The canonical harmony search (HS) algorithm generates a new solution by using random adjustment. However, the beneficial effects of harmony memory are not well considered. In order to make full use of harmony memory to generate new solutions, this paper proposes a new adaptive harmony search algorithm (aHSDE) with a differential mutation, periodic learning and linear population size reduction strategy for global optimization. Differential mutation is used for pitch adjustment, which provides a promising direction guidance to adjust the bandwidth. To balance the diversity and convergence of harmony memory, a linear reducing strategy of harmony memory is proposed with iterations. Meanwhile, periodic learning is used to adaptively modify the pitch adjusting rate and the scaling factor to improve the adaptability of the algorithm. The effects and the cooperation of the proposed strategies and the key parameters are analyzed in detail. Experimental comparison among well-known HS variants and several state-of-the-art evolutionary algorithms on CEC 2014 benchmark indicates that the aHSDE has a very competitive performance.
Due to the volatility and uncertainty of the financial market, investors often use the form of portfolio to actively manage their assets. Portfolio optimization (PO) is becoming more and more important for investors. However, PO is frequently a kind of NP-hard problem in the field of modern financial optimization, which has gradually attracted the attention and interest of researchers. Some efficient mathematical models were built to describe the return and risk of portfolio. A lot of precise and approximate fast algorithms are used to solve the established PO models. The fundamental purpose is to maximize the return and to minimize the risk of portfolio under certain constraints. In recent years, researchers not only limit the goal of PO to the balance between risk and return, but also pay attention to liquidity, environmental, social, and governance (ESG) controversy level, Sortino ratio, and other indicators. The number of PO targets and constraints is further extended. In the past two decades, swarm intelligence (SI) algorithms have been widely introduced to solve PO problems. SI algorithm is mainly inspired from the daily phenomena in nature or self-organization, self-adaptation, and self-learning of biological population. The existing research results show that SI algorithm has the characteristics of high efficiency and can obtain satisfactory solutions in solving PO problems. The recent advances on the classic portfolio optimization concepts, models, and the usual SI-based solving algorithms are presented. Finally, future potential research directions are presented.
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