In this study, an identical parallel machine scheduling problem (IPMSP) with sequence-dependent setup times, which is significantly crucial in literature, is studied. There are different heuristics and metaheuristics for the problem in the literature. The representation method used in these studies is usually the permutation type representation, where each number corresponds to a job. The order of these numbers represents the order of the jobs in the machines. In this study, new solution representations are presented. A classical genetic algorithm and two new genetic algorithms using the proposed solution representations are compared by using randomly generated instances to show the success of the proposed representations. Diversification of the solution space is expanded, and the same results are eliminated with these solution representations. Specifically, the new algorithms generate better results than the classical genetic algorithm for large sized problems.