Abstract
The Kingdom of Saudi Arabia pays special attention and care to pilgrims by harnessing human and physical capabilities to serve the pilgrims, facilitate their performance of their rituals and overcome the difficulties they may face during their stay in the Kingdom. Achieving the Kingdom's objective of facilitating the reception of an increasing number of Muslims from around the world to do the Hajj and Umrah rituals requires conducting scientific research that provides optimal solutions to achieve future goals and aspirations. Hence, this paper seeks to study the current situation of the process of transporting pilgrims from Arafat to Muzdalifah in groups (which is called Tafweej), and then develop this process using the Harmony Search Algorithm (HSA). Several hard and soft constraints are developed to regulate the scheduling process. The results proved that the proposed solution was able to triple the number of pilgrims, satisfying all hard constraints and most soft ones. This finding means that accommodation places in Muzdalifah may be exploited at a rate of three times the present situation.