In this work, the process parameters optimization problems of abrasive waterjet machining process are solved using a recently proposed metaheuristic optimization algorithm named as Jaya algorithm and its posteriori version named as multi-objective Jaya (MO-Jaya) algorithm. The results of Jaya and MO-Jaya algorithms are compared with the results obtained by other well-known optimization algorithms such as simulated annealing, particle swam optimization, firefly algorithm, cuckoo search algorithm, blackhole algorithm and bio-geography based optimization. A hypervolume performance metric is used to compare the results of MO-Jaya algorithm with the results of non-dominated sorting genetic algorithm and non-dominated sorting teaching–learning-based optimization algorithm. The results of Jaya and MO-Jaya algorithms are found to be better as compared to the other optimization algorithms. In addition, a multi-objective decision making method named PROMETHEE method is applied in this work in order to select a particular solution out-of the multiple Pareto-optimal solutions provided by MO-Jaya algorithm which best suits the requirements of the process planer.