Addressing a nonlinear fixed-charge transportation problem using a spanning tree-based genetic algorithm

In this paper, we consider the fixed-charge transportation problem (FCTP) in which a fixed cost, sometimes called a setup cost, is incurred if another related variable assumes a nonzero value. To tackle such an NP-hard problem, there are several genetic algorithms based on spanning tree and Prüfer number representation. Contrary to the findings in previous works, considering the genetic algorithm (GA) based on spanning tree, we present a pioneer method to design a chromosome that does not need a repairing procedure for feasibility, i.e. all the produced chromosomes are feasible. Also, we correct the procedure provided in previous works, which designs transportation tree with feasible chromosomes. We show the previous procedure does not produce any transportation tree in some situations. Besides, some new crossover and mutation operators are developed and used in this work. Due to the significant role of crossover and mutation operators on the algorithm’s quality, the operators and parameters need to be accurately calibrated to ensure the best performance. For this purpose, various problem sizes are generated at random and then a robust calibration is applied to the parameters using the Taguchi method. In addition, two problems with different sizes are solved to evaluate the performance of the presented algorithm and to compare that performance with LINGO and also with the solution presented in previous work.     

遗传算法在求解最小生成树中的运用

以图论和遗传算法为基础,提出了求解最小生成树问题的遗传算法。该算法解决了常用二进制编码不能正确表达最小生成树的问题,利用Prufer数对生成树进行编码;在遗传操作中对变异算子进行了改进,避免了由于变异产生大量不可行解。从而提高了遗传算法的效率;通过数值试验,表明该算法简单,高效,收敛率高。     

Improved genetic algorithm for generalized transportation problem

In this paper, we introduce the genetic algorithm approach to the generalized transportation problem (GTP) and GTP with a fixed charge (fc-GTP). We focus on the use of Prüfer number encoding based on a spanning tree, which is adopted because it is capable of equally and uniquely representing all possible trees. From this point, we also design the criteria by which chromosomes can always be converted to a GTP tree. The genetic crossover and mutation operators are designed to correspond to the genetic representations. With the spanning-tree-based genetic algorithm, less memory space will be used than in the matrix-based genetic algorithm for solving the problem; thereby computing time will also be saved. In order to improve the efficiency of the genetic algorithm, we use the reduced cost for the optimality of a solution and the genetic algorithm to avoid degeneration of the evolutionary process. A comparison of results of numerical experiments between the matrix-based genetic algorithm and the spanning-tree-based genetic algorithm for solving GTP and fc-GTP problems is given. This work was presented, in part, at the Fourth International Symposium on Artificial Life and Robotics, Oita, Japan, January 19–22, 1999     

求解多目标最小生成树的一种新的遗传算法

在改进的非支配排序遗传算法（NSGA-II）的基础上,提出了一种新的基于生成树边集合编码的繁殖算子求解多目标最小生成树问题的遗传算法。通过快速非支配排序法,降低了算法的计算复杂度,引入保存精英策略,扩大采样空间。实验结果表明：对于多目标最小生成树问题,边集合编码具有较好的遗传性和局部性,而且基于此繁殖算子的遗传算法在求解效率和解的质量方面都优于基于PrimRST的遗传算法。     

Ant-Tree: an ant colony optimization approach to the generalized minimum spanning tree problem

The ant colony optimization is a meta-heuristic inspired by knowledge sharing amongst ants using pheromone, which serves as a kind of collective memory. Since the past few years, there have been several successful applications of this new approach for finding approximate solutions for computationally difficult problems in reasonable times. In this paper, we study the generalized minimum spanning tree problem that involves the design of a minimum weight connected network spanning at least one node out of every disjoint subset of the nodes in a graph. This problem has a wealth of pertinence to a wide range of applications in different areas. As the problem is known as computationally challenging, we adopt the ant colony optimization strategy and present a new solution method, called Ant-Tree, to develop approximate solutions. As an initial attempt, our study aims to provide an investigation of the ant colony optimization approach for coping with tree optimization problems. Through computational experiments, we compare the performances of our approach and the method available in the literature. Numerical results indicate that the proposed method is effective in producing quality approximate solutions.     

Uncertain goal programming models for bicriteria solid transportation problem

This paper investigates an uncertain bicriteria solid transportation problem. The supplies, demands, conveyance capacities, transportation cost and transportation time are regarded as uncertain variables. According to two types of methods to rank the uncertain variables, expected value goal programming model and chance-constrained goal programming model for the bicriteria solid transportation problem are constructed. It is proved that the expected value goal programming model and chance-constrained goal programming model can be respectively transformed into the corresponding deterministic equivalents by taking advantage of some properties of uncertainty theory. Based on these equivalence relations, the optimal transportation plans of the uncertain goal programming models can be obtained. Several numerical experiments are presented to illustrate the applications of the models.     

最小生成树问题在暖气供应建设中的应用

介绍通过应用贪心算法中的最小生成树问题的prim算法,来解决机关单位、公司、学校等地方的暖气供应的问题.文章中给出了铺设暖气管的数学模型,举例说明了如何布设暖气管道是既节省材料又创造最大效益的最佳方案,也通过此例说明了贪心算法在解决实际问题中的应用是十分广泛和重要的.     

量子遗传算法在TSP中的应用

本文提出了一种改进的量子遗传算法,其核心是对量子遗传算法中的量子旋转门的调整策略进行改进。在现有的静态、指数型动态调整策略的基础上提出了基于正弦函数的动态调整策略。文中对旅行商问题（TSP）的仿真实验结果表明：改进后的算法的优化质量和效率都优于遗传算法和一般量子遗传算法。     

Genetic algorithm for robot selection and work station assignment problem

In this paper, we introduce Genetic Algorithm (GA) for optimal Robot Selection and Work station Assignment (RS/WA) problem for a CIM system. In particular, the RS/WA problem can be considered as a generalized two-dimensional multi-type bin packing problem that has been shown to be NP-hard. A multichromosome GA combined with heuristic bin packing algorithm is implemented for solving the problem and the effeciency of proposed method is shown by numerical example. Our approach may be applicable to other this kind of bin packing problems.     

Minimizing makespan on a three-machine flowshop batch scheduling problem with transportation using genetic algorithm

This paper studies the minimization of makespan in a three-machine flowshop scheduling problem in which a batch processing machine is located between two single processing machines on first and third stages. In this study also transportation capacity and transportation among machines times are explicitly considered.We establish a mixed integer programming model and propose a heuristic algorithm based on the basic idea of Johnson's algorithm. Since the problem under study is NP-hard, a genetic algorithm is also proposed to minimize makespan. The effectiveness of our solution procedures is evaluated through computational experiments. The results obtained from the computational study have shown that the genetic algorithm is a viable and effective approach that is capable to produce consistently good results.     

Solving bicriteria solid transportation problem with fuzzy numbers by a genetic algorithm

The proposed Genetic Algorithms (GAs) are incorporated with problem-specific knowledge and the decision maker's degree of optimism, and the criteria space approach for bicriteria linear program conductive to find out the nondominated extreme points in the criteria space.     

有时间窗约束车辆路径问题的改进遗传算法

将遗传算法与禁忌搜索结合起来,设计了一种改进的遗传算法求解有时间窗约束车辆路径问题。采用启发式插入算法产生较优良的遗传操作初始种群,通过改进的逆转变异算子更多继承父代的优良性能,以提高遗传算法的计算效率。引入海明距评估遗传进化中种群的多样性。当种群多样性低到一定程度时转入禁忌搜索,以避免遗传算法早熟的缺陷,最终实现全局优化。通过算例验证了该算法的优越性。     

一种求解TSP的混合遗传蚁群算法

结合遗传算法和蚁群算法,提出了一种求解TSP的基于启发式遗传信息的蚁群遗传算法。该算法由蚁群遗传算法和基于启发式遗传信息的蚁群算法两部分组成。蚁群遗传算法将蚁群算法和遗传算法结合起来,提高了遗传算法的种群的多样性;基于启发式遗传信息的蚁群算法是将启发式遗传信息加入到蚁群算法中,防止蚁群算法对信息素过分依赖,缩小最优解的搜索空间。HGI ACGA算法是将启发式遗传信息加入到蚁群遗传算法中,可以提高蚁群算法的收敛速度和寻优能力。实验结果表明,HGI ACGA算法在收敛速度和收敛精度上均优于ACGA和ACA算法。     

采用改进的混合遗传算法求解高校排课问题

为了解决一个存在大量合班现象的高校排课问题,建立了相应的数学模型并采用改进的混合遗传算法进行了求解。在产生初始种群的过程中进行了乱序处理,以提高初始种群中个体的多样性,避免早熟收敛现象的发生;为了防止种群的退化,引入了保留最优个体策略和竞争机制;根据问题的特点设计了与之相适应的遗传算子;为了提高种群进化的效率,交叉概率和变异概率都使用了自适应参数;为了提高算法的局部搜索能力,在交叉操作阶段采用了模拟退火算法。通过Matlab与Access混合编程,实现了对大规模数据的高效处理。实例结果表明,该算法能够有效地解决存在合班现象的高校排课问题。     

求解最大子团的随机抽样免疫遗传算法

针对遗传算法在最大子团求解中保持群体多样性能力不足、早熟、耗时长、成功率低等缺陷,利用随机抽样方法对交叉操作进行重新设计,结合免疫机理定义染色体浓度,设计克隆选择策略,提出了求解最大子团问题的随机抽样免疫遗传算法。用仿真算例说明了新算法在解的质量、收敛速度等各项指标上均有提高,且不比DLS-MC、QUALEX等经典搜索算法差,对某些算例还得到了更好解。     

Nonlinear fixed charge transportation problem by minimum cost flow-based genetic algorithm

Nonlinear Fixed Charge Transportation Problem (NFCTP) is a variant of fixed charge transportation problem, which is to ship available amounts of goods to satisfy the demands at minimal total cost, on condition that any route has a fixed cost irrelative to its shipping amount if it is used, and a variable cost directly proportional to the quadratic of its shipping amount as a nonlinear term. This paper aims at developing an efficient method to solve NFCTP. In this paper, NFCTP is formulated using a mixed integer programming model. Based on steady-state genetic algorithm as framework, and minimum cost flow algorithm as decoder, a hybrid genetic algorithm named NFCTP-HGA is proposed as a solution method of the model. Taking advantage of nonlinear structure and special network structure of NFCTP, the NFCTP-HGA algorithm has good performance in the sense of being implemented on computer, computational time, required memory for computation, and ability to search global optimum. The application of the NFCTP-HGA algorithm is illustrated with examples. Numerical experiments demonstrate that the NFCTP-HGA algorithm is an efficient and robust method to solve NFCTP, especially applicable to large scale problems.     

用基于多目标决策的遗传算法解网络拓扑结构设计问题

多点网络拓扑结构设计问题是NP-完全问题。该文提出了一个基于多目标决策的遗传算法(MCGA)来解决多点网络拓扑结构问题。和其它多目标遗传算法不同的是:首先,对网络节点进行预划分,使得Pareto优的节点归于候选分枝节点集合;其次,修改了Prüfer编码,使得编码中的码元代表候选分枝节点,以利于对分枝节点的搜索;最后,构造了分枝变异算子与非分枝变异算子作为主要的进化算子。该算法以概率1收敛于全局最优解集。数值实验表明该算法优于其它多目标遗传算法。     

一种求解0-1背包问题的改进遗传算法

针对传统遗传算法（SGA）容易“早熟”的不足,提出一种求解0-1背包问题（KP）的改进遗传算法。借鉴二重结构编码的解码处理方法设计了一种新解码方法,在保证解可行性的同时修正种群中无对应可行解的个体;采用模拟退火算法和改进的精英选择算子改进SGA。实例仿真结果验证了改进遗传算法在进化效率和最优解搜索能力上的优越性。     

求解最小生成树的一种小生境遗传禁忌算法

针对最小生成树问题,提出了一种小生境遗传禁忌算法。算法中使用Prfer数对生成树进行编码。在选择交叉之前使用小生境技术,使得被选中交叉的个体之间的适应值的距离大于一定的阈值,从而保证了个体的多样性。遗传变异算子使用禁忌搜索算法,提高了遗传算法的局部搜索能力,加快了算法的收敛速度。模拟实验结果证明该算法是有效的。