Pneumonia is one of the major reasons for child mortality especially in income-deprived regions of the world. Although it can be detected and treated with very less sophisticated instruments and medication, Pneumonia detection still remains a major concern in developing countries. Computer-aided based diagnosis (CAD) systems can be used in such countries due to their lower operating costs than professional medical experts. In this paper, we propose a CAD system for Pneumonia detection from Chest X-rays, using the concepts of deep learning and a meta-heuristic algorithm. We first extract deep features from the pre-trained ResNet50, fine-tuned on a target Pneumonia dataset. Then, we propose a feature selection technique based on particle swarm optimization (PSO), which is modified using a memory-based adaptation parameter, and enriched by incorporating an altruistic behavior into the agents. We name our feature selection method as adaptive and altruistic PSO (AAPSO). The proposed method successfully eliminates non-informative features obtained from the ResNet50 model, thereby improving the Pneumonia detection ability of the overall framework. Extensive experimentation and thorough analysis on a publicly available Pneumonia dataset establish the superiority of the proposed method over several other frameworks used for Pneumonia detection. Apart from Pneumonia detection, AAPSO is further evaluated on some standard UCI datasets, gene expression datasets for cancer prediction and a COVID-19 prediction dataset. The overall results are satisfactory, thereby confirming the usefulness of AAPSO in dealing with varied real-life problems. The supporting source codes of this work can be found at https://github.com/rishavpramanik/AAPSO