Proper arrangement of facility layout is a key issue in management that influences efficiency and the profitability of the manufacturing systems. PARALLEL ROW ORDERING PROBLEM (PROP) is a special case of facility layout PROBLEM and consists of looking for the best location of n facilities while similar facilities (facilities which has some characteristics in common) should be arranged in a ROW and dissimilar facilities should be arranged in a PARALLEL ROW. As PROP is a new introduced NP-hard PROBLEM, only a mixed integer programming model is developed to formulate this PROBLEM. So to solve large scale instances of this PROBLEM, heuristic and meta-heuristic algorithms can be useful. In this paper, two strategies based on genetic algorithm (GA) and a novel population based simulated annealing algorithm (PSA) to solve medium and large instances of PROP are proposed. Also several test PROBLEMs of PROP in two groups with different sizes that have been extracted from the literature are solved to evaluate the proposed algorithms in terms of objective function value and computational time. According to the results, in the first group of instances, both algorithms almost have equal performances, and in the second group PSA shows better performance by increasing the size of test PROBLEMs.

Introduction The exponential distribution, because of its memoryless, has a central rule in reliability theory and survival analysis. But, this distribution is not a suitable model to fit the data sets in practical situations due to its constant hazard rate function. For this reason, some generalizations of the exponential distribution exist in the literature. The generalized exponential distribution is introduced by adding a shape parameter to the exponential distribution via the exponentiated method. This distribution admits both increasing and decreasing hazard rate function. For more information on the generalized exponential distribution and its applications, one can refer to Gupta and Kundu (2007) and Nadarajah (2011). Comparisons of PARALLEL systems with two independent heterogeneous exponential components are studied extensively in the literature. Boland et al. (١, ٩, ٩, 4) proved that the hazard rate order between two PARALLEL systems holds under the majorization order between the vectors of the hazard rate parameters. This result is extended to the likelihood ratio order by Dykstra et al. (1997). In this direction, Zhao and Balakrishnan (2012) obtained some characterization results concerning the hazard rate and likelihood ratio orders using the p-larger and weak majorization orders between the hazard rate parameters vectors. Yan et al. (2012) established sufficient conditions to compare two PARALLEL systems in the hazard rate and likelihood ratio orders. The present work provides a sufficient condition to compare PARALLEL systems comprising two independent heterogeneous generalized exponential components in the likelihood ratio order. Material and Methods The comparison of essential characteristics associated with lifetimes of technical systems is an exciting topic in reliability theory since it usually enables us to approximate complex systems with simpler systems and subsequently obtain various bounds for important ageing characteristics of the complex system. A convenient tool for this purpose is the theory of stochastic ORDERINGs. Results and Discussion Consider two PARALLEL systems with their component lifetimes following a generalized exponential distribution. In this paper, based on existing shape and scale parameters included in the distribution of one of the systems, we introduce a region such that if the vector of scale parameters of another PARALLEL system lies in that region, then the likelihood ratio ORDERING between the two systems hold. An extension of this result is also presented for the case when the lifetimes of components follow exponentiated Weibull distribution. Conclusion In this paper, based on the shape and scale vectors of parameters involved in the lifetime distribution of a PARALLEL system consisting of two independent heterogeneous generalized exponential components, a region is obtained such that if the scale vector of parameters of another PARALLEL system lies in this region, then the likelihood ratio order between systems holds.

In recent years, many studies have been presented on the interpretation and modeling of new PROBLEMs by basic models. One of the most widely used of these basic models is the Bin packing PROBLEM. Over time, the importance and power of this issue in modeling new PROBLEMs becomes clearer. This paper also attempts to interpret and model ``An ORDERING and assigning orders to supplier's PROBLEM'' by using one of the generalizations of the bin packing PROBLEM. There are many generalizations about the bin packing PROBLEM. In this paper, for the first time, generalization of the bin packaging PROBLEM called "developed Variable size and cost bin packing PROBLEM" is modeled, which increases the flexibility of the model in solving current PROBLEMs. Because the presented model is a bi-objective nonlinear programming type and NP-hard one to be solved in a reasonable time, a well-known multi-objective evolutionary algorithm, namely a Non-dominated Sorting Genetic Algorithm (NSGA-II), is proposed. To verify the obtained solution and evaluate the performance of the NSGA-II, the rmvarepsilon-constraint method is developed in solving small-sized PROBLEMs. In large-sized PROBLEMs, the test PROBLEMs are solved by the proposed NSGA-II. Then, the Pareto-optimal solutions are evaluated by mean ideal distance, diversification, and time metrics.

In this paper, we propose a novel patch ORDERING approach to Single Image Super-Resolution (SR) algorithm which is called as Patch ORDERING Approach to Single Image Super Resolution (POSR). We aimed at selecting more informative High-Resolution (HR) and Low-Resolution (LR) patches for single image SR algorithms based on sparse representation and dictionary learning. Our proposed POSR algorithm, first ordered HR and LR patches for each training images based on minimization of total variation measure (TV). Then, it assigned a sampling step for patch selection in each image. In this way, training patches were extracted based on image texture complexity. This leads to training dictionaries with the high and low resolution more efficiently. Unlike other methods which have used additional restrictions in high resolution image reconstruction phase, proposed method, has only used the basic assumption of sparse representation super resolution. The experimental results for quantitative criteria (PSNR, RMSE, SSIM and elapsed time), human observation as a qualitative measure and computational complexity verify the improvements offered by the proposed POSR algorithm.

The Project Scheduling PROBLEM (PSP) is to determine the sequence and schedule of activities of a project in a way that decision-makers' objectives are optimized without violating precedence constraints. Due to the scarcity of resources, in recent decades, the Resource-Constrained Project Scheduling PROBLEM (RCPSP) has attracted the attention of researchers and practitioners. The main feature of the resource-constrained project scheduling PROBLEM is that it takes into account resource constraints, which signi, cantly a, ect the solutions obtained for project scheduling PROBLEMs, in addition to other usual constraints, e. g. precedence constraints. The Resource Leveling PROBLEM (RLP) is a special case of the resource-constrained project scheduling PROBLEM in which the resource usage variation between consecutive time periods is minimized. Traditionally, the project scheduling PROBLEM and the material ORDERING PROBLEM are separately investigated. However, simultaneous planning of both these PROBLEMs, i. e., resource constrained project scheduling and material procurement, which can reduce total project costs, has been rarely addressed. In this study, the resource leveling PROBLEM which aims at controlling the variations of using the resources during the project execution and the material ORDERING PROBLEM are simultaneously addressed. The material ORDERING is considered to be subject to all-unit discount. In this regard, a mixed-integer linear programing model is proposed in which the starting and ending times of activities are determined so that in addition to minimizing the variations of resource utilization, total costs related to the material ORDERING PROBLEM (sum of ORDERING costs as well as holding and purchase costs) are minimized. It is assumed that the intensity of the variable execution directly a, ects the progress of activities. Also, the duration of activities is considered exible. Numerical results con, rm a tradeo,between material ORDERING and resource leveling costs. Finally, GAMS software as well as genetic algorithm are used to solve di, erent-sized test PROBLEMs, and results are discussed.

This article addresses a single ROW facility layout PROBLEM where the objective is to optimize the arrangement of some rectangular facilities with different dimensions on a line. Regarding the NP-Hard nature of the considered PROBLEM, a hybrid meta-heuristic algorithm based on simulated annealing has been proposed to obtain a near optimal solution. A number of test PROBLEMs are randomly generated and the results obtained by the proposed hybrid meta-heuristic are compared with exact solutions. The results imply that the proposed hybrid method provides more efficient solutions for the large-sized PROBLEM instances.

Background and Objectives:-similarity PROBLEM defined as measuring the similarity among objects and finding a group of objects from a dataset that have the most similarity to each other. This PROBLEM has been become an important issue in information retrieval and data mining. Theory of this concept is mathematically proven, but it practically has high memory complexity and is so time consuming. Besides, the solutions found by metaheuristics are not exact. Methods: This paper is conducted to propose an exact method to solve similarity PROBLEM reducing the memory complexity and decreasing the execution time by PARALLELism using Open-MP. The experiments are performed on the application of text document resemblance. Results: It has been shown that the memory complexity of the proposed method is decreased to , and the experimental results show that this method accelerates the speed of the computations about 5 times. Conclusion: The simulated results of the proposed method display a good improvement in speed, the used memory space, and scalability compared with the previous exact method.

This study compares two PARALLEL systems whose components are taken from the unit gamma Gompertz-F family. The comparisons are accomplished according to various stochastic orders, including the usual stochastic order, the reversed hazard rate order, and the likelihood ratio order by way of the majorization of shape parameters. For additional research, we investigate the lifetime of system components to be dependent or independent under conditions that the baseline distribution function of components is identical or non-identical. A numerical example based on real-life data is presented as an illustration.

In this paper the PROBLEM of job shop scheduling with PARALLEL machines in each stages is discussed. The objective is to minimize the maximum completion time (makespan). This PROBLEM is a combination of two classic PROBLEMs of job shop and PARALLEL machines which in this case PARALLEL machines has been used as kind of flexibility in the job shop PROBLEM. The review of literature has shown that this PROBLEM has not been discussed yet. After presenting the mathematical mode, heuristic algorithms are used for solving this NP-hard PROBLEM. Regarding this, five algorithms are presented and a lower bound is developed. Finally all these algorithms have been analyzed. According to results the proposed algorithm of H2 works better than the others when there are few jobs. As the number of jobs increases H1 is more efficient than H2 asymptotically. Also the efficiency of H3 algorithm is the worst among the rest.