Fuzzy Random Bimatrix Games Based on Possibility and Necessity Measures

In this study, we formulate bimatrix games with fuzzy random payoffs, and introduce equilibrium solution concepts based on possibility and necessity measures. It is assumed that each player has linear fuzzy goals for his/her payoff. To obtain equilibrium solutions based on the possibility and necessity measures, we propose two algorithms in which quadratic programming problems are solved repeatedly until equilibrium conditions are satisfied.

Numerical Approach for Detecting the Resonance Effects of Drilling during Assembly of Aircraft Structures

This paper is devoted to the development of a numerical approach that allows quick detection of the conditions favorable for the beginning of noticeable vibrations during drilling. The main novelty of the proposed approach lies in taking into account the deviations of the assembled compliant parts during non-stationary contact analysis by means of variation simulation. The approaches to stationary analysis of assembly quality are expanded and generalized for modeling such non-stationary effects as vibration and resonance. The numerical procedure is based on modeling the stress–strain state of the assembled structures by solving the corresponding transient contact problem. The use of Guyan reduction, the node-to-node contact model and the application of the generalized α method allow the reformulation of the contact problem in terms of a series of quadratic programming problems. The algorithm is thoroughly tested and validated with commercial software. The efficiency of the developed numerical procedure is illustrated by analysis of the test joints of two aircraft panels. The unsteady process of drilling the panels with periodic drilling force was simulated. The influence of deviations in the shape of the parts on the non-stationary interlayer gap was modeled by setting different initial gaps between parts. It is shown that the oscillation amplitudes of the interlayer gap depend on the initial gaps and do not correlate with the mean value of the stationary residual gap. Thus, non-stationary analysis provides new information about the quality of the assembly process, and it should be applied if the assembly process includes periodic impact on the assembled parts.

The PPADMM Method for Solving Quadratic Programming Problems

In this paper, a preconditioned and proximal alternating direction method of multipliers (PPADMM) is established for iteratively solving the equality-constraint quadratic programming problems. Based on strictly matrix analysis, we prove that this method is asymptotically convergent. We also show the connection between this method with some existing methods, so it combines the advantages of the methods. Finally, the numerical examples show that the algorithm proposed is efficient, stable, and flexible for solving the quadratic programming problems with equality constraint.

Using concave optimization methods for inexact quadratic programming problems with an application to waste management

Quadratic programming is potentially capable of strategic decision making in real world problems. However, practical problems rarely conform to crisp parameters, and hence the prospects of these problems with inexact parameters are inevitably higher. The existing studies regarding public welfare schemes/ organizations reveal that their objectives end up as minimization of cost functions and are governed by linear or concave quadratic programming problems. The present study proposes a method that can be applied to concave type quadratic objective function subject to linear constraints with inexact parameters. A comparison is also drawn with existing methods to establish its simplicity and efficiency. Further, a numerical example is illustrated, and finally, a waste management problem is formulated and solved using the proposed method.

Semi-Proximal Augmented Lagrangian-Based Decomposition Methods for Primal Block-Angular Convex Composite Quadratic Conic Programming Problems

We first propose a semi-proximal augmented Lagrangian-based decomposition method to directly solve the primal form of a convex composite quadratic conic-programming problem with a primal block-angular structure. Using our algorithmic framework, we are able to naturally derive several well-known augmented Lagrangian-based decomposition methods for stochastic programming, such as the diagonal quadratic approximation method of Mulvey and Ruszczyński. Although it is natural to develop an augmented Lagrangian decomposition algorithm based on the primal problem, here, we demonstrate that it is, in fact, numerically more economical to solve the dual problem by an appropriately designed decomposition algorithm. In particular, we propose a semi-proximal symmetric Gauss–Seidel-based alternating direction method of multipliers (sGS-ADMM) for solving the corresponding dual problem. Numerical results show that our dual-based sGS-ADMM algorithm can very efficiently solve some very large instances of primal block-angular convex quadratic-programming problems. For example, one instance with more than 300,000 linear constraints and 12.5 million nonnegative variables is solved to the accuracy of 10-5 in the relative KKT residual in less than a minute on a modest desktop computer.

A Fuzzy Interactive BI-objective Model for SVM to Identify the Best Compromise Solution for Measuring the Degree of Infection With Corona Virus Disease (Covid-19)

A support vector machine (SVM) learns the decision surface from two different classes of the input points. In several applications, some of the input points are misclassified and each is not fully allocated to either of these two groups. In this paper a bi-objective quadratic programming model with fuzzy parameters is utilized and different feature quality measures are optimized simultaneously. An α-cut is defined to transform the fuzzy model to a family of classical bi-objective quadratic programming problems. The weighting method is used to optimize each of these problems. For the proposed fuzzy bi-objective quadratic programming model, a major contribution will be added by obtaining different effective support vectors due to changes in weighting values. The experimental results, show the effectiveness of the α-cut with the weighting parameters on reducing the misclassification between two classes of the input points. An interactive procedure will be added to identify the best compromise solution from the generated efficient solutions. The main contribution of this paper includes constructing a utility function for measuring the degree of infection with coronavirus disease (COVID-19).