احادیث کی روشنی میں عصر حاضر کے چند اہم مالی معاملات کا تحقیقی جائزہ

Islam is a global religion and has provided a comprehensive code of life applicable in every age. Economy is one of its foremost priorities and gives basic principles to its followers to exercise a legal and favorable mean of earning. In Islamic economic system there are many ways and sources that have been prohibited or have not been recommended. As in our daily life we face those modes of financing, so in this article they have been comparatively analyzed in light of the sayings of the Prophet (S.A.W) in order to explore its legitimacy.

Development of Hybrid Metaheuristic for Global Optimization.

Metaheuristics is a research area that delivers general purpose high quality optimization algorithms, proved effectual in dealing with complex global optimization problems. Success of metaheuristics greatly depends on their aptitude to establish equilibrium between their essential characters: exploration and exploitation. But the advent of No Free Lunch theorems by Wolpert and Macready established a general opinion that all algorithms perform equally when averaged over the whole function space and hence none of them can be claimed to be the best over the entire function space. For this reason, the basic algorithms require essential refinements and enhancements. The main goal of this thesis is twofold: to develop new effective hybrid metaheuristic strategies for solving selected global optimization problems and to analyze the performances of developed hybrid metaheuristics on mathematical benchmark functions and complex real world problems that can be modeled as global optimization problems. Generally, hybridization is carried out by integrating powerful components of different algorithms. The first hybrid metaheuristic proposed in this work is Controlled Showering Optimization (CSO) algorithm which is a combination of Artificial Showering Algorithm and frame based search mechanism. The second proposed hybrid algorithm is Cooperative Multi-Simplex algorithm (CMSA) that is based on collaborative search of multiple simplexes working under the iterations of a Non- Stagnated Nelder-Mead Simplex algorithm (NS-NMSA). The evolvement of the provably convergent variant NS-NMSA is also carried out in this work by identifying and coping the failures and stagnations of standard Nelder-Mead simplex algorithm. Multi-Simplex Imperialist Competitive Algorithm (MS-ICA) is the third hybrid metaheuristic which is designed by embedding NS-NMSA iterations in Imperialist Competitive Algorithm. The fourth hybrid metaheuristic designed in this continuation is obtained by integrating CMSA and Differential Evolution (DE) algorithm. In a specifically constructed computational framework, this hybrid algorithm in collaboration with Padé approximation is named as hybrid Evolutionary Padé Approximation (EPA) scheme. The efficiencies of developed hybrid metaheuristics are validated empirically along with some theoretical results. Statistical analysis of simulation results of CSO applications to diversified small as well as large scale benchmark functions is conducted for evaluating its computational efficiency and consistency. The posterior non-parametric statistical analyses of the results indicate significantly better performance of CSO algorithm. Theoretical convergence results of NS-NMSA are also accompanied by numerical simulations on reported counter examples and a test suite of 24 benchmark functions. The two proposed hybrid algorithms, CMSA and MS-ICA, are applied to solve physical nonlinear systems of equations and excellent results are observed. Finally the proposed EPA framework is implemented for numerical treatments of the nonlinear model of virus propagation in computer networks and the model of Dengue fever with incubation period of virus. Numerical simulations and residuals based error analysis confirm the abilities of the proposed hybrid EPA scheme to preserve the essential characteristics of the epidemiological models.