Growth of the world population, increasing demand for fossil fuel consumption and consequently increasing threat of global warming, has extended the need for production and use of clean fuels and normal hydrogen is an important utility in the production of clean fuels. In this paper, a mathematical optimization method is applied which is based on non-linear Programming of superstructure for minimizing the consumption of hydrogen. The method considers all the pressure constraints and is suited for revamping industrial systems. The optimum placement of new equipments like purification unit has been also considered. It is tried to verify the method adopted, in addition, an industrial case study has been carried out.

Nonlinear Knapsack Problems (NKP) are the alternative formulation for the multiple-choice knapsack problems. A powerful approach for solving NKP is dynamic Programming which may obtain the global optimal solution even in the case of discrete solution space for these problems. Despite the power of this solution approach, it computationally performs very slowly when the solution space of the problems grows rapidly. In this paper the authors developed a procedure for improving the computational efficiency of the dynamic Programming for solving KNP. They incorporate three routines; the imbedded state, surrogate constraints, and bounding scheme, in the dynamic Programming solution approach and developed an algorithmic routine for solving the KNP. An experimental study for comparing the computational efficiency of the proposed approach with the general dynamic Programming approach is also presented.

A constrained Nonlinear optimization method based on Nonlinear Programming techniques has been applied to map geometry of bedrock of sedimentary basins by inversion of gravity anomaly data. In the inversion, the applying model is a 2-D model that is composed of a set of juxtaposed prisms whose lower depths have been considered as unknown model parameters. The applied inversion method is a Nonlinear one, which minimizes the objective functions by definition of different objective functions and an initial simple model to improve the initial model parameters.In this study, for different cases, sufficient objective functions are defined based on the condition which is encountered in the inverse problem. To control the under- determinacy part of the inverse problem and to prevent unreasonable instability in the resultant model, damping terms are added to the objective function. The act of synthetic inversion for different cases of parameterization has been examined and the results are analyzed. The results have almost depicted the recovery of the model and also fitting of the original and model response data. In addition, the method has been used to invert real gravity data in Aman Abad area. From the inversion results, depths of the basin, features like fractures and uplift in bedrock, along specific profiles have been determined. Thicker parts of sediments in the basin along the profiles have also been recognized, which have the potential for exploring drinking water in this area.