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Accelerating the sparse matrix-vector multiplication (SpMV) on the graphics processing units (GPUs) has attracted considerable attention recently. We observe that on a specific multiple-GPU platform, the SpMV performance can usually be greatly improved when a matrix is partitioned into several blocks according to a predetermined rule and each block is assigned to a GPU with an appropriate storage format. This motivates us to propose a novel multi-GPU parallel SpMV optimization model. Our model involves two stages. In the first stage, a simple rule is defined to divide any given matrix among multiple GPUs, and then a performance model, which is independent of the problems and dependent on the resources of devices, is proposed to accurately predict the execution time of SpMV kernels. Using these models, we construct in the second stage an optimally multi-GPU parallel SpMV algorithm that is automatically and rapidly generated for the platform for any problem. Given that our model for SpMV is general, independent of the problems, and dependent on the resources of devices, this model is constructed only once for each type of GPU. The experiments validate the high efficiency of our proposed model.

Buy-price auction has been successfully used as a new channel of online sales. This paper studies an online sequential buy-price auction problem, where a seller has an inventory of identical products and needs to clear them through a sequence of online buy-price auctions such that the total profit is maximized by optimizing the buy price in each auction. We propose a methodology by dynamic programming approach to solve this optimization problem. Since the consumers’ behavior affects the seller’s revenue, the consumers’ strategy used in this auction is first investigated. Then, two different dynamic programming models are developed to optimize the seller’s decision-making: one is the clairvoyant model corresponding to a situation where the seller has complete information about consumer valuations, and the other is the Bayesian learning model where the seller makes optimal decisions by continuously recording and utilizing auction data during the sales process. Numerical experiments are employed to demonstrate the impacts of several key factors on the optimal solutions, including the size of inventory, the number of potential consumers, and the rate at which the seller discounts early incomes. It is shown that when the consumers’ valuations are uniformly distributed, the Bayesian learning model is of great efficiency if the demand is adequate.

In this paper, a new approach is proposed to solve group decision making (GDM) problems where the preference information on alternatives provided by decision makers (DMs) is represented in incomplete fuzzy preference relations. In order to make the collective opinion close each decision maker's opinion as near as possible, an optimization model is constructed to integrate the incomplete fuzzy preference relations and to compute the collective ranking values of alternatives. The ranking of alternatives or selection of the most desirable alternative(s) is directly obtained from the derived collective ranking values. A numerical example is also used to illustrate the applicability of the proposed approach.

In a broad spectrum, software metrics play a vital role in attribute assessment, which successively moves software projects. The metrics measure gives many crucial facets of the system, enhancing the system quality of software developed. Moreover, maintenance is the correction process that works out in the software system once the software is initially made. The noteworthy characteristic of any software is ‘change,’ and as a result, additional concern ought to be taken in developing software. So, the software is expected to be modified effortlessly (maintainable). Predicting software maintainability is still challenging, and accurate prediction models with low error rates are required. Since there are so many modern programming languages on the horizon. To accurately measure software maintainability, new techniques have to been introduced. This paper proposes a maintainability index (MI) by considering various software metrics by which the error gets minimized. It also intends to adopt a renowned optimization algorithm, namely Firefly (FF), for the optimum result. The proposed Base Model-FF is compared to other traditional models like BM-Differential Evolution (BM-DE), BM-Artificial Bee Colony (BM-ABC), BM-Particle Swarm Optimization (BM-PSO), and BM-Genetic Algorithm (BM- GA) in terms of performance metrics like Differential ratio, correlation coefficient, and Random Mean Square Error (RMSE).

This research represents a comprehensive exploration of optimization policies pertaining to burn-in, quality control, and preventive maintenance for light-emitting devices. Utilizing a MATLAB-based computational model, we embarked on an in-depth investigation of the complex interplay and dependencies between these policies. Our findings illustrated that, with optimal burn-in time, cut-off threshold, and replacement interval, the total cost per usage duration was significantly reduced. Additionally, we investigated the system performance with and without quality control. It was observed that an increase in burn-in time corresponded to an increase in cost. The absence of quality control resulted in a similar pattern with the replacement period, where the cost remained constant after a certain replacement period. Conversely, the implementation of quality control indicated a direct relationship between burn-in time and cost, and an inverse relationship between replacement period and cost.

In real portfolio selection, the investor usually exhibits some psychological behaviors such as reference dependence, loss aversion and so on and also has the requirements of wealth expectation in his/her mental accounts, but the in-depth study on this aspect is still lacking. The objective of this paper is to develop a method for the portfolio selection in which the multiple psychological behaviors (i.e., the reference dependence, the probability overestimation or underestimation, the loss aversion and the diminishing sensitivity) and the mental accounts of the investor are considered simultaneously. First, for the multiple psychological behaviors of the investor, the calculation formula of overall comprehensive utility of portfolio of all the candidate assets is given according to the cumulative prospect theory. Then, a portfolio optimization model with the probabilistic constraints is constructed to determine the desirable portfolio. For the model, the objective is to maximize the overall comprehensive utility of portfolio of the assets, and the requirements of the wealth expectations in the mental accounts of the investor and the limitation of initial investment wealth are considered as the constraints. Further, the definition of the available state set is given, and the available state sets for each mental account can be determined according to the definition. Based on the determined available state sets, the model can be converted into the multiple linear integer programming problems. By solving the linear integer programming problems, the optimal portfolio can be obtained. In addition, a numerical example is used to illustrate the use of the proposed method. Finally, an empirical study is given to validate our research work.

The aim of this research is to develop optimization models in deriving optimum target of key characteristic (KC). There are two kinds of product KCs introduced in this paper, namely performance and dimension product KC. The performance product KC target values must be determined by balancing customer and designer utilities subject to design cost and time provided by a company. The KCs of a product can be visualized using a KC flow-down which shows the hierarchical structure of the product. The flow-down may consist of many levels from product KC to process KC. Using axiomatic design as a methodology to map the flow-down, we conclude that product KC, assembly-components KC, and process KC are in functional domain, physical domain, and process domain respectively. In this paper, the objective function of the model for deriving optimum product KC target is to minimize utility gap between customer and designer subject to design cost and time. The assembly-component KCs have to be derived considering the product KC targets. In the absence of product KC target, the objective function of the model is to maximize the desired effect or minimizing the undesired effect. In the existence of product KC target, the objective function of the model is to attain the target considering technical constraints of the product. We use a shaft design problem as a numerical example to show the implementation of the models.

An option available to a small business owner who wishes to sell his company is to help a buyer with the financing. However, while intent on selling the business, she/he typically does not want to become a supplier of permanent capital. The seller can provide bridge financing until the buyer lines up a permanent capital source. This paper presents an EXCEL algorithm for estimating the amount the buyer must borrow to restructure the bridge loan. The algorithm is set up to minimize the buyer's interest expense while meeting loan covenants a lender imposes. The restructured financing can include a combination of short- and long-term loans in order to take advantage of the lower cost of short-term financing. An example demonstrates how the algorithm works.

In Pakistan, a hierarchical healthcare system is an efficient way of addressing the issue of limited and insufficient healthcare services. Identifying the various degrees of disease based on the doctor’s diagnosis is an important step in developing the hierarchical healthcare treatment structure. This research presents a framework for dealing with the issue of diagnosis values presented as “picture fuzzy numbers (PFNs)”. Specifically, the goal of this study is to establish some innovative operational laws and “aggregation operators” (AOs) in a picture fuzzy environment. In this regard, we proposed some new neutral or fair operational laws that incorporate the concept of proportional distribution in order to achieve a neutral or fair remedy to the positive, neutral and negative aspects of PFNs. Based on the developed operational laws, we proposed the “picture fuzzy fairly weighted average operator” and the “picture fuzzy fairly ordered weighted averaging operator”. Compared to previous techniques, the proposed AOs provide more generalized and reliable. Furthermore, using proposed AOs with multiple decision-makers and partial weight information under PFNs, a “multi-criteria decision-making” algorithm is developed. Finally, we provide an example to show how the novel approach can aid hierarchical treatment systems. This is essential for merging the healthcare capabilities of the general public and optimizing the medical care system’s service performance.

Mangasarian and Stone⁹ observed that the problem of computation of equilibrium points of bimatrix games is equivalent to solving a certain quadratic programming problem with linear constraints. We extend this approach of Mangasarian and Stone⁹ for generalized bimatrix game problem and SC/AR-AT mixture class of stochastic game problem. We establish an alternative necessary and sufficient condition for the existence of optimal stationary strategies for a mixture class of zero-sum stochastic game in which the set of states are partitioned into sets S₁, S₂ and S₃ so that the law of motion is controlled by Player I alone when the game is played in S₁, Player II alone when the game is played in S₂ and in S₃ the reward and transition probabilities are additive. We formulate and discuss about the computation of value vector and optimal stationary strategies for SC/AR-AT mixture class of stochastic game as an optimization model for both discounted and undiscounted case.

In order to improve the economy of power grid, optimize the allocation of resources, and improve the power grid investment income, we apply diverse portfolio theory. At present, the main user side given random power supply approaches is consist of regional electricity, cross-regional transmission, and with the aid of energy storage system to charge and discharge. The different current ways have different characteristics. We take the three paths as resources, each path under random power network interconnection benefits as income, synthetically considering various constraints and reasonably setting up random power to participate in the proportion of three paths. We take the system total benefit maximization as the objective function for multivariate combination way to assist the construction of electric power resource utilization model. Then we can obtain the optimal grid power resources.