Parallel machine scheduling problem is a scheduling problem in which jobs are scheduled on available machines in a parallel manner. The aim of the problem is to minimize or reduce the makespan value that is the total completion time of all the jobs. Swarm Intelligence-based algorithms are performing well for solving the various scheduling problems. The Grasshopper Optimization Algorithm (GOA), is a swarm intelligence-based algorithm that relies on the natural behavior of grasshoppers. This research proposes an improved rendition of GOA using a membership-based function called the Open Left. The proposed approach is termed as Open Left Grasshopper Optimization Algorithm (OLGOA). This paper proposes an effective solution for solving parallel machine scheduling problems using OLGOA. The obtained outcomes are evaluated and judged against renowned strategies available in recent studies. The outcomes support the suggested methodology.