## 1 Introduction
### Literature Review
#### 1.2.1 Portfolio Optimization Approaches  
Instead of sticking to one-dimensional models, researchers have adopted approaches that combine big-picture policy decisions with everyday operational realities, resulting in hybrid modelling that tackles the many facets of energy planning. [PERSON] and [PERSON] [27] articulate a hybrid modelling approach integrating bottom-up and top-down processes for hierarchical multi-objective optimization in energy sector planning. This bottom-up and top-down approach tackles the challenges and barriers developing nations like India face in pursuing sustainable energy development. The methodology articulated by the authors requires additional modifications to adequately address the varying objectives and challenges presented in diverse developing countries. The research, as reported by [PERSON], [PERSON] [28], significantly contributes to portfolio optimization by illustrating the efficacy of multi-objective genetic algorithms (MOGAs) in addressing complex portfolio optimization challenges within the electricity market. The authors have contributed substantially by integrating an additional objective to augment diversification benefits alongside the established mean-variance-skewness (MVS) criteria. As a result, this approach provides enhanced trade-off solutions for enterprises involved in power generation. However, it is overwhelmed by the possible computational complexity and resource consumption linked to applying multi-objective genetic algorithms (MOGAs) to high-dimensional optimization tasks. These factors may impede their practical application in real-time decision-making contexts within the electricity market. [PERSON] and [PERSON] [29] present a novel Mean-Downside Risk-Skewness (MDRS) model for portfolio selection, incorporating evolutionary multi-objective optimization algorithms. This approach enhances the decision-making process under conditions of uncertainty by balancing expected returns, downside risk, and skewness through fuzzy logic. The complexity inherent in the proposed MDRS model, characterized by NP-hard optimization problems due to the cardinality constraint, potentially poses challenges in identifying optimal solutions for practical applications. This limitation is noteworthy. [PERSON] and [PERSON] [30] propose an agent-based multi-objective co-evolutionary algorithm designed explicitly for portfolio optimization. The authors introduce innovative architectures and methodologies to augment population diversity's sustainability. Nonetheless, their dependence on historical data spanning a mere two years may fail to sufficiently encapsulate the varied market conditions and dynamics essential for thoroughly assessing the proposed algorithm's effectiveness. The Adaptive Ranking Multi-Objective Particle Swarm Optimization (ARMOPSO) methodology has been proposed to effectively address various variants of the mean-variance portfolio selection problem within a cohesive framework Silva, [PERSON] [31]. This approach significantly enhances both the efficiency and robustness of portfolio optimization processes. However, it may encounter challenges in effectively managing infeasibilities and ensuring stability across various problem instances, which affects the quality of the resultant non-dominated solutions. In a related development, [PERSON], [PERSON] [32] have introduced a novel cardinality-constrained multi-objective optimization model for portfolio selection. This model incorporates investor preferences via a credibility framework to effectively address risk and loss aversion in investment decision-making. A limitation of this work is that the proposed model may face challenges in generating feasible portfolios due to the quasi-concave nature of the cardinality constraint, which can complicate the optimization process. [PERSON] and [PERSON] [33] researched using a tri-criterion portfolio selection model, which builds upon the conventional Markowitz mean-variance framework.