基数约束投资组合问题的一种混合元启发式算法求解

针对资产数目和投资资金比例受约束的投资组合选择这一NP难问题,基于混沌搜索、粒子群优化和引力搜索算法提出了一种新的混合元启发式搜索算法。该算法能很好地平衡开发能力和勘探能力,有效抑制了算法早熟收敛现象。标准测试函数的测试结果表明混合算法与标准的粒子群优化和引力搜索算法相比具有更好的寻优效率;实证分析进一步对混合算法与遗传算法及粒子群优化算法在求解这类投资组合选择问题的性能进行了比较。数值结果表明,混合算法在搜索具有高预期回报的非支配投资组合方面表现更好,取得了更为满意的结果。     

Portfolio selection using neural networks

In this paper we apply a heuristic method based on artificial neural networks (NN) in order to trace out the efficient frontier associated to the portfolio selection problem. We consider a generalization of the standard Markowitz mean-variance model which includes cardinality and bounding constraints. These constraints ensure the investment in a given number of different assets and limit the amount of capital to be invested in each asset. We present some experimental results obtained with the NN heuristic and we compare them to those obtained with three previous heuristic methods. The portfolio selection problem is an instance from the family of quadratic programming problems when the standard Markowitz mean-variance model is considered. But if this model is generalized to include cardinality and bounding constraints, then the portfolio selection problem becomes a mixed quadratic and integer programming problem. When considering the latter model, there is not any exact algorithm able to solve the portfolio selection problem in an efficient way. The use of heuristic algorithms in this case is imperative. In the past some heuristic methods based mainly on evolutionary algorithms, tabu search and simulated annealing have been developed. The purpose of this paper is to consider a particular neural network (NN) model, the Hopfield network, which has been used to solve some other optimisation problems and apply it here to the portfolio selection problem, comparing the new results to those obtained with previous heuristic algorithms.     

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.     

A hybrid algorithm for constrained portfolio selection problems

Since Markowitz’s seminal work on the mean-variance model in modern portfolio theory, many studies have been conducted on computational techniques and recently meta-heuristics for portfolio selection problems. In this work, we propose and investigate a new hybrid algorithm integrating the population based incremental learning and differential evolution algorithms for the portfolio selection problem. We consider the extended mean-variance model with practical trading constraints including the cardinality, floor and ceiling constraints. The proposed hybrid algorithm adopts a partially guided mutation and an elitist strategy to promote the quality of solution. The performance of the proposed hybrid algorithm has been evaluated on the extended benchmark datasets in the OR Library. The computational results demonstrate that the proposed hybrid algorithm is not only effective but also efficient in solving the mean-variance model with real world constraints.     

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.     

The capacitated minimum spanning tree problem: revisiting hop-indexed formulations

The capacitated minimum spanning tree problem is to find a minimum spanning tree with an additional cardinality constraint on the number of nodes in any subtree off a given root node. In this paper we propose two improvements on a previous cutting-plane method proposed by Gouveia and Martins (Networks 35(1) (2000) 1) namely, a new set of inequalities that can be seen as hop-indexed generalization of the well known generalized subtour elimination (GSE) constraints and an improved separation heuristic for the original set of GSE constraints. Computational results show that the inclusion of the new separation routine and the inclusion of the new inequalities in Gouveia and Martins’ iterative method (see (Networks 35(1) (2000) 1)) produce improvements on previously reported lower bounds. Furthermore, with the improved method, several of previous unsolved instances have been solved to optimality.     

A constrained portfolio selection model at considering risk-adjusted measure by using hybrid meta-heuristic algorithms

Portfolio selection is a key issue in the business world and financial fields. This article presents a new decision making method of portfolio optimization (PO) issues in different risk measures by using new evolutionary computing method and cardinality constrains which is mentioned as hybrid meta-heuristic algorithms. Based on mean–variance (MV) Method by Markowitz we collected three risk levels; mean absolute deviation (MAD), semi variance (SV) and variance with skewness (VWS). The developed algorithms are Electromagnetism-like algorithm (EM), particle swarm optimization (PSO), genetic algorithm (GA), genetic network programming (GNP) and simulated annealing (SA). Also a diversification mechanism strategy is implemented and hybridized with the developed algorithms to increase the diversity and overcome local optimality. The sustainability of this proposed model is verified by 50 factories on the Iranian stock exchange. Finally, experimental results of proposed algorithms with cardinality constraint are compared with each other by four effective metrics in which the algorithms performance for achieving the optimal solution discussed. In addition, we have done the analysis of variance technique to confirm the validity and accurately analyze of the results which the success of this method was proved.     

QoS multicast routing using a quantum-behaved particle swarm optimization algorithm

QoS multicast routing in networks is a very important research issue in networks and distributed systems. It is also a challenging and hard problem for high-performance networks of the next generation. Due to its NP-completeness, many heuristic methods have been employed to solve the problem. This paper proposes the modified quantum-behaved particle swarm optimization (QPSO) method for QoS multicast routing. In the proposed method, QoS multicast routing is converted into an integer programming problem with QoS constraints and is solved by the QPSO algorithm combined with loop deletion operation. The QPSO-based routing method, along with the routing algorithms based on particle swarm optimization (PSO) and genetic algorithm (GA), is tested on randomly generated network topologies for the purpose of performance evaluation. The simulation results show the efficiency of the proposed method on QoS the routing problem and its superiority to the methods based on PSO and GA.     

广义粒子群优化模型

粒子群优化算法提出至今一直未能有效解决的离散及组合优化问题．针对这个问题,文中首先回顾了粒子群优化算法在整数规划问题的应用以及该算法的二进制离散优化模型,并分析了其缺陷．然后,基于传统算法的速度一位移更新操作,在分析粒子群优化机理的基础上提出了广义粒子群优化模型（GPSO）,使其适用于解决离散及组合优化问题．GPSO模型本质仍然符合粒子群优化机理,但是其粒子更新策略既可根据优化问题的特点设计,也可实现与已有方法的融合．该文以旅行商问题（TSP）为例,针对遗传算法（GA）解决该问题的成功经验,使用遗传操作作为GPSO模型中的更新算子,进一步提出基于遗传操作的粒子群优化模型,并以Inverover算子作为模型中具体的遗传操作设计了基于GPSO模型的TSP算法．与采用相同遗传操作的GA比较,基于GPSO模型的算法解的质量与收敛稳定性提高,同时计算费用显著降低．     

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.     

Wavelet evolutionary network for complex-constrained portfolio rebalancing

Portfolio rebalancing problem deals with resetting the proportion of different assets in a portfolio with respect to changing market conditions. The constraints included in the portfolio rebalancing problem are basic, cardinality, bounding, class and proportional transaction cost. In this study, a new heuristic algorithm named wavelet evolutionary network (WEN) is proposed for the solution of complex-constrained portfolio rebalancing problem. Initially, the empirical covariance matrix, one of the key inputs to the problem, is estimated using the wavelet shrinkage denoising technique to obtain better optimal portfolios. Secondly, the complex cardinality constraint is eliminated using k-means cluster analysis. Finally, WEN strategy with logical procedures is employed to find the initial proportion of investment in portfolio of assets and also rebalance them after certain period. Experimental studies of WEN are undertaken on Bombay Stock Exchange, India (BSE200 index, period: July 2001–July 2006) and Tokyo Stock Exchange, Japan (Nikkei225 index, period: March 2002–March 2007) data sets. The result obtained using WEN is compared with the only existing counterpart named Hopfield evolutionary network (HEN) strategy and also verifies that WEN performs better than HEN. In addition, different performance metrics and data envelopment analysis are carried out to prove the robustness and efficiency of WEN over HEN strategy.     

A heuristic method for learning Bayesian networks using discrete particle swarm optimization

Bayesian networks are a powerful approach for representing and reasoning under conditions of uncertainty. Many researchers aim to find good algorithms for learning Bayesian networks from data. And the heuristic search algorithm is one of the most effective algorithms. Because the number of possible structures grows exponentially with the number of variables, learning the model structure from data by considering all possible structures exhaustively is infeasible. PSO (particle swarm optimization), a powerful optimal heuristic search algorithm, has been applied in various fields. Unfortunately, the classical PSO algorithm only operates in continuous and real-valued space, and the problem of Bayesian networks learning is in discrete space. In this paper, two modifications of updating rules for velocity and position are introduced and a Bayesian networks learning based on binary PSO is proposed. Experimental results show that it is more efficient because only fewer generations are needed to obtain optimal Bayesian networks structures. In the comparison, this method outperforms other heuristic methods such as GA (genetic algorithm) and classical binary PSO.     

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.     

Generation bidding strategy in a pool based electricity market using Shuffled Frog Leaping Algorithm

In an electricity market generation companies need suitable bidding models to maximize their profits. Therefore, each supplier will bid strategically for choosing the bidding coefficients to counter the competitors bidding strategy. In this paper optimal bidding strategy problem is solved using a novel algorithm based on Shuffled Frog Leaping Algorithm (SFLA). It is memetic meta-heuristic that is designed to seek a global optimal solution by performing a heuristic search. It combines the benefits of the Genetic-based Memetic Algorithm (MA) and the social behavior-based Particle Swarm Optimization (PSO). Due to this it has better precise search which avoids premature convergence and selection of operators. Therefore, the proposed method overcomes the short comings of selection of operators and premature convergence of Genetic Algorithm (GA) and PSO method. Important merit of the proposed SFALA is that faster convergence. The proposed method is numerically verified through computer simulations on IEEE 30-bus system consist of 6 suppliers and practical 75-bus Indian system consist of 15 suppliers. The result shows that SFLA takes less computational time and producing higher profits compared to Fuzzy Adaptive PSO (FAPSO), PSO and GA.     

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.     

A new Chance-Variance optimization criterion for portfolio selection in uncertain decision systems

The Markowitz’s mean-variance (M-V) model has received widespread acceptance as a practical tool for portfolio optimization, and his seminal work has been widely extended in the literature. The aim of this article is to extend the M-V method in hybrid decision systems. We suggest a new Chance-Variance (C-V) criterion to model the returns characterized by fuzzy random variables. For this purpose, we develop two types of C-V models for portfolio selection problems in hybrid uncertain decision systems. Type I C-V model is to minimize the variance of total expected return rate subject to chance constraint; while type II C-V model is to maximize the chance of achieving a prescribed return level subject to variance constraint. Hence the two types of C-V models reflect investors’ different attitudes toward risk. The issues about the computation of variance and chance distribution are considered. For general fuzzy random returns, we suggest an approximation method of computing variance and chance distribution so that C-V models can be turned into their approximating models. When the returns are characterized by trapezoidal fuzzy random variables, we employ the variance and chance distribution formulas to turn C-V models into their equivalent stochastic programming problems. Since the equivalent stochastic programming problems include a number of probability distribution functions in their objective and constraint functions, conventional solution methods cannot be used to solve them directly. In this paper, we design a heuristic algorithm to solve them. The developed algorithm combines Monte Carlo (MC) method and particle swarm optimization (PSO) algorithm, in which MC method is used to compute probability distribution functions, and PSO algorithm is used to solve stochastic programming problems. Finally, we present one portfolio selection problem to demonstrate the developed modeling ideas and the effectiveness of the designed algorithm. We also compare the proposed C-V method with M-V one for our portfolio selection problem via numerical experiments.     

Simulation-based heuristic method for container supply chain network optimization

With the emerging of free trade zones (FTZs) in the world, the service level of container supply chain plays an important role in the efficiency, quality and cost of the world trade. The performance of container supply chain network directly impacts its service level. Therefore, it is imperative to seek an appropriate method to optimize the container supply chain network architecture. This paper deals with the modeling and optimization problem of multi-echelon container supply chain network (MCSCN). The problem is formulated as a mixed integer programming model (MIP), where the objective is subject to the minimization of the total supply chain service cost. Since the problem is well known to be NP-hard, a novel simulation-based heuristic method is proposed to solving it, where the heuristic is used for searching near-optimal solutions, and the simulation is used for evaluating solutions and repairing unfeasible solutions. The heuristic algorithm integrates genetic algorithm (GA) and particle swarm optimization (PSO) algorithm, where the GA is used for global search and the PSO is used for local search. Finally, computational experiments are conducted to validate the performance of the proposed method and give some managerial implications.     

粒子群算法及其在布局优化中的应用

复杂工程布局(如卫星舱布局)方案设计问题,在理论上属带性能约束的布局优化问题(NPC问题),很难求解。论文以卫星舱布局为例,将粒子群算法(PSO)应用于布局问题,构造此类问题的粒子表达方法,建立了此类问题的粒子群算法。文中通过3个算例(其中一个为已知最优解的算例)的数值计算,验证了该算法的可行性和有效性。     

Solution to profit based unit commitment problem using particle swarm optimization

In this paper, an algorithm to solve the profit based unit commitment problem (PBUCP) under deregulated environment has been proposed using Particle Swarm Optimization (PSO) intelligent technique to maximize the GENCOs profit. Deregulation in power sector increases the efficiency of electricity production and distribution, offer lower prices, higher quality, a secure and a more reliable product. The proposed algorithm has been developed from the view point of a generation company wishing to maximize its profit in the deregulated power and reserve markets. UC schedule depends on the market price in the deregulated market. In deregulated environment utilities are not required to meet the demand. GENCO can consider a schedule that produce less than the predicted load demand and reserve but creates maximum profit. More number of units are committed when the market price is higher. When more number of generating units are brought online more power is generated and participated in the deregulated market to get maximum profit. This paper presents a new approach of GENCOs profit based unit commitment using PSO technique in a day ahead competitive electricity markets. The profit based unit commitment problem is solved using various PSO techniques such as Chaotic PSO (CPSO), New PSO (NPSO) and Dispersed PSO (DPSO) and the results are compared. Generation, spinning reserve, non-spinning reserve, and system constraints are considered in proposed formulation. The proposed approach has been tested on IEEE-30 bus system with 6 generating units as an individual GENCO. The results obtained are quite encouraging and useful in deregulated market. The algorithm and simulation are carried out using Matlab software.     

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.