Ishfaq Ahmad

Work place: Department of Mathematics and Statistics, Faculty of Basic and Applied Sciences, International Islamic University, 44000 Islamabad, Pakistan



Research Interests: Computational Mathematics, Mathematics of Computing, Mathematics


Dr Ishfaq Ahmad is an associate professor of statistics at International Islamic University International Islamic University Islamabad. He did his PHD in statistics from Chinese Academy of Sciences Beijing. In 2017 he joined Department of Mathematics as Assistant professor at King Khalid University Saudi Arabia. He has supervised many postgraduate students and widely published in journals of international repute.

Author Articles
Development a New Crossover Scheme for Traveling Salesman Problem by aid of Genetic Algorithm

By Ehtasham-ul-Haq Abid Hussain Ishfaq Ahmad

DOI:, Pub. Date: 8 Dec. 2019

This research work provides a detailed working principle and analysis technique of multi- offspring crossover operator. The proposed approach is an extension of the basic partially- mapped crossover (PMX) based upon survival of the fittest theory. It improves the performance of the genetic algorithm (GA) for solving the well-known combinatorial optimization problem, the traveling salesman problem (TSP). This study is based on numerical experiments of the proposed with other traditional crossover operators for eighteen benchmarks TSPLIB instances. The simulation results show a considerable improvement because the proposed operator enhances the opportunity of having better offspring. Moreover, the t-test also establishes the improved significance of the proposed operator. Its preferable results not only confirm the advantages over others, but also show the long run survival of a generation having a number of offspring more than the number of parents with the help of mathematical ecology theory.

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