## 1 Introduction
In the context of synergy between pattern recognition and machine learning, Explainable Artificial Intelligence (XAI) can be used to understand the rules that are generated. The inherent non-human-interpretable nature of AI models has led to limited work aimed at developing models that can effectively elucidate their decision-making processes and actions [14]. The evolution and role of XAI have significantly shaped the healthcare industry, offering transparency and trustworthiness in AI-assisted medical diagnoses [15], which is essential for gaining acceptance and facilitating collaboration between AI systems and medical professionals (Figure 1)  
The insights gained by leveraging the integration of machine learning, pattern recognition, and XAI hold significant potential in the domain of medical image analysis for breast cancer detection; each of these fields consists of several processes. One approach that enhances this integration is the use of metaheuristics, which employ techniques inspired by nature to perform abstract optimization [16]. Although a limited number of studies have explored breast cancer thermogram diagnosis using optimization algorithms, the review article [17] presents an overview of advancements in this field. The authors of this paper are also aware of the ongoing debate surrounding metaheuristic-based optimization [18]. In order to address some of those concerns while employing these algorithms, our work stands as a significant contribution to this research area:  
1. Our primary goals encompass the comprehensive solution to the challenges of achieving dynamic optimization problems. The development of Hybrid PSO (HPSO) and Hybrid SMO (HSMO) methodologies for tackling continuous variable optimization and discrete problems. The proposed approaches allow the optimization algorithm to ensure effective solutions in a varied search space. 2. Harnessing the power of multi-objective optimization techniques, the proposed optimizers aim to provide a deeper understanding of model behavior across varying problem formulations. We used multi-objective ML approaches to strive to optimize multiple aspects of model performance simultaneously. These include hyperparameter optimization, prediction performance, sparseness, and interpretability. 3. Through our research, the automated aspects on finding textures and features through machine learning-based optimization functions that best represent breast cancer classification patterns by producing handcrafted features from breast thermogram images using different methods, such as LBP, HOG, Gabor and canny edge and SVM for classification, are employed. 4. Using visual explanation techniques that generate interpretable graphical representations enables healthcare practitioners to intuitively grasp the rationale behind each classification, making complex patterns associated with breast thermograms more comprehensible. 5. The proposed HSMO and HPSO optimizer incorporates the SHapley Additive exPlanations (SHAP) framework into the evaluation process; this method ensures that the importance of different features is considered. This method adds another layer of complexity and variation to the solutions being explored. 6. The other goal of this paper is to evaluate the convergence behaviors of distinct metaheuristic algorithms (HPSO, HSMO, Binary Particle Swarm Optimization algorithm (BPSO), and Binary Spider Monkey Optimization algorithm (BSMO) to identify similarities and differences in their solutions and second, to ensure consistent results upon repeated runs. The organization of this paper is as follows: Section 2 presents related work. The detailed methodology is explained in Section 3. Section 4 outlines the experimental setup. Section 5 presents the results and related discussions. Finally, we conclude our work in Section 7. Figure 1: The evolution and role of XAI in decision making by stakeholders.