Artificial Bee Colony (ABC) algorithm is a classical Swarm Intelligence Optimization Algorithm (SIOA), which has been widely used to solve various optimization problems. However, these problems mainly focus on single-objective and ordinary Multi-objective Optimization Problems (MOPs). For Many-objective Optimization Problems (MaOPs), ABC shows some difficulties: (1) the selection pressure based on Pareto dominance degrades severely; and (2) it is not easy to balance convergence and population diversity. In this paper, a new Many-Objective ABC variant with Hybrid Strategies (namely HSMaOABC) is proposed to deal with MaOPs. Firstly, the fitness function is redefined based on objective values and cosine similarity to handle multiple objectives. Then, a new selection method is designed on the basis of the new fitness function. In order to enhance convergence, an elite set guided search strategy is utilized for the employed bee stage, and dimensional learning is incorporated for the onlooker bee stage. Finally, a modified environmental selection strategy is employed based on Penalty-based Boundary Intersection (PBI) distance. To evaluate the performance of HSMaOABC, the DTLZ and MaF benchmarks with 3, 5, 8, and 15 objectives are used. Experimental results demonstrate that HSMaOABC obtains competitive performance when compared with nine other well-known approaches.

The fidelity of financial market simulation is restricted by the so-called “non-identifiability” difficulty when calibrating high-frequency data. This paper first analyzes the inherent loss of data information in this difficulty, and proposes to use the Kolmogorov-Smirnov test (K-S) as the objective function for high-frequency calibration. Empirical studies verify that K-S has better identifiability of calibrating high-frequency data, while also leads to a much harder multi-modal landscape in the calibration space. To this end, we propose the adaptive stochastic ranking based negatively correlated search algorithm for improving the balance between exploration and exploitation. Experimental results on both simulated data and real market data demonstrate that the proposed method can obtain up to 36.0% improvement in high-frequency data calibration problems over the compared methods.

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.