.最后给出了算法的实验算例,进一步说明了算法的可行性与可靠性.     

矩形布局问题吸引子法研究

吸引子法是布局定位函数中的一种,在解决布局问题中取得了较好的效果.论文的研究,获得了吸引子法的一些基本性质:诸如定位函数的三维图像为一个平面、定位函数值相等的点共线、吸引子法使矩形块堆积在一个角上等.此外,通过研究布入点的几何意义,提出了一种手动快速布局方法.最后通过研究吸引子放置位置对布局的影响,还得出了隐性吸引子这一重要的性质.     

On solving three-dimensional open-dimension rectangular packing problems

In this article, a recently proposed three-dimensional open-dimension rectangular packing problem is considered, in which the objective is to find a minimal volume rectangular container that packs a set of rectangular boxes. The literature has tackled small-sized instances of this problem by means of optimization solvers, position-free mixed-integer programming (MIP) formulations and piecewise linearization approaches. In this study, the problem is alternatively addressed by means of grid-based position MIP formulations, whereas still considering optimization solvers and the same piecewise linearization techniques. A comparison of the computational performance of both models is then presented, when tested with benchmark problem instances and with new instances, and it is shown that the grid-based position MIP formulation can be competitive, depending on the characteristics of the instances. The grid-based position MIP formulation is also embedded with real-world practical constraints, such as cargo stability, and results are additionally presented.     

改进的最低水平线搜索算法求解矩形排样问题

矩形优化排样问题是一个在制造业领域生产实践中普遍遇到的问题,采用了一种改进的最低水平线搜索算法求解此类问题.首先分析了原始的最低水平线搜索算法在排样中存在的缺陷,并针对该缺陷为其设计了一个评价函数,排样时对所有未排零件进行评价,选择评价值最高的零件排入当前位置,从而克服了算法在搜索过程中的随机性,优化了算法的搜索方向.实验仿真的结果表明,提出的算法可以得到较好的排样效果,并且其解决问题的规模越大,优化性能越好,适合于求解大规模排样问题.     

A superior linearization method for signomial discrete functions in solving three-dimensional open-dimension rectangular packing problems

This article studies the three-dimensional open-dimension rectangular packing problem (3D-ODRPP) in which a set of given rectangular boxes is packed into a large container of minimal volume. This problem is usually formulated as a mixed-integer nonlinear programming problem with a signomial term in the objective. Existing exact methods experience difficulty in solving large-scale problems within a reasonable amount of time. This study reformulates the original problem as a mixed-integer linear programming problem by a novel method that reduces the number of constraints in linearizing the signomial term with discrete variables. In addition, the range reduction method is used to tighten variable bounds for further reducing the number of variables and constraints in problem transformation. Numerical experiments are presented to demonstrate that the computational efficiency of the proposed method is superior to existing methods in obtaining the global optimal solution of the 3D-ODRPP.     

可靠性优化的一种新的算法

建立了可靠性冗余优化模型,提出了一种基于粒子群优化算法的可靠性优化的新方法,该方法结合了遗传算法的思想。实例结果表明,粒子群算法比模拟退火算法和遗传算法效果好。     

A particle packing algorithm for packed beds with size distribution

A particle packing algorithm for simulating realistic packed beds of spheres with size distribution is described. The algorithm used the Monte Carlo method combined with the simulated annealing minimisation algorithm to solve the packed bed simulations. The objective function which was minimised was a combination of two functions, one describing the deviation from the target mean coordination number of the spheres in each size interval and the other the average fraction of overlapping volume of the spheres per contact. In this way a realistic bed structure was maintained while at the same time controlling the coordination number of the spheres. The algorithm used an experimentally validated model to predict the mean coordination number of the spheres in each size interval.     

A recursive algorithm for the rectangular guillotine strip packing problem

This article presents a recursive heuristic algorithm to generate cutting patterns for the rectangular guillotine strip packing problem in which a set of rectangular items must be cut from the strip such that the consumed strip length is minimized. The strip is placed with its length along the horizontal direction, and is divided into several segments with vertical cuts. The length of a segment is determined by the item placed at the bottom. Orthogonal cuts divide the segments into blocks and finished items. For the current block considered, the algorithm selects an item, puts it at the bottom-left corner of the block, and divides the unoccupied region into two smaller blocks with an orthogonal cut. Rotation of the items by 90 is allowed. Both lower and upper bounds are used to prune unpromising branches. The computational results indicate that the algorithm performs better than several recently published algorithms.     

退火-遗传算法寻优及其实现

分析了遗传算法及退火算法的优缺点,提出用退火算法改进遗传算法局部的最优值搜索效率低问题。退火算法与遗传算法融合后,使算法在寻优结果上更加迅速精确。通过水泥的配比工程实例,与单纯的遗传算法的结果进行对比,说明该方法是有效的。     

自适应模拟退火结合共轭梯度法求解薄膜厚度

根据薄膜光学计算理论和最优化理论,提出了用自适应模拟退火法结合共轭梯度法确定薄膜厚度的新方法。该方法建立的数学模型先采用自适应模拟退火算法搜索,再采用共轭梯度算法精确查找。它不但减少了无损伤测量方法对初始计算条件的过多依赖,而且在保证精确度的情况下极大地提高了计算速度,同时有很高的适应性。实验中,应用该方法求解了三层膜系的厚度,计算时间为3s,计算误差小于4nm。     

Simulated annealing based parallel genetic algorithm for facility layout problem

The facility layout problem (FLP), a typical combinational optimisation problem, is addressed in this paper by implementing parallel simulated annealing (SA) and genetic algorithms (GAs) based on a coarse-grained model to derive solutions for solving the static FLP with rectangle shape areas. Based on the consideration of minimising the material flow factor cost (MFFC), shape ratio factor (SRF) and area utilisation factor (AUF), a total layout cost (TLC) function is derived by conducting a weighted summation of MFFC, SRF and AUF. The evolution operations (including crossover, mutation, and selection) of GA provide a population-based global search in the space of possible solutions, and the SA algorithm can lead to an efficient local search near the optimal solution. By combing the characteristics of GA and SA, better solutions will be obtained. Moreover, the parallel implementation of simulated annealing based genetic algorithm (SAGA) enables a quick search for the optimal solution. The proposed method is tested by performing a case study simulation and the results confirm its feasibility and superiority to other approaches for solving FLP.     

Global optimization for the three-dimensional open-dimension rectangular packing problem

This article addresses the three-dimensional open-dimension rectangular packing problem (3D-ODRPP), which aims to pack a given set of unequal-size rectangular boxes within an enveloping rectangular space such that the volume of the occupied space is minimized. Even though the studied 3D-ODRPP is NP hard, the development of sophisticated global optimization methods has been stimulated. The mathematical programming formulation for the 3D-ODRPP has evolved into an effective and efficient mixed-integer linear programming (MILP) model. This study proposes an advanced exact scheme yielding a guaranteed global optimal solution given that all the instance data are non-negative rational numbers. The developed MILP retains not only fewer variables but also fewer constraints than the state-of-the-art models. The superior effectiveness and efficiency of the developed scheme are demonstrated with numerical experiments, where two sets of benchmark instances from references, real-world instances and instances with rational data are included.