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Particle track reconstruction, in which the trajectories of charged particles are determined, is a critical and time consuming component of the full event reconstruction chain. The underlying software is complex and consists of a number of mathematically intense algorithms, each dealing with a particular tracking sub-process. These algorithms have many input parameters that need to be supplied in advance. However, it is difficult to determine the configuration of these parameters that produces the best performance. Currently, the input parameter values are decided on the basis of prior experience or by the use of brute force techniques. A parameter optimization approach that is able to automatically tune these parameters for high performance is greatly desirable. In the current work, we explore various machine learning based optimization methods to devise a suitable technique to optimize parameters in the complex track reconstruction environment. These methods are evaluated on the basis of a metric that targets high efficiency while keeping the duplicate and fake rates small. We focus on derivative free optimization approaches that can be applied to problems involving non-differentiable loss functions. For our studies, we consider the tracking algorithms defined within A Common Tracking Software (ACTS) framework. We test our methods using simulated data from ACTS software corresponding to the ACTS Generic detector and the ATLAS ITk detector geometries.