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The objective of moveout parameter inversion is to derive sets of parameter models that can be used for moveout correction and stacking at each common midpoint location to increase the signal‐to‐noise ratio of the data and to provide insights into the kinematic characteristics of the data amongst other things. In this paper, we introduce a data‐driven user‐constrained optimization scheme that utilizes manual picks at a point on each reflector within a common midpoint gather to constrain the search space in which an optimization procedure can search for the optimal parameter sets at each reflection. The picks are used to create boundary curves which can be derived approximately via an optimization technique or analytically via the derivation of an analytical bounds function. In this paper, we derive analytical forms of bounds functions for four different moveout cases. These are normal moveout, non‐hyperbolic moveout, azimuthally dependent normal moveout and azimuthally dependent non‐hyperbolic moveout. The optimization procedure utilized here to search for the optimal moveout parameters is the particle swarm optimization technique. However, any metaheuristic optimization procedure could be modified to account for the constraints introduced in this paper. The technique is tested on two‐layer synthetic models based on three of the four moveout cases discussed in this paper. It is also applied to an elastic forward modelled synthetic model called the HESS model, and finally to real 2D land data from Alaska. The resultant stacks show a marked improvement in the signal‐to‐noise ratio compared to the raw stacks. The results for the normal moveout, non‐hyperbolic moveout and azimuthally dependent normal moveout tests suggest that the method is viable for said models. Results demonstrate that our method offers potential as an alternative to conventional parameter picking and inversion schemes, particularly for some cases where the number of parameters in the moveout approximation is 2 or greater. [ABSTRACT FROM AUTHOR]