in this paper, a linear programming problem is considered involving interval grey numbers as an extension of the classical linear programming problem to an inexact environment as well as fuzzy and stochastic environment. Hence, here a new approach for solving interval grey number linear programming problems is introduced without converting them to classical linear programming problems. The proposed method is established based on the PRIMAL SIMPLEX ALGORITHM where the cost coefficient row includes grey numbers. As an essential tool in the solving process, a theoretical discussion on grey arithmetic and in particular an ordering role for grey numbers is necessary to evaluate the optimality conditions of a candidate feasible solution. It is also emphasized that the discussed model and the solution process is useful for real situations and practical cases, when a kind of the grey number linear programming is appeared, such as Water Resource Management and Planning, Economics, etc. Finally, the proposed approach is illustrated by a numerical example.

Fuzzy set theory has been applied to many fields, such as operations research, control theory, and management sciences. We consider two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems. We state our recently established results and develop fuzzy PRIMAL SIMPLEX ALGORITHMs for solving these problems. Finally, we give illustrative examples.

The fuzzy PRIMAL-dual SIMPLEX method is a new and efficient method for solving linear programming problems with fuzzy variables. This ALGORITHM is based on duality results and, similar to the dual SIMPLEX method, begins with dual feasibility and proceeds to PRIMAL feasibility. An important difference between the dual SIMPLEX method and the PRIMAL-dual method is that in the PRIMAL-dual ALGORITHM, it is not required that the dual feasible solution to be basic. In this paper, we develop the PRIMAL-dual SIMPLEX method for solving fuzzy multiobjective linear programming problems. To this end, we utilize the fuzzy weighted sum scalarization method to present a fuzzy single objective optimization problem related to the fuzzy multiobjective linear programming problem. Then, by partitioning the weights of the weighted sum problem, we generalize the single objective PRIMAL-dual ALGORITHM to fuzzy multiobjective problems. By using the presented ALGORITHM, we can find a set of fuzzy Pareto optimal solutions. Presenting a set of fuzzy Pareto optimal solutions to the decision maker, enables him\her to select the best solution based on his\her preferences. Finally, we apply the proposed ALGORITHM for solving a three-objective optimization problem with fuzzy variables and compare the results with some existing methods.

Special conditions of wireless sensor networks, such as energy limitation, make it essential to accelerate the convergence of ALGORITHMs in this field, especially in the distributed compressive sensing (DCS) scenarios, which have a complex reconstruction phase. This paper presents a DCS reconstruction ALGORITHM that provides a higher convergence rate. The proposed ALGORITHM is a distributed PRIMAL-dual ALGORITHM in a bidirectional incremental cooperation mode where the parameters change with time. The parameters are changed systematically in the convex optimization problems in which the constraint and cooperation functions are strongly convex. The proposed method is supported by simulations, which show the higher performance of the proposed ALGORITHM in terms of convergence rate, even in stricter conditions such as the small number of measurements or the lower degree of sparsity.

A Long-term planning model is presented in this study optimizing Karoon-Dez reservoir system operation m Iran with hydropower generation, water supply, and environmental objectives. The matrix implementation of the large-scale resulting optimization model has been solved using dual-PRIMAL interior-point methods (DPIPMs) and multiobjective programming. These ALGORITHMs have shown to be promising especially when they take the advantage of sparsity structure of associated matrix formulation of the optimization problem with linear and quadratic functions. The computational time required for solving the Karoon-Dez reservoir system studied was less than 45 minutes. This is promising especially knowing that handling such an optimization model is very difficult using other techniques such as generalized reduced gradient (GRG) ALGORITHM of nonlinear programming and discrete dynamic programming with adequate fine representation of state variables of the model.

In this paper, an efficient extension of network SIMPLEX ALGORITHM is presented. In static scheduling problem, where there is no change in situation, the challenge is that the large problems can be solved in a short time. In this paper, the Static Scheduling problem of Automated Guided Vehicles in container terminal is solved by Network SIMPLEX ALGORITHM (NSA) and NSA+, which extended the standard NSA. The ALGORITHMs are based on graph model and their performances are at least 100 times faster than traditional SIMPLEX ALGORITHM for Linear Programs. Many random data are generated and fed to the model for 50 vehicles. We compared results of NSA and NSA+ for the static automated vehicle scheduling problem. The results show that NSA+ is significantly more efficient than NSA. It is found that, in practice, NSA and NSA+ take polynomial time to solve problems in this application.

In static scheduling problem, where there is no change in situation, the challenge is that the large problems can be solved in a short time. In this paper, the Static Scheduling problem of Automated Guided Vehicles in container terminal is solved by the Network SIMPLEX ALGORITHM (NSA). The ALGORITHM is based on graph model and their performances are at least 100 times faster than traditional SIMPLEX ALGORITHM for Linear Programs. Many random data are generated and fed to the model for 50 vehicles. The results show that NSA is fast and efficient. It is found that, in practice, NSA takes polynomial time to solve problems in this application.

In this paper, we consider the effects of exogenous disturbances on the closed-loop system of the congestion control problem in a network with general structure. This investigation is important since many of data flows in internet network are considered as unmodeled flows. In contrast to previous works, we suppose that both senders and links in the network have dynamics. Each sender updates its sending rate to minimize its own cost function. The network is modeled based on fluid flow approximation with nonlinear dynamics for the links. In this research, we first derive the conditions for the existence of the system equilibrium point taking into account the constraint sets of the problem. Then, we prove input-to-state stability (ISS) of the closed-loop system for the congestion control problem with input and output disturbances in the network links. We further show that the obtain results are valid even when the routing matrix of the network varies. Finally, we verify the theoretical results by simulation on two different multi-link networks.