A significant challenge in neuroscience is understanding how visual information is encoded in the retina. Such knowledge is extremely important for the purpose of designing bioinspired sensors and artificial retinal systems that will, in so far as may be possible, be capable of mimicking vertebrate retinal behaviour. In this study, we report the tuning of a reliable computational bioinspired retinal model with various algorithms to improve the mimicry of the model. Its main contribution is two-fold. First, given the multi-objective nature of the problem, an automatic multi-objective optimisation strategy is proposed through the use of four biological-based metrics, which are used to adjust the retinal model for accurate prediction of retinal ganglion cell responses. Second, a subset of population-based search heuristics—genetic algorithms (SPEA2, NSGA-II and NSGA-III), particle swarm optimisation (PSO) and differential evolution (DE)—are explored to identify the best algorithm for fine-tuning the retinal model, by comparing performance across a hypervolume metric. Nonparametric statistical tests are used to perform a rigorous comparison between all the metaheuristics. The best results were achieved with the PSO algorithm on the basis of the largest hypervolume that was achieved, well-distributed elements and high numbers on the Pareto front.