## 2 Need for New Metaheuristic- and Learning-Based Approaches
Such financial irrelevance is exacerbated by the fact that traditional optimization methods tend to over-weight assets with large returns and small variances and under-weight assets with small returns and large variances [53]. However, reference [2] maintain that the presence of theoretical and practical limitations does not invalidate [PERSON]'s theory of portfolio selection. Rather, traditional optimization methods need to be modified and new methods need to be developed, so that the existing gap between theory and practice can be bridged. In order to address some of the theoretical and practical limitations of more classical approaches, metaheuristic methods to portfolio optimization have emerged in the literature [8; 25; 26; 27; 28]. Metaheuristics emerged from simple heuristics that were proposed to address some of the weaknesses inherited by traditional optimization methods. A heuristic is a common-sense and experience-based solution search method. Reference [14] proposes a simple heuristic based on the beta as a risk measure to solve the portfolio selection problem. Reference [54] builds upon the expected return-variance ratio to develop a heuristic that determines an optimal portfolio location on the efficient frontier More specifically, they construct a decision rule that determines whether the asset will enter the portfolio and calculates its weight in the portfolio. A simplification to the decision rule in [54] is made by [55]. In particular, he derives a heuristic that is based on the expected return-semi-variance ratio that assumes the average correlation between securities to be zero. The use of the semi-variance as a measure of risk owes to the notion that investors are more concerned about downside risk than upside risk. Reference [55] demonstrates that the return-risk heuristic that uses the downside risk measure provides better investment performance than traditional optimization methods for long-term investments, albeit not for short-term ones. A comparison between the return-risk heuristic and two traditional optimization methods is performed by [53]. He finds that the return-risk heuristic produces the highest return along with the highest standard deviation and the lowest semi-deviation among the three portfolios. However, heuristics always return a local optimum, which may or may not be global optimum. The use of these simple return-risk heuristics for the constrained portfolio optimization problem has been discontinued in the last two decades. In fact, an increasing number of studies have tended to focus on metaheuristics. Metaheuristic search methods are less restrictive than traditional optimization methods and thus can be tailored to solve a particular optimization problem that features a number of constraints. Metaheuristics have been employed in several studies on portfolio optimization, such as [32; 39; 40; 41; 56; 57; 58; 59] to name just few. However, most of these studies feature the use of random initialization to the portfolio selection problem or simply downplay their strategies of portfolio initialization. Reference [41] are maybe an exception to this rule. In addition to the randomly generated initial solution, these authors propose two simple heuristics. First, they construct the portfolio that produces the maximum possible return, independently of the risk. Second, they use the final solution of the previously computed point on the efficient frontier. The amount of processor time it takes for the local search algorithm to reach the optimal solution on the efficient frontier may be shorter if a sensible simple heuristic is used to construct an initial solution. Although this paper focuses on the use of metaheuristics to solve rich versions of the portfolio optimization problem, applications of machine learning and deep learning algorithms can be explored as well.