基于多品种生产的预制梁厂设计优化模型的研究

针对我国现阶段基于多品种生产的预制梁厂设计和排产传统方法的缺陷,通过对预制梁厂设计和生产影响因素的调查与分析,结合优化理论与方法,建立了基于多品种生产的预制梁台设计和预制梁厂排产优化模型,并进行了实例验证,将优化方法同传统算法相比较,证明优化模型具有明显的优势,能够较好地辅助施工单位进行预制梁厂设计和生产决策。     

图模型匹配:一种新的凹松弛函数及算法

将问题中的置换矩阵放松为双随机矩阵是近年来近似图匹配算法的一个重要发展方向. 它的本质在于将离散的图匹配问题转换成一个连续优化问题,而一般来讲, 相对于离散优化,连续优化问题的近似求解将更为容易. 但随之带来的一个问题是如何有效地将连续优化得到的双随机矩阵重新映射回一个置换矩阵. 最近文献中提出了一种针对于无向无自环图的凹松弛(Concave relaxation)函数,使得算法中的双随机矩阵可以平滑地收敛到一个置换矩阵, 并得到优异的匹配精度.但除了无向且无自环图,文献中还没有针对其他类型图模型的凹松弛函数. 本文提出一种针对于有向无自环图匹配问题的凹松弛函数, 并在此基础上给出一种图匹配算法.大量对比实验验证了本文提出模型及算法的有效性.     

基于凸松弛方法的医学 B 超图像快速分割

利用活动轮廓线方法进行图像分割的一个重要缺陷是目标函数是非凸的, 这不仅使得分割结果容易陷于局部极小, 而且还使得一些快速算法无法开展.本文首先从贝叶斯风险估计的方法出发,针对B超幅度图像, 给出一种基于Rayleigh分布的活动轮廓线模型. 然后结合凸松弛的方法,得到一个新的放松的凸模型.原有模型和放松后模型的关系可由定理1给出. 最后结合分裂Bregman算法, 给出基于B超分割模型的快速算法.与传统梯度下降法相比较,本文提出的算法不仅能得到全局最优解,而且在算法收敛速度上也 大大优于梯度下降法.     

Type II robotic assembly line balancing problem: An evolution strategies algorithm for a multi-objective model

In this paper a different type II robotic assembly line balancing problem (RALB-II) is considered. One of the two main differences with the existing literature is objective function which is a multi-objective one. The aim is to minimize the cycle time, robot setup costs and robot costs. The second difference is on the procedure proposed to solve the problem. In addition, a new mixed-integer linear programming model is developed. Since the problem is NP-hard, three versions of multi-objective evolution strategies (MOES) are employed. Numerical results show that the proposed hybrid MOES is more efficient.     

Combined forecasts in portfolio optimization: A generalized approach

In this paper a general mathematical model for portfolio selection problem is proposed. By considering a forecasting performance according to the distributional properties of residuals, we formulate an extended mean-variance-skewness model with 11 objective functions. Returns and return errors for each asset obtained using different forecasting techniques, are combined in optimal proportions so as to minimize the mean absolute forecast error. These proportions are then used in constructing six criteria related to the mean, variance and skewness of return forecasts of assets in the future and forecasting errors of returns of assets in the past. The obtained multi-objective model is scalarized by using the conic scalarization method which guarantees to find all non-dominated solutions by considering investor preferences in non-convex multi-objective problems. The obtained scalar problem is solved by utilizing F-MSG algorithm. The performance of the proposed approach is tested on a real case problem generated on the data derived from Istanbul Stock Exchange. The comparison is conducted with respect to different levels of investor preferences over return, variance, and skewness and obtained results are summarized.     

A computational study on the quadratic knapsack problem with multiple constraints

The quadratic knapsack problem (QKP) has been the subject of considerable research in recent years. Despite notable advances in special purpose solution methodologies for QKP, this problem class remains very difficult to solve. With the exception of special cases, the state-of-the-art is limited to addressing problems of a few hundred variables and a single knapsack constraint.In this paper we provide a comparison of quadratic and linear representations of QKP based on test problems with multiple knapsack constraints and up to eight hundred variables. For the linear representations, three standard linearizations are investigated. Both the quadratic and linear models are solved by standard branch-and-cut optimizers available via CPLEX. Our results show that the linear models perform well on small problem instances but for larger problems the quadratic model outperforms the linear models tested both in terms of solution quality and solution time by a wide margin. Moreover, our results demonstrate that QKP instances larger than those previously addressed in the literature as well as instances with multiple constraints can be successfully and efficiently solved by branch and cut methodologies.     

Solving knapsack problems on GPU

A parallel implementation via CUDA of the dynamic programming method for the knapsack problem on NVIDIA GPU is presented. A GTX 260 card with 192 cores (1.4 GHz) is used for computational tests and processing times obtained with the parallel code are compared to the sequential one on a CPU with an Intel Xeon 3.0 GHz. The results show a speedup factor of 26 for large size problems. Furthermore, in order to limit the communication between the CPU and the GPU, a compression technique is presented which decreases significantly the memory occupancy.     

Optimal cyclic single crane scheduling for two parallel train oilcan repairing lines

Crane is widely used to move a heavy object from one place to another not only in manufacturing industry but also service industry. As an important resource in the train oilcan repairing, crane scheduling affects directly the productivity of the systems. In this paper, we study cyclic single crane scheduling problem with two parallel train oilcan repairing lines, where jobs are loaded into the line at one end and unloaded at the other end. The processing time at each workstation must be within a given range. There is no buffer between these stations. A crane is used to move jobs between the workstations in two parallel lines. The objective is to schedule the moves to minimize the production cycle. We proposed a time way diagram for two parallel lines and developed a mixed integer linear programming model. Then we extended the model to the scheduling problem with multi-station to eliminate the bottleneck in lines. Examples are given to demonstrate the effectiveness of the model.     

Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis

A mixed integer linear model for selecting the best decision making unit (DMU) in data envelopment analysis (DEA) has recently been proposed by Foroughi [Foroughi, A. A. (2011a). A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers and Industrial Engineering, 60(4), 550–554], which involves many unnecessary constraints and requires specifying an assurance region (AR) for input weights and output weights, respectively. Its selection of the best DMU is easy to be affected by outliers and may sometimes be incorrect. To avoid these drawbacks, this paper proposes three alternative mixed integer linear programming (MILP) models for identifying the most efficient DMU under different returns to scales, which contain only essential constraints and decision variables and are much simpler and more succinct than Foroughi’s. The proposed alternative MILP models can make full use of input and output information without the need of specifying any assurance regions for input and output weights to avoid zero weights, can make correct selections without being affected by outliers, and are of significant importance to the decision makers whose concerns are not DMU ranking, but the correct selection of the most efficient DMU. The potential applications of the proposed alternative MILP models and their effectiveness are illustrated with four numerical examples.