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.     

Bicriteria network design using a spanning tree-based genetic algorithm

The optimization problems in communication networks have received the attention of many researchers in such related fields as network designer, network analysis, and network administration. The use of computer communication networks has been increasing rapidly in order to share expensive hardware/software resources and provide access to main systems from distant locations. These network problems have many applications in telecommunications, computer networking, and related domains in electric, gas, and sewer networks. In computer networking, LANs (local area networks) are commonly used as the communication infrastructure that meets the demands of users in the local environment. These networks typically consist of several LAN segments connected together via bridges. The use of these transparent bridges requires.loop-free paths between LAN segments. Therefore, only spanning tree topologies can be used as active LAN configurations. Recently, genetic algorithms have greatly advanced in related research fields such as network optimization problems, combinatorial optimization, multiobjective optimization, and so on. Genetic algorithms have also received a great deal of attention because of their ability as optimization techniques for many real-world problems. In this paper, we attempt to solve the LAN topology design problem with bicriteria which minimize the cost and average message delay using genetic algorithms, and propose a method of searching the Pareto solutions. We also employ the Prüfer number in order to represent the chromosomes, because the interconnection between the network service centers must yield spanning tree configurations. Finally, we conduct experiments to certify the quality of the networks designs obtained by using genetic algorithms. This work was presented, in part, at the Third International Symposium on Artificial Life and Robotics, Oita, Japan, January 19–21, 1998     

A note on “Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm” by Jung-Bok Jo,Yinzhen Li,Mitsuo Gen,Computers & Industrial Engineering (2007)

In 2007, a spanning tree-based genetic algorithm approach for solving nonlinear fixed charge transportation problem proposed by Jo et al. [Jo, J. B., Li, Y., Gen, M. (2007). Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers & Industrial Engineering. doi:10.1016/j.cie.2007.06.022] was published in Computers & Industrial Engineering journal. In 2008, comments like calculation of total cost, indication of problem size were given by Kannan et al. [Kannan, G., Kumar, P. S., Vinay V. P. (2008). Comments on ‘‘Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm” by Jung-Bok Jo, Yinzhen Li, Mitsuo Gen, Computers & Industrial Engineering (2007). Computers & Industrial Engineering. doi:10.1016/j.cie.2007.12.019] for the published model of [Jo, J. B., Li, Y., Gen, M. (2007). Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers & Industrial Engineering.doi:10.1016/j.cie.2007.06.022]. In this note, as a response to the comments of Kannan et al., the formula for calculating the total cost of nonlinear fixed charge transportation problem is illustrated with examples, to which the near-optimal solutions are given.     

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.     

Solving a timetabling problem using hybrid genetic algorithms

All over the world, human resources are used on all kinds of different scheduling problems, many of which are time-consuming and tedious. Scheduling tools are thus very welcome. This paper presents a research project, where Genetic Algorithms (GAs) are used as the basis for solving a timetabling problem concerning medical doctors attached to an emergency service. All the doctors express personal preferences, thereby making the scheduling rather difficult. In its natural form, the timetabling problem for the emergency service is stated as a number of constraints to be fulfilled. For this reason, it was decided to compare the strength of a Co-evolutionary Constraint Satisfaction (CCS) technique with that of two other GA approaches. Distributed GAs and a simple special-purpose hill climber were introduced, to improve the performance of the three algorithms. Finally, the performance of the GAs was compared with that of some standard, nonGA approaches. The distributed hybrid GAs were by far the most successful, and one of these hybrid algorithms is currently used for solving the timetabling problem at the emergency service. © 1997 John Wiley & Sons, Ltd.     

多式联运运输问题的混合遗传算法

多式联运运输方式的选择关系到货物运输所需费用、时间等。该文对需经过多式联运过程的运输问题进行了研究。首先分析了多式联运运输问题的数学模型;其次通过引入关于运输量及运输方式的混合编码,结合两种混合遗传算子,提出了一种求解多式联运运输问题的混合遗传算法;最后用数值例子对算法的有效性进行了验证。     

Using genetic algorithm and TOPSIS technique for multiobjective transportation problem: a hybrid approach

A hybrid approach to solve the multiobjective transportation problem (TP) is presented. The TP as a special type of the network optimization problems that has the special data structure in solution characterized as transportation graph. In encoding TP, we introduce a new chromosome's structure which is adopted as it is capable of representing all possible feasible solutions. Also, in order to keep the feasibility of the chromosome, the crossover and the mutation were modified. The proposed approach maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of ?-dominance. Moreover, to help the decision maker to extract the best compromise solution from a finite set of alternatives, a technique for order performance by similarity to ideal solution (TOPSIS) method is adopted. Numerical simulations show the effectiveness and efficiency of the proposed approach.     

基于遗传算法的动态MC2运输问题求解

动态MC²运输问题是描述多阶段供求波动的运输问题,其模型框架可以应用到很多领域。目前对动态MC²运输模型的求解主要采用传统的单纯形法,针对该问题的特殊性采用具有全局搜索能力的遗传算法进行求解。通过三维数组编码,设计有效的交叉、变异算子和适应度函数,克服了单纯形法求解该问题出现的并行性差、求解整数规划困难的不足。用Matlab7.0编程对算法进行检验,结果表明经过特殊设计的遗传算法能够很好地解决动态MC²运输问题。     

Various hybrid methods based on genetic algorithm with fuzzy logic controller

In this paper we propose several efficient hybrid methods based on genetic algorithms and fuzzy logic. The proposed hybridization methods combine a rough search technique, a fuzzy logic controller, and a local search technique. The rough search technique is used to initialize the population of the genetic algorithm (GA), its strategy is to make large jumps in the search space in order to avoid being trapped in local optima. The fuzzy logic controller is applied to dynamically regulate the fine-tuning structure of the genetic algorithm parameters (crossover ratio and mutation ratio). The local search technique is applied to find a better solution in the convergence region after the GA loop or within the GA loop. Five algorithms including one plain GA and four hybrid GAs along with some conventional heuristics are applied to three complex optimization problems. The results are analyzed and the best hybrid algorithm is recommended.     

An integer program and a hybrid genetic algorithm for the university timetabling problem

The university timetabling problem (UTP) has been studied by numerous research groups for decades. In addition to addressing hard and soft constraints, we extend the UTP by considering consecutiveness and periodicity constraints of multi-session lectures, which are common in many eastern Asian universities. Because schedulers can decide the consecutiveness and periodicity constraints for the multi-session lectures within a limited ratio, we consider these novel decision variables in our model. We develop a mixed integer linear program for the UTP. For the analysis, we convert the UTP into the three-dimensional container packing problem (3DCPP) and create a hybrid genetic algorithm (HGA), which has been shown to be efficient in solving the 3DCPP. We also develop a tabu search algorithm based on the existing UTP literature and compare the findings with that of our HGA. The results show that our HGA obtains a better solution than the tabu search algorithm in a reasonable amount of time.     

求解固定费用运输问题的遗传算法

为克服基于边集编码的遗传算法求解固定费用运输问题的不足,对采用先根遍历边构成有序边集编码的生成树,提出了森林补充式多点交叉操作的遗传算法.经证明,对于有m个源节点和n个目的节点的固定费用运输问题,该算法的空间复杂度为O((m n-1)2),时间复杂度为Oβ(m n-1)3),β为最大迭代次数.实验数据表明,随着问题规模和求解难度的增加,该算法与边集编码的遗传算法解的质量都呈下降趋势,但所得解的质量优于边集编码的遗传算法.     

求解旅行商问题的混合粒子群优化算法

结合遗传算法、蚁群算法和模拟退火算法的思想，提出用混合粒子群算法来求解著名的旅行商问题．与模拟退火算法、标准遗传算法进行比较，24种混合粒子群算法的效果都比较好，其中交叉策略D和变异策略F的混合粒子群算法的效果最好，而且简单有效．对于目前仍没有较好解法的组合优化问题，通过此算法修改很容易解决．     

基于遗传算法的动态MC2运输问题求解

动态MC²运输问题是描述多阶段供求波动的运输问题,其模型框架可以应用到很多领域。目前对动态MC²运输模型的求解主要采用传统的单纯形法,针对该问题的特殊性采用具有全局搜索能力的遗传算法进行求解。通过三维数组编码,设计有效的交叉、变异算子和适应度函数,克服了单纯形法求解该问题出现的并行性差、求解整数规划困难的不足。用Matlab7.0编程对算法进行检验,结果表明经过特殊设计的遗传算法能够很好地解决动态MC²运输问题。     

基于遗传算法的混合流水线车间调度多目标求解*

为了解决传统的多目标优化算法难以很好实现企业的实际决策需要问题,针对混合流水线车间调度（HFSP）的多目标优化调度问题,提出了一种新的多目标遗传算法。根据企业实际需求,采用分模块两层建模的思想,将多目标分为约束性目标和优化性目标。算法根据目标性质的不同分别进行不同的搜索。最后将新算法应用于HFSP多目标优化问题进行实例验证。结果表明,所提出的算法具有很好的可行性,与其他多目标优化方法相比,该算法具有明显的优越性、实用性和可操作性。     

A vehicle routing problem solved by using a hybrid genetic algorithm

The main purpose of this study is to find out the best solution of the vehicle routing problem simultaneously considering heterogeneous vehicles, double trips, and multiple depots by using a hybrid genetic algorithm. This study suggested a mathematical programming model with a new numerical formula which presents the amount of delivery and sub-tour elimination. This model gives an optimal solution by using OPL-STUDIO(ILOG CPLEX). This study also suggests a hybrid genetic algorithm (HGA) which considers the improvement of generation for an initial solution, three different heuristic processes, and a float mutation rate for escaping from the local solution in order to find the best solution. The suggested HGA is also compared with the results of a general genetic algorithm and existing problems suggested by Eilon and Fisher. We found better solutions rather than the existing genetic algorithms.     

Unit commitment problem with ramp rate constraint using a binary-real-coded genetic algorithm

The unit commitment problem (UCP) is a nonlinear mixed-integer optimization problem, encountered as one of the toughest problems in power systems. The problem becomes even more complicated when dynamic power limit based ramp rate constraint is taken into account. Due to the inadequacy of deterministic methods in handling large-size instances of the UCP, various metaheuristics are being considered as alternative algorithms to realistic power systems, among which genetic algorithm (GA) has been investigated widely since long back. Such proposals have been made for solving only the integer part of the UCP, along with some other approaches for the real part of the problem. Moreover, the ramp rate constraint is usually discussed only in the formulation part, without addressing how it could be implemented in an algorithm. In this paper, the GA is revisited with an attempt to solve both the integer and real parts of the UCP using a single algorithm, as well as to incorporate the ramp rate constraint in the proposed algorithm also. In the computational experiment carried out with power systems up to 100 units over 24-h time horizon, available in the literature, the performance of the proposed GA is found quite satisfactory in comparison with the previously reported results.     

A hybrid genetic algorithm for the phylogeny problem using path-relinking as a progressive crossover strategy

A phylogenetic tree relates taxonomic units using their similarities over a set of characteristics. Given a set of taxonomic units and their characteristics, the phylogeny problem under the parsimony criterion consists in finding a phylogenetic tree with a minimum number of evolutionary steps. We developed a hybrid genetic algorithm for the problem of building a phylogenetic tree minimizing parsimony. The algorithm combines local search with a crossover strategy based on path-relinking, an intensification technique originally used in the context of other metaheuristics such as scatter search and GRASP. Computational experiments on benchmark and randomly generated instances show that the proposed algorithm is very robust and outperforms other heuristics in terms of solution quality and running times.     

Solving the high school timetabling problem using a hybrid cat swarm optimization based algorithm

In this contribution we present the application of a hybrid cat swarm optimization (CSO) based algorithm for solving the school timetabling problem. This easy to use, efficient and fast algorithm is a hybrid variation of the classic CSO algorithm. Its efficiency and performance is demonstrated by conducting experiments with real-world input data. This data, collected from various high schools in Greece, has also been used as test instances by many other researchers in their publications. Results reveal that this hybrid CSO based algorithm, applied to the same school timetabling test instances using the same evaluation criteria, exhibits better performance in less computational time compared to the majority of other existing approaches, such as Genetic Algorithms (GAs), Evolutionary Algorithms (EAs), Simulated Annealing (SA), Particle Swarm Optimization (PSO) and Artificial Fish Swarm (AFS). The algorithm's main process constitutes a variation of the classic CSO algorithm, properly altered so as to be applied for solving the school timetabling problem. This process contains the main algorithmic differences of the proposed approach compared to other algorithms presented in the respective literature.     

Solving facilities location problem in the presence of alternative processing routes using a genetic algorithm

Facilities location problem deals with the optimization of location of manufacturing facilities like machines, departments, etc. in the shop floor. This problem greatly affects performance of a manufacturing system. It is assumed in this paper that there are multiple products to be produced on several machines. Alternative processing routes are considered for each product and the problem is to determine the processing route of each product and the location of each machine to minimize the total distance traveled by the materials within the shop floor. This paper presents a mixed-integer non-linear mathematical programming formulation to find optimal solution of this problem. A technique is used to linearize the formulated non-linear model. However, due to the NP-hardness of this problem, even the linearized model cannot be optimally solved by the conventional mathematical programming methods in a reasonable time. Therefore, a genetic algorithm is proposed to solve the linearized model. The effectiveness of the GA approach is evaluated with numerical examples. The results show that the proposed GA is both effective and efficient in solving the attempted problem.     

用遗传算法实现罚函数法解多选择背包问题

多选择背包问题最为复杂,传统的整数规划算法难以适用.另僻蹊径,采用数学上的罚函数法来求解.对罚函数法进行改进,使得能对多选择背包问题的数学模型进行求解.重点研究了如何把3种约束条件转化成目标函数的惩罚项.再从遗传算法的角度,来研究如何实现这种新的罚函数法.最终使用Visual C 6编程实现,并与前人的算法进行比较,取得了较好的效果.