A genetic algorithm for the uncapacitated single allocation planar hub location problem

Given a set of n interacting points in a network, the hub location problem determines location of the hubs (transfer points) and assigns spokes (origin and destination points) to hubs so as to minimize the total transportation cost. In this study, we deal with the uncapacitated single allocation planar hub location problem (PHLP). In this problem, all flow between pairs of spokes goes through hubs, capacities of hubs are infinite, they can be located anywhere on the plane and are fully connected, and each spoke must be assigned to only one hub. We propose a mathematical formulation and a genetic algorithm (PHLGA) to solve PHLP in reasonable time. We test PHLGA on simulated and real life data sets. We compare our results with optimal solution and analyze results for special cases of PHLP for which the solution behavior can be predicted. Moreover, PHLGA results for the AP and CAB data set are compared with other heuristics.     

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.     

A genetic algorithm approach to solving the anti-covering location problem

Abstract: In this paper we address the problem of locating a maximum weighted number of facilities such that no two are within a specified distance from each other. A natural process of evolution approach, more specifically a genetic algorithm, is proposed to solve this problem. It is shown that through the use of a commercially available spreadsheet-based genetic algorithm software package, the decision-maker with a fundamental knowledge of spreadsheets can easily set up and solve this optimization problem. Also, we report on our extensive computational experience using three different data sets.     

Constraint Logic Programming and Integer Programming approaches and their collaboration in solving an assignment scheduling problem

Generalised Assignment Problems (GAP), traditionally solved by Integer Programming techniques, are addressed in the light of current Constraint Programming methods. A scheduling application from manufacturing, based on a modified GAP, is used to examine the performance of each technique under a variety of problem characteristics. Experimental evidence showed that, for a set of assignment problems, Constraint Logic Programming (CLP) performed consistently better than Integer Programming (IP). Analysis of the CLP and IP processes identified ways in which the search was effective. The insight gained from the analysis led to an Integer Programming approach with significantly improved performance. Finally, the issue of collaboration between the two contrasting approaches is examined with respect to ways in which the solvers can be combined in an effective manner.     

On solving the assembly line worker assignment and balancing problem via beam search

Certain types of manufacturing processes can be modelled by assembly line balancing problems. In this work we deal with a specific assembly line balancing problem that is known as the assembly line worker assignment and balancing problem (ALWABP). This problem appears in settings where tasks must be assigned to workers, and workers to work stations. Task processing times are worker specific, and workers might even be incompatible with certain tasks. The ALWABP was introduced to model assembly lines typical for sheltered work centers for the Disabled.     

New heuristic algorithms for solving the planar p-median problem

In this paper we propose effective heuristics for the solution of the planar p-median problem. We develop a new distribution based variable neighborhood search and a new genetic algorithm, and also test a hybrid algorithm that combines these two approaches. The best results were obtained by the hybrid approach. The best known solution was found in 466 out of 470 runs, and the average solution was only 0.000016% above the best known solution on 47 well explored test instances of 654 and 1060 demand points and up to 150 facilities.     

A planar single facility location and border crossing problem

In this study, we tackle the problem of locating a facility in a region where a fixed line barrier divides the region into two. The resulting subregions communicate with each other through a number of passage points located on the line barrier. Our contribution is threefold. First, we formulate the problem as a Mixed Integer Nonlinear Programming (MINLP) model and provide an optimal solution methodology based on an Outer Approximation (OA) algorithm. Second, we discuss the minimax version of this problem for locating an emergency facility and use the OA algorithm to solve the problem. We then provide simple example problems and extensive computational results for both problems. Finally, we propose a one-infinity approximation approach for the latter problem which yields a linear model. Practical uses of the models have been discussed in the border crossing context.     

Near-optimal heuristics for an assignment problem in mass storage

This paper deals with the assignment of items to an array based on access probabilities so that the expected access time is minimized. The only necessary condition for optimality known to date is that of pairwise majorization. This condition, however, is far from being sufficient. Procedures are developed (1) to enumerate all configurations that satisfy this condition and (2) to obtain tight lower bounds for the optimal solution. An algorithm based on stepwise minimization is proposed and is demonstrated to give near-optimal performance. Numerical results are presented to show that the heuristics yield an actual cost within 0.8 % of the optimal regardless of the underlying distribution and the array size. Furthermore, this algorithm only depends on the ranking of access frequencies and not on the exact values.     

A genetic algorithm-based approach for solving the resource-sharing and scheduling problem

We introduce a heuristic that is based on a unique genetic algorithm (GA) to solve the resource-sharing and scheduling problem (RSSP). This problem was previously formulated as a continuous-time mixed integer linear programming model and was solved optimally using a branch-and-bound (B&B) algorithm. The RSSP considers the use of a set of resources for the production of several products. Producing each product requires a set of operations with precedence relationships among them. Each operation can be performed using alternative modes which define the subset of the resources needed, and an operation may share different resources simultaneously. The problem is to select a single mode for each operation and accordingly to schedule the resources, while minimizing the makespan time. The GA we propose is based on a new encoding schema that adopts the structure of a DNA in nature. In our experiments we compared the effectiveness and runtime of our GA versus a B&B algorithm and two truncated B&B algorithms that we developed on a set of 118 problem instances. The results demonstrate that the GA solved all the problems (10 runs each), and reaches optimality in 75% of the runs, had an average deviation of less than 1% from the optimal makespan, and a runtime that was much less sensitive to the size of the problem instance.     

基于遗传模拟退火算法的立体仓库储位优化

针对自动化立体仓库储位分配问题,结合仓库运作特点和安全性要求,构建了自动化立体仓库储位优化问题的多目标模型,并提出了求解模型的基于Sigmoid曲线的改进自适应遗传模拟退火算法（SAGA）。首先,以降低货品出入库时间、同组货品距离和货架重心为目标建立储位优化模型;然后,为了克服遗传算法（GA）局部搜索能力差和易陷入局部最优的缺点,引入基于Sigmoid曲线的自适应交叉变异操作和逆转操作,同时完成与SAGA的融合;最后,对改进遗传SAGA进行算法优化性、稳定性和收敛性测试。仿真实验表明,相比模拟退火（SA）算法的求解结果,该算法对货品出入库时间的优化度提高了37.7949个百分点、对同组货品距离提高了58.4630个百分点、对货架重心优化度提高了25.9275个百分点,并且该算法具有更好的稳定性和收敛性。由此验证了改进遗传SAGA求解问题的有效性,该算法可为自动化立体仓库储位优化提供决策方法。     

改进型粒子群算法及其在选址问题中的应用

为了解决基本粒子群算法不易跳出局部最优的问题,提出了一种协同粒子群优化算法。在算法中通过加入权值递减的惯性因子和变异算子以克服基本PSO易早熟、不易收敛以及缺乏多样性的不足。将算法应用于极小极大选址问题的实验结果表明,算法能够有效地求解极小极大选址问题,具有较好的应用价值。     

An addendum on the incremental assignment problem

In Toroslu and Üçoluk [I.H. Toroslu, G. Üçoluk, Incremental assignment problem, Information Sciences 177 (2007) 1523-1529] the incremental assignment problem is defined as follows. A new pair of vertices and their incident edges are added to a weighted bipartite graph whose maximum-weighted matching is already known, and the maximum-weighted matching of the extended graph is sought. An O(n²) algorithm for the problem has been derived, with n the size of a partition in the bipartite graph. We point out that such a result can be found in literature.     

人数少于任务数的全指派问题的迭代算法

针对人数少于任务数的情况,按每人至少承担一项任务,至多承担L项任务,但每项任务只允许一人承担的指派原则,给出了一种求解这种指派问题的迭代算法,该算法操作简便、易于用计算机运行。构建该算法的方法,用于某些其它指派问题,可以使相应的算法更加便捷。     

自动化仓储系统不规则货位优化问题研究

针对不规则货位的自动化仓储系统的特点,以提高系统效率和空间利用率为优化控制目标,研究了自动化仓储系统不规则货位优化分配策略,提出了首先对不规则的货位进行货位区优化,对每个货位区进行货位优化的数学模型,提出两级遗传算法解决货位优化问题。结果表明,该优化方法有效地提高了系统的效率,实现了密集存储,为自动化仓储系统中不规则货位的货位分配优化提供了理论依据和实践途径。     

A dock-door assignment problem for the Korean mail distribution center

This paper addresses operational problems of the cross-docking system in a mail distribution center. The center has two types of doors, receiving doors and shipping doors. The assignment of destinations to shipping doors, clustering of destinations to form groups, and determination of the number of groups are major operational problems directly related with the efficiency of the center. To solve the problems, a non-linear mathematical model is developed with the objective of minimizing the travel distance of the pallets in the center. For the model, two solution methods, three-phase heuristic procedure and genetic algorithm, are developed. A lower bound is also found to evaluate the validity of the solution methods. A case with the real world data is solved and a substantial improvement is obtained by the model compared with the current operating system.     

一种求解企业员工指派问题的离散状态转移算法

员工指派问题是运筹学中的一类整数规划问题,为了寻找最佳的员工指派方案,使得完成所有任务的总成本代价最小,本文研究了一种新的离散状态转移算法.在一次状态转移的基础上提出了二次状态转移的概念,从而扩大了候选解集的范围,并提高候选解集的多样性.为了克服算法在迭代后期更新缓慢的缺点,提出了停滞回溯策略,即当算法陷入局部最优解时进行回溯操作,从历史停滞解中随机选择一个更新当前最优解.通过与模拟退火算法进行测试比较实验,证明了本文所提出算法的有效性,同时该算法提高了求解员工指派问题的成功率与稳定性.     

A heuristic procedure for the integrated facility layout design and flow assignment problem

We present an efficient iterative heuristic procedure for solving the integrated layout design and product flow assignment problem. The layout design decisions involve planar location of unequal-area machines with duplicates. The product flows are assigned to machines according to the product processing routes. The integrated decision problem is a nonlinear mixed integer model which cannot be efficiently solved using classical methods for large problems. We propose a novel integrated heuristic procedure based on the alternating heuristic, a perturbation algorithm and sequential location heuristic. Since the alternating heuristic between facility layout design and product-machine assignment sub-problems terminates with local optima, we developed a perturbation algorithm based on assignment decisions. The results of an experimental study show that proposed procedure is both efficient and effective in identifying quality solutions for small to very large-sized problems.     

Accumulated risk of body postures in assembly line balancing problem and modeling through a multi-criteria fuzzy-genetic algorithm

Monotonous body postures during repetitive jobs negatively affect assembly-line workers with the developing of Work-related Musculoskeletal Disorders (WMSDs). Ergonomics specialists have offered auxiliary posture diversity to deal with the lack of varieties, especially for high-risk ones. Meanwhile, Assembly Line Balancing (ALB) problem has been recognized as a prior thinking to (re)configure assembly lines via the balancing of their tasks among their workstations. Some conventional criteria, cycle time and overall workload are often considered during the balancing. This paper presents a novel model of ALB problem that incorporates assembly worker postures into the balancing. In addition to the conventional ALB criteria, a new criterion of posture diversity is defined and contributes to enhance the model. The proposed model suggests configurations of assembly lines via the balancing; so that the assigned workers encounter the opportunities of changing their body postures, regularly. To address uncertainties in the conventional criteria, a fuzzy goal programming is used, and an appropriate genetic algorithm is developed to deal with the model. Various computational tests are performed on the different models made with combinations of the three criteria mentioned above. Comparing the pay-offs among the combinations, results show that well balanced task allocation can be obtained through the proposed model.     

The patient bed assignment problem solved by autonomous bat algorithm

The patient bed assignment problem consists of managing, in the best possible way, a set of beds with particular features and assigning them to a set of patients with special requirements. This assignment problem can be seen an optimization problem, of which the intended aims are usually to minimize the number of internal movements within a unit and to maximize bed usage according to the levels of criticality of the patients, among others. The usual approaches for solving this problem follow a traditional model based on the constraint programming paradigm, mainly using hard constraints. However, in real-life problems, constraints that should ideally be satisfied are often violated. In this paper, we present a new model for the patient bed assignment problem based on the minimum sum of unsatisfied constraints. This technique enables the consideration of soft constraints in the potential solutions that exhibit the best performance. The aim is to find the assignment that minimizes a weighted sum of the unsatisfied constraints. To this end, we use an autonomous binary version of the bat algorithm, which is an optimization technique inspired by the bio-sonar behaviour of microbats, to find the best set of potential solutions without requiring any expert user knowledge to achieve an efficient solution process. To validate our proposal, we use our model to solve problem instances based on data from several hospitals, and we perform a detailed comparative statistical analysis with a traditional constraint programming solver and several well-known optimization algorithms, including the classic bat algorithm. Promising results show that our approach is capable of efficiently solving 30 instances with decreased solution times.     

An efficient procedure for finding best compromise solutions to the multi-objective assignment problem

In this paper, we consider the problem of determining a best compromise solution for the multi-objective assignment problem. Such a solution minimizes a scalarizing function, such as the weighted Tchebychev norm or reference point achievement functions. To solve this problem, we resort to a ranking (or k-best) algorithm which enumerates feasible solutions according to an appropriate weighted sum until a condition, ensuring that an optimal solution has been found, is met. The ranking algorithm is based on a branch and bound scheme. We study how to implement efficiently this procedure by considering different algorithmic variants within the procedure: choice of the weighted sum, branching and bounding schemes. We present an experimental analysis that enables us to point out the best variants, and we provide experimental results showing the remarkable efficiency of the procedure, even for large size instances.