A novel approach to metabolic network analysis using a Nash Equilibrium formulation is proposed. Enzymes are considered to be players in a multi-player game in which each player attempts to minimize the dimensionless Gibbs free energy associated with the biochemical reaction(s) it catalyzes subject to elemental mass balances. Mathematical formulation of the metabolic network as a set of nonline...

The safety and reliability of an electrical network depend on the performance protections utilized. Therefore, optimal coordination protective devices plays essential role. In this paper, a new algorithm, Equilibrium Optimizer (EO), which is based physical equation mass balance, implemented in problem Optimal Coordination Directional Overcurrent Relays (DOCRs). Moreover, proposed method uses Li...

Nonconvex nonlinear programming (NLP) problems arise frequently in water resources management, e.g., reservoir operations, groundwater remediation, and integrated water quantity and quality management. Such problems are usually large and sparse. Existing software for global optimization cannot cope with problems of this size, while current local sparse NLP solvers, e.g., MINOS (Murtagh and Saun...

Optimally minimizing delay times at signalized intersections can significantly improve both traffic flow and safety. However, most traffic flow optimizing tools do not measure the effect on safety. This study uses nonlinear programming (NLP) algorithms to optimally minimize delay times and employs both Safety performance functions (SPFs) and empirical Bayes (EB) before-after methodology to meas...

Recently, smart grids have been considered as one of the vital elements in upgrading current power systems to a system with more reliability and efficiency. Distributed generation is necessary for most of these new networks. Indeed, in all cases that DGs are used in distribution systems, protection coordination failures may occur in multiple configurations of smart grids using DGs. In different...

This paper expresses the output power of renewable generators and load demand as interval data develops economic dispatch (IED), well reactive optimization (IRPO) models. The two models are generalized into a specific type linear programming (LIP) nonlinear (NLIP), respectively. A security limits method (SLM) is proposed to solve LIP NLIP problems. As for LIP, maximum radii variables first calc...

In this article, a combinatorial optimization approach for estimating the electrical parameters in single-phase distribution transformers by considering voltage and current measures is presented. A nonlinear programming model was formulated to represent parametric estimation problem. This mathematical developed applying Kirchhoff’s laws equivalent electric circuit of transformer. To solve NLP e...

Solving linear programming (LP) and nonlinear (NLP) problems is momentous because of their wide applications in real-life problems. There no unified way to find the global optimum for NLPs. But on other hand, simplex algorithm, as dominating methodology LPs several decades moves only boundary (vertices) ignores vast majority feasible region process searching. In this article, we study two gradi...

We present a direct numerical method for the solution of an optimal control problem controlling growth LDL (Low-density Lipoprotein), HDL (High-density Lipoprotein) and plaque. The is constrained with system coupled nonlinear free mixed boundary partial differential equations consisting three parabolics one elliptic ordinary equations. In first step, original transformed from into fixed conditi...