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Self-adaptation in evolutionary computation refers to the encoding of parameters into the chromosome to allow for the self-organization process to act on the parameters in addition to the design variables. This paper investigates the feasibility of introducing a self-adaptive mutation operator into a real-coded evolutionary algorithm called the generalized generation gap (G3) algorithm. G3 is currently one of the most efficient as well as effective state-of-the-art real-coded genetic algorithms (RCGAs) but the drawback is that its performance on multimodal optimization problems is known to be poor compared to unimodal optimization problems. In this research, our objective is to introduce a self-adaptive mutation operator into G3, of which the mutation decision parameter is evolved along with the search variables during the evolutionary optimization process. The proposed algorithm is tested using four well-known multimodal benchmark test problems with many local optima surrounding their global optimum. It was found that the performance of the modified G3 algorithm with self-adaptive mutation outperformed the original G3 algorithm in two out of the four test problems in terms of the solution precision achieved.