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Besides chemical composition, microstructure plays a key role to control the properties of engineering materials. A strong correlation exists between microstructure and many mechanical and physical properties of a metal. It has the utmost importance to understand the microstructure and distinguish the microstructure accurately for the appropriate selection of engineering materials in product fabrication. Computer vision and machine learning play a major role to extract the feature and predict the most probable class of a 7-class microstructural image with a high degree of accuracy. Features contain information about the image, and the classification function is defined in terms of features. Feature selection plays an important role in the classification problem to improve the classification accuracy and also to reduce the computational time by eliminating redundant or non-influential features. The current research aims at classifying microstructure image datasets by an improved wrapper-filter based feature selection method using texture-based feature descriptor. Before applying the feature selection method, a feature descriptor, called rotational local tetra pattern (RLTrP), is applied to extract the features from the input images. Then, an ensemble of three filter methods is developed by considering the union of the top-n features selected by Chi-square, Fisher score, and Gini impurity-based filter methods. The objective of this ensemble is to combine all possible important features selected by three filter methods which will be used to create an initial population of the wrapper-based meta-heuristic feature selection algorithm called, harmony search (HS). The novelty of this HS method lies in the objective function, which is defined as a function of Pearson correlation coefficient and mutual information to calculate the fitness value. The proposed method not only optimizes features with reduced dimension but also improves the performance of classification accuracy of the 7-class microstructural images. Moreover, the proposed HS model has also been compared with some standard optimization algorithms like whale optimization algorithm, particle swarm optimization, and Grey wolf optimization on the present dataset, and in every case, the HS method ensures better agreement between feature selection and classification accuracy than the other methods.