The mean–variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms

This paper compares the effectiveness of five state-of-the-art multiobjective evolutionary algorithms (MOEAs) together with a steady state evolutionary algorithm on the mean–variance cardinality constrained portfolio optimization problem (MVCCPO). The main computational challenges of the model are due to the presence of a nonlinear objective function and the discrete constraints. The MOEAs considered are the Niched Pareto genetic algorithm 2 (NPGA2), non-dominated sorting genetic algorithm II (NSGA-II), Pareto envelope-based selection algorithm (PESA), strength Pareto evolutionary algorithm 2 (SPEA2), and e-multiobjective evolutionary algorithm (e-MOEA). The computational comparison was performed using formal metrics proposed by the evolutionary multiobjective optimization community on publicly available data sets which contain up to 2196 assets.     

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.     

Expected model for portfolio selection with random fuzzy returns

This paper researches portfolio selection problem in combined uncertain environment of randomness and fuzziness. Due to the complexity of the security market, expected values of the security returns may not be predicted accurately. In the paper, expected returns of securities are assumed to be given by fuzzy variables. Security returns are regarded as random fuzzy variables, i.e. random returns with fuzzy expected values. Following Markowitz's idea of quantifying investment return by the expected value of the portfolio and risk by the variance, a new type of mean–variance model is proposed. In addition, a hybrid intelligent algorithm is provided to solve the new model problem. A numeral example is also presented to illustrate the optimization idea and the effectiveness of the proposed algorithm.     

Bacterial Foraging Optimization Approach to Portfolio Optimization

In this paper we propose a heuristic approach based on bacterial foraging optimization (BFO) in order to find the efficient frontier associated with the portfolio optimization (PO) problem. The PO model with cardinality and bounding constraints is a mixed quadratic and integer programming problem for which no exact algorithms can solve in an efficient way. Consequently, various heuristic algorithms, such as genetic algorithms and particle swarm optimization, have been proposed in the past. This paper aims to examine the potential of a BFO algorithm in solving the PO problem. BFO is a new swarm intelligence technique that has been successfully applied to several real world problems. Through three operations, chemotaxis, reproduction, and elimination-dispersal, the proposed BFO algorithm can effectively solve a PO problem. The performance of the proposed approach was evaluated in computational tests on five benchmark data sets, and the results were compared to those obtained from existing heuristic algorithms. The proposed BFO algorithm is found to be superior to previous heuristic algorithms in terms of solution quality and time.     

基于参数方差调节萤火虫算法的三维路径规划

为了提高萤火虫算法大范围搜索时的速度和精度,提出了一种参数方差调节萤火虫算法。首先分析基本萤火虫算法,在此基础上提出了参数方差调节萤火虫算法的核心思想：计算种群亮度的方差评估种群的敛散性,根据进程调节参数,进而达到改进萤火虫算法的目的,并给出了算法的实现步骤和流程;然后在四个优化测试函数中将参数方差调节萤火虫算法与基本萤火虫算法、遗传算法、粒子群算法进行比较和分析,发现参数方差调节萤火虫算法在测试中能迅速的找到符合精度要求的解,且成功率是100%,具有较好的稳定性,较之其他算法优势明显;最后通过构建计算能量消耗的目标函数在有实际背景和地理参数的自主式水下潜器三维路径规划的仿真实验中应用参数方差调节萤火虫算法,在三维海底环境中规划出符合要求的路,从而证明了参数方差调节萤火虫算法在三维路径规划中的实用性。     

Parallel Optimization of Sparse Portfolios with AR-HMMs

In this paper we optimize mean reverting portfolios subject to cardinality constraints. First, the parameters of the corresponding Ornstein–Uhlenbeck (OU) process are estimated by auto-regressive Hidden Markov Models (AR-HMM), in order to capture the underlying characteristics of the financial time series. Portfolio optimization is then performed by maximizing the return achieved with a predefined probability instead of optimizing the predictability parameter, which provides more profitable portfolios. The selection of the optimal portfolio according to the goal function is carried out by stochastic search algorithms. The presented solutions satisfy the cardinality constraint in terms of providing a sparse portfolios which minimize the transaction costs (and, as a result, maximize the interpretability of the results). In order to use the method for high frequency trading (HFT) we utilize a massively parallel GPGPU architecture. Both the portfolio optimization and the model identification algorithms are successfully tailored to be running on GPGPU to meet the challenges of efficient software implementation and fast execution time. The performance of the new method has been extensively tested both on historical daily and intraday FOREX data and on artificially generated data series. The results demonstrate that a good average return can be achieved by the proposed trading algorithm in realistic scenarios. The speed profiling has proven that GPGPU is capable of HFT, achieving high-throughput real-time performance.     

A realistic variant of bi-objective unrelated parallel machine scheduling problem: NSGA-II and MOACO approaches

The problem investigated in this study involves an unrelated parallel machine scheduling problem with sequence-dependent setup times, different release dates, machine eligibility and precedence constraints. This problem has been inspired from a realistic scheduling problem in the shipyard. The optimization criteria are to simultaneously minimize mean weighted flow time and mean weighted tardiness. To formulate this complicated problem, a new mixed-integer programming model is presented. Considering the NP-complete characteristic of this problem, two famous meta-heuristics including a non-dominated sorting genetic algorithm (NSGA-II) and a multi-objective ant colony optimization (MOACO) which is a modified and adaptive version of BicriterionAnt algorithm are developed. Obviously, the precedence constraints increase the complexity of the scheduling problem in strong sense in order to generate feasible solutions, especially in parallel machine environment. Therefore a new corrective algorithm is proposed to obtain the feasibility in all stages of the algorithms. Due to the fact that appropriate design of parameter has a significant effect on the performance of algorithms, we calibrate the parameters of these algorithms by using new approach of Taguchi method. The performances of the proposed meta-heuristics are evaluated by a number of numerical examples. The results indicated that the suggested MOACO statistically outperformed the proposed NSGA-II in solving the test problems. In addition, the application of the proposed algorithms is justified by a real block erection scheduling problem in the shipyard.     

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.     

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．     

A GRASP based solution approach to solve cardinality constrained portfolio optimization problems

In the current work, a solution methodology which combines a meta-heuristic algorithm with an exact solution approach is presented to solve cardinality constrained portfolio optimization (CCPO) problem. The proposed method is comprised of two levels, namely, stock selection and proportion determination. In stock selection level, a greedy randomized adaptive search procedure (GRASP) is developed. Once the stocks are selected the problem reduces to a quadratic programming problem. As GRASP ensures cardinality constraints by selecting predetermined number of stocks and quadratic programming model ensures the remaining problem constraints, no further constraint handling procedures are required. On the other hand, as the problem is decomposed into two sub-problems, total computational burden on the algorithm is considerably reduced. Furthermore, the performance of the proposed algorithm is evaluated by using benchmark data sets available in the OR Library. Computational results reveal that the proposed algorithm is competitive with the state of the art algorithms in the related literature.     

An artificial bee colony algorithm with feasibility enforcement and infeasibility toleration procedures for cardinality constrained portfolio optimization

One of the most studied variant of portfolio optimization problems is with cardinality constraints that transform classical mean–variance model from a convex quadratic programming problem into a mixed integer quadratic programming problem which brings the problem to the class of NP-Complete problems. Therefore, the computational complexity is significantly increased since cardinality constraints have a direct influence on the portfolio size. In order to overcome arising computational difficulties, for solving this problem, researchers have focused on investigating efficient solution algorithms such as metaheuristic algorithms since exact techniques may be inadequate to find an optimal solution in a reasonable time and are computationally ineffective when applied to large-scale problems. In this paper, our purpose is to present an efficient solution approach based on an artificial bee colony algorithm with feasibility enforcement and infeasibility toleration procedures for solving cardinality constrained portfolio optimization problem. Computational results confirm the effectiveness of the solution methodology.     

基于均值漂移算法和时空上下文算法的目标跟踪

在严重遮挡时,时空上下文STC(Spatio-Temporal Context)算法对目标位置的判断是正确的,而均值漂移MS(Mean Shift)算法对目标位置的判断会发生很大幅度的抖动,甚至跟踪错误目标。在遮挡结束后,时空上下文算法很难重新跟踪到正确目标,而均值漂移算法可以重新检测到跟踪目标。结合二者的优缺点,提出基于均值漂移算法和时空上下文算法的目标跟踪算法MSandSTC。该算法主要解决目标被严重遮挡的问题。在许多具有挑战性的数据集上的实验表明所提算法具有较好的实时性和鲁棒性。     

Combining genetic algorithms with BESO for topology optimization

This paper proposes a new algorithm for topology optimization by combining the features of genetic algorithms (GAs) and bi-directional evolutionary structural optimization (BESO). An efficient treatment of individuals and population for finite element models is presented which is different from traditional GAs application in structural design. GAs operators of crossover and mutation suitable for topology optimization problems are developed. The effects of various parameters used in the proposed GA on the optimization speed and performance are examined. Several 2D and 3D examples of compliance minimization problems are provided to demonstrate the efficiency of the proposed new approach and its capability of obtaining convergent solutions. Wherever possible, the numerical results of the proposed algorithm are compared with the solutions of other GA methods and the SIMP method.     

A hybrid biogeography-based optimization algorithm for job shop scheduling problem

In this paper, a hybrid biogeography-based optimization (HBBO) algorithm has been proposed for the job-shop scheduling problem (JSP). Biogeography-based optimization (BBO) is a new bio-inpired computation method that is based on the science of biogeography. The BBO algorithm searches for the global optimum mainly through two main steps: migration and mutation. As JSP is one of the most difficult combinational optimization problems, the original BBO algorithm cannot handle it very well, especially for instances with larger size. The proposed HBBO algorithm combines the chaos theory and “searching around the optimum” strategy with the basic BBO, which makes it converge to global optimum solution faster and more stably. Series of comparative experiments with particle swarm optimization (PSO), basic BBO, the CPLEX and 14 other competitive algorithms are conducted, and the results show that our proposed HBBO algorithm outperforms the other state-of-the-art algorithms, such as genetic algorithm (GA), simulated annealing (SA), the PSO and the basic BBO.     

李群均值学习算法

首先分析李群均值的计算方法,在此基础上,进一步提出李群均值学习算法,其思想是在李群流形上寻找一个由总体样本内均值的李代数元素决定的单参数子群,这个单参数子群是原李群上的一条测地线,定义样本到测地线投影的概念,同时将李群样本向该测地线投影,并尽可能使投影后各类别间的散度与类内散度比值最大化,从而实现非线性李群空间的类别判别。实验表明,基于李群均值的学习算法和KNN、FLDA算法相比,具有较好的分类效果。     

MCEDA: A novel many-objective optimization approach based on model and clustering

To solve many-objective optimization problems (MaOPs) by evolutionary algorithms (EAs), the maintenance of convergence and diversity is essential and difficult. Improved multi-objective optimization evolutionary algorithms (MOEAs), usually based on the genetic algorithm (GA), have been applied to MaOPs, which use the crossover and mutation operators of GAs to generate new solutions. In this paper, a new approach, based on decomposition and the MOEA/D framework, is proposed: model and clustering based estimation of distribution algorithm (MCEDA). MOEA/D means the multi-objective evolutionary algorithm based on decomposition. The proposed MCEDA is a new estimation of distribution algorithm (EDA) framework, which is intended to extend the application of estimation of distribution algorithm to MaOPs. MCEDA was implemented by two similar algorithm, MCEDA/B (based on bits model) and MCEDA/RM (based on regular model) to deal with MaOPs. In MCEDA, the problem is decomposed into several subproblems. For each subproblem, clustering algorithm is applied to divide the population into several subgroups. On each subgroup, an estimation model is created to generate the new population. In this work, two kinds of models are adopted, the new proposed bits model and the regular model used in RM-MEDA (a regularity model based multi-objective estimation of distribution algorithm). The non-dominated selection operator is applied to improve convergence. The proposed algorithms have been tested on the benchmark test suite for evolutionary algorithms (DTLZ). The comparison with several state-of-the-art algorithms indicates that the proposed MCEDA is a competitive and promising approach.     

基于平均熵的自适应人工蜂群算法

针对基本人工蜂群算法容易陷入局部最优和早熟等问题,提出一种改进的人工蜂群算法(ASABC)。利用平均熵机制初始化种群,增加种群的多样性,避免算法陷入早熟;同时,采用自适应调节邻域搜索步长的策略来提高算法的局部搜索能力,提升算法的计算精度;为了平衡算法的全局搜索能力和局部搜索能力,引入自适应比例选择策略来代替人工蜂群算法的适应度比例选择方法。对8个标准测试函数的仿真实验结果表明,与3种常见的智能优化方法相比,改进的算法具有显著的局部搜索能力和较快的收敛速度。     

改进的指纹图像自适应分割方法

指纹分割是指纹图像预处理中的重要一步。对传统的指纹分割算法分析比较,并且在基于灰度方差的指纹分割算法的基础上,利用指纹图像区域脊线和谷线间隔均匀出现的纹理特征提出一种自适应指纹图像分割算法,避免了凭经验确定阈值的问题。实验结果表明,相比于基于灰度方差的指纹图像分割算法,该算法的分割效果更好,对噪声的抵抗能力更强,且对不同类型的指纹图像有较高的适应性。     

基于多目标优化策略的在线学习资源推荐方法

目前在线学习资源推荐较多采用单目标转化方法,推荐过程中对学习者偏好考虑相对不足,影响学习资源推荐精度.针对上述问题,文中提出基于多目标优化策略的在线学习资源推荐模型(MOSRAM),在学习者规划时间内,以同时获得学习者对学习资源类型偏好度最大和难度水平适应度最佳为优化目标,设计具有向邻居均值学习能力和探索新区域能力的多目标粒子群优化算法(NEMOPSO),提出以MOSRAM为核心的在线学习资源推荐方法(NEMOPSO-RA).不同问题规模下融合经典多目标优化算法的推荐方法对比实验表明,NEMOPSO-RA可以有效提高在线学习资源的推荐精度和推荐性能.     

求解随机时变背包问题的精确算法与进化算法

随机时变背包问题(RTVKP)是一种新的动态背包问题,也是一种新的动态组合优化问题,目前它的求解算法主要是动态规划的精确算法、近似算法和遗传算法.本文首先利用动态规划提出了一个求解RTVKP问题的新精确算法,对算法时间复杂度的比较结果表明:它比已有的精确算法更适于求解背包载重较大的一类RTVKP实例.然后,分别基于差分演化和粒子群优化与贪心修正策略相结合,提出了求解RTVKP问题的两个进化算法.对5个RTVKP实例的数值计算结果比较表明: 精确算法一般不宜求解大规模的RTVKP实例,而基于差分演化、粒子群优化和遗传算法与贪心修正策略相结合的进化算法却不受实例规模与数据大小的影响,对于振荡频率大且具有较大数据的大规模RTVKP实例均能求得的一个极好的近似解.