Neural network-based mean–variance–skewness model for portfolio selection

In this study, a novel neural network-based mean–variance–skewness model for optimal portfolio selection is proposed integrating different forecasts and trading strategies, as well as investors’ risk preference. Based on the Lagrange multiplier theory in optimization and the radial basis function (RBF) neural network, the model seeks to provide solutions satisfying the trade-off conditions of mean–variance–skewness. The feasibility of the RBF network-based mean–variance–skewness model is verified with a simulation experiment. The experimental results show that, for all examined investor risk preferences and investment assets, the proposed model is a fast and efficient way of solving the trade-off in the mean–variance–skewness portfolio problem. In addition, we also find that the proposed approach can also be used as an alternative tool for evaluating various forecasting models.     

Fuzzy mean–variance–skewness portfolio selection models by interval analysis

In portfolio selection problem, the expected return, risk, liquidity etc. cannot be predicted precisely. The investor generally makes his portfolio decision according to his experience and his economic wisdom. So, deterministic portfolio selection is not a good choice for the investor. In most of the recent works on this problem, fuzzy set theory is widely used to model the problem in uncertain environments. This paper utilizes the concept of interval numbers in fuzzy set theory to extend the classical mean–variance (MV) portfolio selection model into mean–variance–skewness (MVS) model with consideration of transaction cost. In addition, some other criteria like short and long term returns, liquidity, dividends, number of assets in the portfolio and the maximum and minimum allowable capital invested in stocks of any selected company are considered. Three different models have been proposed by defining the future financial market optimistically, pessimistically and in the combined form to model the fuzzy MVS portfolio selection problem. In order to solve the models, fuzzy simulation (FS) and elitist genetic algorithm (EGA) are integrated to produce a more powerful and effective hybrid intelligence algorithm (HIA). Finally, our approaches are tested on a set of stock data from Bombay Stock Exchange (BSE).     

Evolutionary multi-objective optimization algorithms for fuzzy portfolio selection

In this paper, we consider a recently proposed model for portfolio selection, called Mean-Downside Risk-Skewness (MDRS) model. This modelling approach takes into account both the multidimensional nature of the portfolio selection problem and the requirements imposed by the investor. Concretely, it optimizes the expected return, the downside-risk and the skewness of a given portfolio, taking into account budget, bound and cardinality constraints. The quantification of the uncertain future return on a given portfolio is approximated by means of LR-fuzzy numbers, while the moments of its return are evaluated using possibility theory. The main purpose of this paper is to solve the MDRS portfolio selection model as a whole constrained three-objective optimization problem, what has not been done before, in order to analyse the efficient portfolios which optimize the three criteria simultaneously. For this aim, we propose new mutation, crossover and reparation operators for evolutionary multi-objective optimization, which have been specially designed for generating feasible solutions of the cardinality constrained MDRS problem. We incorporate the operators suggested into the evolutionary algorithms NSGAII, MOEA/D and GWASF-GA and we analyse their performances for a data set from the Spanish stock market. The potential of our operators is shown in comparison to other commonly used genetic operators and some conclusions are highlighted from the analysis of the trade-offs among the three criteria.     

Portfolio optimization problems in different risk measures using genetic algorithm

This paper introduces a heuristic approach to portfolio optimization problems in different risk measures by employing genetic algorithm (GA) and compares its performance to mean–variance model in cardinality constrained efficient frontier. To achieve this objective, we collected three different risk measures based upon mean–variance by Markowitz; semi-variance, mean absolute deviation and variance with skewness. We show that these portfolio optimization problems can now be solved by genetic algorithm if mean–variance, semi-variance, mean absolute deviation and variance with skewness are used as the measures of risk. The robustness of our heuristic method is verified by three data sets collected from main financial markets. The empirical results also show that the investors should include only one third of total assets into the portfolio which outperforms than those contained more assets.     

A portfolio selection model with borrowing constraint based on possibility theory

Compared with the conventional probabilistic mean-variance methodology, fuzzy number can better describe an uncertain environment with vagueness and ambiguity. In this paper, the portfolio selection model with borrowing constraint is proposed by means of possibilistic mean, possibilistic variance, and possibilistic covariance under the assumption that the returns of assets are fuzzy numbers. And a quadratic programming model with inequality constraints is presented when the returns of assets are trapezoid fuzzy numbers. Furthermore, Lemke algorithm is utilized to solve the model. Finally, a numerical example of the portfolio selection problem is given to illustrate our proposed effective means and variances. The results of the numerical example also show that the investor can make different decisions according to different requirements for the values of expected returns. And the efficient portfolio frontier of the model with borrowing constraints can be easily obtained.     

Portfolio selection problem with nonlinear wealth equations under non-extensive statistical mechanics for time-varying SDE

This paper is dedicated to the study of continuous-time mean–variance optimal portfolio selection problem with non-linear wealth equations under non-extensive statistical mechanics for the time-varying stochastic differential equation model. Firstly, we allow the returns and variance of risky assets are time-varying functions, which can fit the financial data better. Secondly, we consider an investor with the non-linear wealth equation. In fact, the wealth equations are not linear in many cases. The investor has to pay some taxes, which leads to a non-linear wealth equation. Moreover, since the return of the stocks price may be affected by a large investors portfolio selection, the wealth equation is non-linear in this case. Thirdly, the non-linear wealth equation driven by Tsallis distribution is constructed under non-extensive statistical mechanics, which can capture the characteristics of fat tails and aiguilles of the risky asset’s return. The viscosity solution of the HJB equation for the portfolio problem is proposed by the optimal stochastic control theory and Lagrange multiplier method. Finally, the efficient portfolio strategy and efficient frontier under non-extensive statistical mechanics are obtained. Furthermore, numerical analysis and real data study are discussed to show our results.     

A self-adaptive multi-objective harmony search algorithm based on harmony memory variance

Although harmony search (HS) algorithm has shown many advantages in solving global optimization problems, its parameters need to be set by users according to experience and problem characteristics. This causes great difficulties for novice users. In order to overcome this difficulty, a self-adaptive multi-objective harmony search (SAMOHS) algorithm based on harmony memory variance is proposed in this paper. In the SAMOHS algorithm, a modified self-adaptive bandwidth is employed, moreover, the self-adaptive parameter setting based on variation of harmony memory variance is proposed for harmony memory considering rate (HMCR) and pitch adjusting rate (PAR). To solve multi-objective optimization problems (MOPs), the proposed SAMOHS uses non-dominated sorting and truncating procedure to update harmony memory (HM). To demonstrate the effectiveness of the SAMOHS, it is tested with many benchmark problems and applied to solve a practical engineering optimization problem. The experimental results show that the SAMOHS is competitive in convergence performance and diversity performance, compared with other multi-objective evolutionary algorithms (MOEAs). In the experiment, the impact of harmony memory size (HMS) on the performance of SAMOHS is also analyzed.     

考虑员工合作关系的单元装配系统构建方法

针对流水线装配向单元装配转换的基本问题,考虑员工之间的合作关系,以最小化总装配周期和最小化员工总工作时间为目标,建立流水装配线向单元装配系统转换的多目标优化模型.针对模型的特征,采用基于NSGA-II的多目标优化算法进行求解.通过数值实验证明考虑员工合作关系的必要性,并分析员工合作系数的均值和方差的变化对单元系统构建的组成和性能的影响.结果表明,整体合作程度较高及合作关系差异较大时,单元系统的性能提升程度较为明显.     

最大化个人偏好的多目标优化进化算法

针对多目标优化过程中如何将个人偏好信息融入寻优搜索过程的问题,本文提出一种最大化个人偏好 以确定搜索方向的多目标优化进化算法．该算法首先采用权重和法将多目标问题转换为单目标问题,再利用遗传算 法进行全局搜索,在满足个人偏好约束条件下,每一代进化结束后通过解约束优化问题获得能够使种群综合适应度 具有最大方差的权重组合,从而最大化个人偏好以选择综合最优的个体进行遗传操作．按照不同个人偏好应用于传 动系统进行控制器设计,仿真结果表明该算法能够获得满足个人偏好约束条件下的全局最优解．     

基于模糊偏好的多目标成像卫星调度方法研究

不确定条件下的成像卫星调度问题是一个多目标优化问题。借鉴连续函数的鲁棒性优化思想,提出了一种基于邻域的鲁棒性指标,考虑多种约束条件,建立了多目标成像卫星调度模型。在考虑目标间偏好的情况下,提出了一种基于模糊偏好的多目标遗传算法。实例研究表明,该模型和算法能够有效地解决不确定条件下的成像卫星调度问题。     

Enhanced goal attainment method for solving multi-objective security-constrained optimal power flow considering dynamic thermal rating of lines

Security-constrained optimal power flow (SCOPF) is an important problem in power system operation. Dynamic thermal rating (DTR), as an effective method to increase transmission capacity of power systems, has been recently considered in some optimal power flow (OPF) and SCOPF models. Additionally, in today power systems, OPF problem involves various objectives leading to multi-objective OPF models. In this paper, a new multi-objective SCOPF model considering DTR of transmission lines is presented. In addition, a new multi-objective solution method is proposed to solve the multi-objective SCOPF problem. The proposed method is an enhanced version of goal attainment technique in which the search capability of this technique to cover borders of the Pareto frontier is enhanced. The proposed multi-objective DTR-included SCOPF model as well as the proposed multi-objective solution method are tested on the IEEE 118-bus test system and the obtained results are compared with the results of other alternatives.     

基于多目标优化的投资组合分析

对理性的投资者而言,除了关注投资收益和风险外,资产组合中数目的多少也是其关注的重要方面。在一定的收益和风险水平下,资产的数目越少越容易管理。利用NSGA-II算法对Markowitz的扩展模型进行多目标优化,通过实证分析进行验证。由分析结果可知,在一定的收益和风险水平下,资产组合中的数目是可以降低的,对投资者来说可以大大降低其资产组合的管理成本。     

Robust multiperiod portfolio management in the presence of transaction costs

We study the viability of different robust optimization approaches to multiperiod portfolio selection. Robust optimization models treat future asset returns as uncertain coefficients in an optimization problem, and map the level of risk aversion of the investor to the level of tolerance of the total error in asset return forecasts. We suggest robust optimization formulations of the multiperiod portfolio optimization problem that are linear and computationally efficient. The linearity of the optimization problems is an advantage when complex additional requirements need to be imposed on the portfolio structure, e.g., limitations on positions in certain assets or tax constraints. We compare the performance of our robust formulations to the performance of the traditional single period mean-variance formulation frequently employed in the financial industry.     

Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment

In designing phase of systems, design parameters such as component reliabilities and cost are normally under uncertainties. This paper presents a methodology for solving the multi-objective reliability optimization model in which parameters are considered as imprecise in terms of triangular interval data. The uncertain multi-objective optimization model is converted into deterministic multi-objective model including left, center and right interval functions. A conflicting nature between the objectives is resolved with the help of intuitionistic fuzzy programming technique by considering linear as well as the nonlinear degree of membership and non-membership functions. The resultants max–min problem has been solved with particle swarm optimization (PSO) and compared their results with genetic algorithm (GA). Finally, a numerical instance is presented to show the performance of the proposed approach.     

Fuzzy portfolio model with fuzzy-input return rates and fuzzy-output proportions

In the finance market, a short-term investment strategy is usually applied in portfolio selection in order to reduce investment risk; however, the economy is uncertain and the investment period is short. Further, an investor has incomplete information for selecting a portfolio with crisp proportions for each chosen security. In this paper we present a new method of constructing fuzzy portfolio model for the parameters of fuzzy-input return rates and fuzzy-output proportions, based on possibilistic mean–standard deviation models. Furthermore, we consider both excess or shortage of investment in different economic periods by using fuzzy constraint for the sum of the fuzzy proportions, and we also refer to risks of securities investment and vagueness of incomplete information during the period of depression economics for the portfolio selection. Finally, we present a numerical example of a portfolio selection problem to illustrate the proposed model and a sensitivity analysis is realised based on the results.     

Extended omega ratio optimization for risk‐averse investors

The omega ratio, a performance measure, is the ratio of the expected upside deviation of return to the expected downside deviation of return from a predetermined threshold described by an investor. It has been exhibited that the omega ratio optimization is equivalent to a linear program under a mild condition and thus easily tractable. But the omega ratio optimization fails to hedge against many other risks involved in portfolio return that may adversely affect the interests of a risk‐averse investor. On the other hand, there are widely accepted mean‐risk models for portfolio selection that seek to maximize mean return and minimize the associated risk but in general fail to maximize the relative performance ratio around the threshold return. In this paper, we aim to propose a model called ‘extended omega ratio optimization’ that combines the features of the omega ratio optimization model and mean‐risk models. The proposed model introduces constraint on a general risk function in the omega ratio optimization model in such a way that the resultant model remains linear and thus tractable. Our empirical experience with real data from S&P BSE sensex index shows that the optimal portfolios from the extended omega ratio optimization model(s) improved over the optimal portfolios from the omega ratio optimization in having less associated risk and over the optimal portfolios from the corresponding mean‐risk model(s) in having a high value omega ratio.     

基于灰色综合关联分析的多目标优化方法

针对现有多目标优化方法存在的搜索性能弱、效率低等问题,提出一种基于灰色综合关联分析的多目标优化方法.该多目标优化方法采用单目标优化算法构建高质量的参考序列,计算参考序列与优化解的目标函数值序列之间的灰色综合关联度,定义基于灰色综合关联度的解支配关系准则,将灰色综合关联度作为多目标优化算法的适应度值.以带顺序相关调整时间的多目标流水车间调度问题作为应用对象,建立总生产成本、最大完工时间、平均流程时间及机器平均闲置时间的多目标函数优化模型.提出基于灰色关联分析的多目标烟花算法,对所建立的多目标优化模型进行优化求解.仿真实验表明,所提出多目标烟花算法的性能优于3种基于不同多目标优化方法的烟花算法及两种经典多目标算法,验证了所提出的多目标优化方法及多目标算法的可行性和有效性.     

A memetic algorithm for cardinality-constrained portfolio optimization with transaction costs

A memetic approach that combines a genetic algorithm (GA) and quadratic programming is used to address the problem of optimal portfolio selection with cardinality constraints and piecewise linear transaction costs. The framework used is an extension of the standard Markowitz mean–variance model that incorporates realistic constraints, such as upper and lower bounds for investment in individual assets and/or groups of assets, and minimum trading restrictions. The inclusion of constraints that limit the number of assets in the final portfolio and piecewise linear transaction costs transforms the selection of optimal portfolios into a mixed-integer quadratic problem, which cannot be solved by standard optimization techniques. We propose to use a genetic algorithm in which the candidate portfolios are encoded using a set representation to handle the combinatorial aspect of the optimization problem. Besides specifying which assets are included in the portfolio, this representation includes attributes that encode the trading operation (sell/hold/buy) performed when the portfolio is rebalanced. The results of this hybrid method are benchmarked against a range of investment strategies (passive management, the equally weighted portfolio, the minimum variance portfolio, optimal portfolios without cardinality constraints, ignoring transaction costs or obtained with L₁ regularization) using publicly available data. The transaction costs and the cardinality constraints provide regularization mechanisms that generally improve the out-of-sample performance of the selected portfolios.     

基于隐马尔可夫链的自适应MODE及应用

不同的控制参数设定和生成策略（交叉和变异）都会对多目标差分进化算法的性能产生显著影响。为实现其控制参数和变异策略的实时自适应调整,提出一种基于隐马尔可夫链的自适应多目标差分进化算法。该算法利用隐马尔可夫模型对种群信息进行分析并得到最优序列,通过最优序列与实际状态序列的对比得出变异缩放因子[F]与交叉概率[CR]的最大似然估计值,从而实现控制参数的自适应调整;同时,通过隐马尔可夫模型得到一组策略链来辅助多目标差分进化算法来选择合适的变异策略。通过与其他9种多目标进化算法在16个测试函数上的对比研究,结果表明所提算法的整体性能优于其他比较算法。最后,将该算法用于求解海铁联运能耗优化问题,所得结果能够为决策者提供多种可行方案。     

基于大规模多目标优化的跳频序列设计方法

针对跳频序列设计中存在的规模小和难以兼顾多指标的问题,提出一种基于大规模多目标优化的跳频序列设计方法。首先,综合考虑跳频序列的多项性能指标,建立跳频序列多目标优化模型;然后,引入大规模多目标优化算法,并提出决策变量洗牌策略和反向差分进化,通过重新分配决策变量位置以形成具有多样性的非支配集,并通过使反向个体参与差分进化来为后续进化持续提供有效的方向;最后,通过提出算法对模型进行优化得到跳频序列集。实验结果表明,提出的算法相较于其他多目标优化算法具有更强的寻优能力,得到跳频序列集的性能指标具有明显优势;提出的设计方法在不同干扰环境中相较于设计其他方法具有更低的误码率,验证了提出方法的有效性和优越性。