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Continuous power consumption from standard fuel resources is responsible for producing large-scale environmental greenhouse gases. Production of biodiesel fuels from the vegetable oils can be considered an alternative source. Effect of greenhouse gases can also be diminished. The production of biodiesel is done by a chemical process namely transesterification and usually maximized by using the Response Surface Methodology (RSM) tool. This paper presents a new approach to optimize the production of biodiesel by introducing a new variant of recently published metaheuristic Harris Hawk Optimization (HHO). The developed variant is based on the replacement of random numbers of normal distribution at the initialization phase by the random numbers generated from the Laplacian distribution. The proposed variant is named as the Laplacian Harris Hawk Optimization (LHHO) algorithm. The contribution of this paper is in twofold: firstly the performance of the proposed algorithm is verified over a well-known set of benchmark functions, and then, we applied the LHHO to maximize biodiesel production. Comparison of LHHO is carried out with five other recent metaheuristic algorithms. An optimization routine is formulated in the form of a single-objective function with a temperature, methanol to oil ratio, and catalyst concentration as the optimization variables. These parameters are optimized to maximize the production of biodiesel. The results obtained using the proposed LHHO show significant improvement as compared to other algorithms.