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The optimization of information transfer through molecule diffusion and chemical reactions is one of the leading research directions in Molecular Communication (MC) theory. The highly nonlinear nature of the processes underlying these channels poses challenges in adopting analytical approaches for their information-theoretic modeling and analysis. In this paper, a novel iterative methodology is proposed to numerically estimate achievable information rates. Based on the Nelder-Mead optimization, this methodology does not necessitate analytical for-mulations of MC components and their stochastic behavior, and, when applied to well-known scenarios, it demonstrates consistent results with theoretical bounds and superior performance to prior literature. A numerical example that abstracts communications between genetically engineered cells via simulation is presented and discussed in light of possible future applications to support the design and engineering of realistic MC systems.