Evolutionary multi-objective portfolio optimization in practical context

This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.     

Dynamic multi-objective evolutionary algorithms for single-objective optimization

This paper proposes a new method for handling the difficulty of multi-modality for the single-objective optimization problem (SOP). The method converts a SOP to an equivalent dynamic multi-objective optimization problem (DMOP). A new dynamic multi-objective evolutionary algorithm (DMOEA) is implemented to solve the DMOP. The DMOP has two objectives: the original objective and a niche-count objective. The second objective aims to maintain the population diversity for handling the multi-modality difficulty during the search process. Experimental results show that the performance of the proposed algorithm is significantly better than the state-of-the-art competitors on a set of benchmark problems and real world antenna array problems.     

A pareto-based evolutionary algorithm using decomposition and truncation for dynamic multi-objective optimization

Maintaining a balance between convergence and diversity of the population in the objective space has been widely recognized as the main challenge when solving problems with two or more conflicting objectives. This is added by another difficulty of tracking the Pareto optimal solutions set (POS) and/or the Pareto optimal front (POF) in dynamic scenarios. Confronting these two issues, this paper proposes a Pareto-based evolutionary algorithm using decomposition and truncation to address such dynamic multi-objective optimization problems (DMOPs). The proposed algorithm includes three contributions: a novel mating selection strategy, an efficient environmental selection technique and an effective dynamic response mechanism. The mating selection considers the decomposition-based method to select two promising mating parents with good diversity and convergence. The environmental selection presents a modified truncation method to preserve good diversity. The dynamic response mechanism is evoked to produce some solutions with good diversity and convergence whenever an environmental change is detected. In the experimental studies, a range of dynamic multi-objective benchmark problems with different characteristics were carried out to evaluate the performance of the proposed method. The experimental results demonstrate that the method is very competitive in terms of convergence and diversity, as well as in response speed to the changes, when compared with six other state-of-the-art methods.     

提高多目标进化算法分布性的动态调整机制

为提高多目标进化算法的分布性,提出一种基于极坐标的动态调整机制。在极坐标下,根据解集的拥挤程度,计算个体解的缩放系数。在进化过程中利用该缩放系数动态调整解集支配关系,适当提高分布性好的解在支配关系中的地位以改善解的分布。对测试函数的仿真试验结果表明,将该机制应用于经典算法能显著提高算法的分布性,同时保持良好的收敛性。     

An evolutionary algorithm with directed weights for constrained multi-objective optimization

When solving constrained multi-objective optimization problems (CMOPs), keeping infeasible individuals with good objective values and small constraint violations in the population can improve the performance of the algorithms, since they provide the information about the optimal direction towards Pareto front. By taking the constraint violation as an objective, we propose a novel constraint-handling technique based on directed weights to deal with CMOPs. This paper adopts two types of weights, i.e. feasible and infeasible weights distributing on feasible and infeasible regions respectively, to guide the search to the promising region. To utilize the useful information contained in infeasible individuals, this paper uses infeasible weights to maintain a number of well-diversified infeasible individuals. Meanwhile, they are dynamically changed along with the evolution to prefer infeasible individuals with better objective values and smaller constraint violations. Furthermore, 18 test instances and 2 engineering design problems are used to evaluate the effectiveness of the proposed algorithm. Several numerical experiments indicate that the proposed algorithm outperforms four compared algorithms in terms of finding a set of well-distributed non-domination solutions.     

Physical programming for preference driven evolutionary multi-objective optimization

Preference articulation in multi-objective optimization could be used to improve the pertinency of solutions in an approximated Pareto front. That is, computing the most interesting solutions from the designer's point of view in order to facilitate the Pareto front analysis and the selection of a design alternative. This articulation can be achieved in an a priori, progressive, or a posteriori manner. If it is used within an a priori frame, it could focus the optimization process toward the most promising areas of the Pareto front, saving computational resources and assuring a useful Pareto front approximation for the designer. In this work, a physical programming approach embedded in an evolutionary multi-objective optimization is presented as a tool for preference inclusion. The results presented and the algorithm developed validate the proposal as a potential tool for engineering design by means of evolutionary multi-objective optimization.     

改进混沌烟花算法的多目标调度优化研究

为满足生产中的不同需求,以最小化完成时间、最小化工件总延期时间、最小化机器总空闲时间为目标函数,建立多目标优化模型。提出一种改进混沌烟花算法,通过逻辑自映射产生混沌序列避免算法陷入局部最优,并设计了一种双元锦标赛与动态淘汰制相结合的帕累托非劣解集的构造方法。通过对六个不同规模标准问题的仿真测试,验证了该算法在求解多目标作业车间问题时具有较高求解精度和稳定性。     

混合分解和强度帕累托多目标进化算法

在多目标进化优化中,使用分解策略的基于分解的多目标进化算法(MOEA/D)时间复杂度低,使用〖BP(〗强度帕累托策略的〖BP)〗强度帕累托进化算法-2(SPEA2)能得到分布均匀的解集。结合这两种策略,提出一种新的多目标进化算法用于求解具有复杂、不连续的帕累托前沿的多目标优化问题(MOP)。首先,利用分解策略快速逼近帕累托前沿;然后,利用强度帕累托策略使解集均匀分布在帕累托前沿,利用解集重置分解策略中的权重向量集,使其适配于特定的帕累托前沿;最后,利用分解策略进一步逼近帕累托前沿。使用的反向世代距离(IGD)作为度量标准,将新算法与MOEA/D、SPEA2和paλ-MOEA/D在12个基准问题上进行性能对比。实验结果表明该算法性能在7个基准问题上最优,在5个基准问题上接近于最优,且无论MOP的帕累托前沿是简单或复杂、连续或不连续的,该算法均能生成分布均匀的解集。     

求解多目标优化问题的一种多子群体进化算法

提出一种新的多目标粒子群优化（MOPSO）算法,根据多目标优化问题（MOP）的特点,将一个进化群体分成若干个子群体,利用非劣支配的概念构造全局最优区域,用以指导整个粒子群的进化．通过子群体间的信息交换．使整个群体分布更均匀,并且避免了局部最优,保证了解的多样性,通过很少的迭代次数便可得到分布均匀的Pareto有效解集．数值实验表明了该算法的有效性.     

Time Complexity of Evolutionary Algorithms for Combinatorial Optimization： A Decade of Results

Computational time complexity analyzes of evolutionary algorithms (EAs) have been performed since the mid-nineties. The first results were related to very simple algorithms,such as the (1 1)-EA,on toy problems.These efforts produced a deeper understanding of how EAs perform on different kinds of fitness landscapes and general mathematical tools that may be extended to the analysis of more complicated EAs on more realistic problems.In fact,in recent years,it has been possible to analyze the (1 1)-EA on combinatorial optimization problems with practical applications and more realistic population-baeed EAs on structured toy problems. This paper presents a survey of the results obtained in the last decade along these two research lines.The most common mathematical techniques are introduced,the basic ideas behind them are discussed and their elective applications are highlighted.Solved problems that were still open are enumerated as are those still awaiting for a solution.New questions and problems arisen in the meantime are also considered.     

Utopian point based decomposition for multi-objective optimization problems with complicated Pareto fronts

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) has been considered as a promising method for solving multi-objective optimization problems (MOPs). It devotes most of its effort on convergence by optimizing a set of scalar optimization subproblems in a collaborative manner, while maintaining the diversity by using a set of uniformly distributed weight vectors. However, more recent studies illustrated that MOEA/D faces difficulties on MOPs with complicated Pareto fronts, mainly because the uniformity of weight vectors no longer lead to an evenly scattered approximation of the Pareto fronts in these cases. To remedy this, we suggest replacing the ideal point in the reciprocal Tchebycheff decomposition method with a more optimistic utopian point, with the aim of alleviating the sensitivity of MOEA/D to the Pareto front shape of MOPs. Experimental studies on benchmark and real-world problems have shown that such simple modification can significantly improve the performances of MOEA/D with reciprocal Tchebycheff decomposition on MOPs with complicated Pareto fronts.     

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.     

一种改进的多目标优化算法

为了提高非劣解向Pareto最优面收敛的速度以及解的多样性,设计了一种新的杂交算子并改进了NS-GA-Ⅱ算法。在此算法中,采用中心均值重组算子策略增强算法全局快速搜索能力,以获得最佳的Pareto近似解,同时,改进NSGA-Ⅱ快速非支配排序和拥挤机制将父代与子代的双种群进行截短,确保最优解不会丢失并保证解的多样性。数据实验表明,该算法能在解的收敛性、分布性以及自适应程度上均表现较好。     

A prediction strategy based on center points and knee points for evolutionary dynamic multi-objective optimization

In real life, there are many dynamic multi-objective optimization problems which vary over time, requiring an optimization algorithm to track the movement of the Pareto front (Pareto set) with time. In this paper, we propose a novel prediction strategy based on center points and knee points (CKPS) consisting of three mechanisms. First, a method of predicting the non-dominated set based on the forward-looking center points is proposed. Second, the knee point set is introduced to the predicted population to predict accurately the location and distribution of the Pareto front after an environmental change. Finally, an adaptive diversity maintenance strategy is proposed, which can generate some random individuals of the corresponding number according to the degree of difficulty of the problem to maintain the diversity of the population. The proposed strategy is compared with four other state-of-the-art strategies. The experimental results show that CKPS is effective for evolutionary dynamic multi-objective optimization.     

新的混合智能优化算法及其多目标优化应用

针对人工鱼群算法后期收敛速度较慢、解精度不高的不足,按照分阶段寻优和变参数寻优的改进策略,并结合禁忌搜索算法中的相关规则,提出一种新的混合智能优化算法。该算法将寻优过程分为锁定最优解或者局部解邻域和求得高精度最优解两个阶段,每个阶段设置不同的参数并结合禁忌搜索算法以提高收敛速度和最优解精度。典型函数验证表明,该算法收敛速度快、精度高;同时,对于多目标优化问题,该算法可以提高Pareto最优解集质量,扩大决策分布范围,维持决策多样性,有利于决策者作出决策。     

一类区间多目标粒子群优化算法

针对区间参数多目标优化问题,提出一种基于模糊支配的多目标粒子群优化算法。首先,定义基于决策者悲观程度的模糊支配关系,用于比较解的优劣;然后,定义一种适于区间目标值的拥挤距离,以更新外部存储器并从中选择领导粒子;最后,对多个区间多目标测试函数进行仿真实验,实验结果验证了所提出算法的有效性。     

Illustration of fairness in evolutionary multi-objective optimization

It is widely assumed that evolutionary algorithms for multi-objective optimization problems should use certain mechanisms to achieve a good spread over the Pareto front. In this paper, we examine such mechanisms from a theoretical point of view and analyze simple algorithms incorporating the concept of fairness. This mechanism tries to balance the number of offspring of all individuals in the current population. We rigorously analyze the runtime behavior of different fairness mechanisms and present illustrative examples to point out situations, where the right mechanism can speed up the optimization process significantly. We also indicate drawbacks for the use of fairness by presenting instances, where the optimization process is slowed down drastically.     

一种基于群智能的快速多目标优化算法

粒子群优化算法是一种典型的仿真群智能的算法。探讨了利用粒子群算法求解多目标优化问题,为了提高算法速度,采用了几何Pareto选择算法作为文档算法,用多方向搜索的办法寻找极端点。实验表明：该算法得到的解的数量多,速度快并且近似前沿的程度比较高。     

Structure optimization of neural networks for evolutionary design optimization

We study the use of neural networks as approximate models for the fitness evaluation in evolutionary design optimization. To improve the quality of the neural network models, structure optimization of these networks is performed with respect to two different criteria: One is the commonly used approximation error with respect to all available data, and the other is the ability of the networks to learn different problems of a common class of problems fast and with high accuracy. Simulation results from turbine blade optimizations using the structurally optimized neural network models are presented to show that the performance of the models can be improved significantly through structure optimization.We would like to thank the BMBF, grant LOKI, number 01 IB 001 C, for their financial support of our research.     

一种用于多目标优化的混合粒子群优化算法

将粒子群算法与局部优化方法相结合,提出了一种混合粒子群多目标优化算法（HMOPSO）。该算法针对粒子群局部优化性能较差的缺点,引入多目标线搜索与粒子群算法相结合的策略,以增强粒子群算法的局部搜索能力。HMOPSO首先运行PSO算法,得到近似的Pareto最优解;然后启动多目标线搜索,发挥传统数值优化算法的优势,对其进行进一步的优化。数值实验表明,HMOPSO具有良好的全局优化性能和较强的局部搜索能力,同时HMOPSO所得的非劣解集在分散性、错误率和逼近程度等量化指标上优于MOPSO。