Combinatorial Optimization Problems (COPs) are a class of optimization problems that are commonly encountered in industrial production and everyday life. Over the last few decades, traditional algorithms, such as exact algorithms, approximate algorithms, and heuristic algorithms, have been proposed to solve COPs. However, as COPs in the real world become more complex, traditional algorithms struggle to generate optimal solutions in a limited amount of time. Since Deep Neural Networks (DNNs) are not heavily dependent on expert knowledge and are adequately flexible for generalization to various COPs, several DNN-based algorithms have been proposed in the last ten years for solving COPs. Herein, we categorize these algorithms into four classes and provide a brief overview of their applications in real-world problems.

Portfolio optimization is a classical and important problem in the field of asset management, which aims to achieve a trade-off between profit and risk. Previous portfolio optimization models use traditional risk measurements such as variance, which symmetrically delineate both positive and negative sides and are not practical and stable. In this paper, a new model with cardinality constraints is first proposed, in which the idiosyncratic volatility factor is used to replace traditional risk measurements and can capture the risks of the portfolio in a more accurate way. The new model has practical constraints which involve the sparsity and irregularity of variables and make it challenging to be solved by traditional Multi-Objective Evolutionary Algorithms (MOEAs). To solve the model, a Learning-Guided Evolutionary Algorithm based on $I_{ϵ+}$ indicator ( $I_{ϵ+}$LGEA) is developed. In $I_{ϵ+}$LGEA, the $I_{ϵ+}$ indicator is incorporated into the initialization and genetic operators to guarantee the sparsity of solutions and can help improve the convergence of the algorithm. And a new constraint-handling method based on $I_{ϵ+}$ indicator is also adopted to ensure the feasibility of solutions. The experimental results on five portfolio trading datasets including up to 1226 assets show that $I_{ϵ+}$LGEA outperforms some state-of-the-art MOEAs in most cases.