BSTBGA: A hybrid genetic algorithm for constrained multi-objective optimization problems

Most of the existing multi-objective genetic algorithms were developed for unconstrained problems, even though most real-world problems are constrained. Based on the boundary simulation method and trie-tree data structure, this paper proposes a hybrid genetic algorithm to solve constrained multi-objective optimization problems (CMOPs). To validate our approach, a series of constrained multi-objective optimization problems are examined, and we compare the test results with those of the well-known NSGA-II algorithm, which is representative of the state of the art in this area. The numerical experiments indicate that the proposed method can clearly simulate the Pareto front for the problems under consideration.     

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.     

A hybrid genetic algorithm for constrained multi-objective optimization under uncertainty and target matching problems

This work presents a new approach for interval-based uncertainty analysis. The proposed approach integrates a local search strategy as the worst-case-scenario technique of anti-optimization with a constrained multi-objective genetic algorithm. Anti-optimization is a term for an approach to safety factors in engineering structures which is described as pessimistic and searching for least favorable responses, in combination with optimization techniques but in contrast to probabilistic approaches. The algorithm is applied and evaluated to be efficient and effective in producing good results via target matching problems: a simulated topology and shape optimization problem where a ‘target’ geometry set is predefined as the Pareto optimal solution and a constrained multiobjective optimization problem formulated such that the design solutions will evolve and converge towards the target geometry set.     

A hybrid cooperative search algorithm for constrained optimization

Many engineering design problems can be formulated as constrained optimization problems which often consist of many mixed equality and inequality constraints. In this article, a hybrid coevolutionary method is developed to solve constrained optimization problems formulated as min–max problems. The new method is fast and capable of global search because of combining particle swarm optimization and gradient search to balance exploration and exploitation. It starts by transforming the problem into unconstrained one using an augmented Lagrangian function, then using two groups to optimize different components of the solution vector in a cooperative procedure. In each group, the final stage of the search procedure is accelerated by via a simple local search method on the best point reached by the preceding exploration based search. We validated the effectiveness and robustness of the proposed algorithm using several engineering problems taken from the specialised literature.     

A penalty PALM method for sparse portfolio selection problems

In this paper, we propose a penalty proximal alternating linearized minimization method for the large-scale sparse portfolio problems in which a sequence of penalty subproblems are solved by utilizing the proximal alternating linearized minimization framework and sparse projection techniques. For exploiting the structure of the problems and reducing the computation complexity, each penalty subproblem is solved by alternately solving two projection problems. The global convergence of the method to a Karush-Kuhn-Tucker point or a local minimizer of the problem can be proved under the characteristic of the problem. The computational results with practical problems demonstrate that our method can find the suboptimal solutions of the problems efficiently and is competitive with some other local solution methods.     

A PROMETHEE-based approach to portfolio selection problems

In this paper, we study the use of PROMETHEE outranking methods for portfolio selection problems. Starting from a new formulation of the PROMETHEE V method, we develop several alternative approaches based on the concepts of boundary portfolios and c-optimal portfolios. The proposed methods are compared in an extensive computational study. Results of these experiments show that methods based on the concept of c-optimal portfolios provide a good approximation to the (often computationally untractable) PROMETHEE ranking of all portfolios, while requiring only small computational effort even for large problems. For smaller problems, a PROMETHEE ranking of all boundary portfolios can be performed and provides a close approximation of the total ranking.     

A hybrid algorithm for distribution problems

Distribution is a major factor in the supply chain for Sodra Cell, a leading manufacturer of pulp intended for paper production. Each year, the company transports large quantities of pulp using ships, trains, and trucks; here we focus on scheduling the ships and optimizing deliveries to minimize distribution costs.     

A novel hybrid algorithm for feature selection

Feature selection is an important filtering method for data analysis, pattern classification, data mining, and so on. Feature selection reduces the number of features by removing irrelevant and redundant data. In this paper, we propose a hybrid filter–wrapper feature subset selection algorithm called the maximum Spearman minimum covariance cuckoo search (MSMCCS). First, based on Spearman and covariance, a filter algorithm is proposed called maximum Spearman minimum covariance (MSMC). Second, three parameters are proposed in MSMC to adjust the weights of the correlation and redundancy, improve the relevance of feature subsets, and reduce the redundancy. Third, in the improved cuckoo search algorithm, a weighted combination strategy is used to select candidate feature subsets, a crossover mutation concept is used to adjust the candidate feature subsets, and finally, the filtered features are selected into optimal feature subsets. Therefore, the MSMCCS combines the efficiency of filters with the greater accuracy of wrappers. Experimental results on eight common data sets from the University of California at Irvine Machine Learning Repository showed that the MSMCCS algorithm had better classification accuracy than the seven wrapper methods, the one filter method, and the two hybrid methods. Furthermore, the proposed algorithm achieved preferable performance on the Wilcoxon signed-rank test and the sensitivity–specificity test.     

求解多目标投资组合优化模型的遗传算法

针对考虑最小交易量、交易费用,以及单项目最大投资上限约束的多目标投资组合模型,对目标函数添加惩罚函数项来处理约束条件的方法.本文通过对交叉算子、变异算子的改进,设计了一种遗传算法进行求解.实验算例表明,该算法是有效的.     

A parallel algorithm for constrained two-staged two-dimensional cutting problems

In this paper, we solve the two-staged two-dimensional cutting problem using a parallel algorithm. The proposed approach combines two main features: beam search (BS) and strip generation solution procedures (SGSP). BS employs a truncated tree-search, where a selected subset of generated nodes are retuned for further search. SGSP, a constructive procedure, combines a (sub)set of strips for providing both partial lower and complementary upper bounds. The algorithm explores in parallel a subset of selected nodes following the master-slave paradigm. The master processor serves to guide the search-resolution and each slave processor develops its proper way, trying a global convergence. The aim of such an approach is to show how the parallelism is able to efficiently solve large-scale instances, by providing new solutions within a consistently reduced runtime. Extensive computational testing on instances, taken from the literature, shows the effectiveness of the proposed approach.     

一种求解约束多目标问题的协作进化算法

针对约束多目标进化算法求解约束多目标问题时难以平衡收敛性、多样性和可行性的问题,提出一种协作进化算法(ConMOEA).将自适应形状估计进化算法(AGE-MOEA)和非支配排序遗传算法(NSGA-II)优势融合,采用Deb约束支配原则非支配排序组合种群实现个体优选,在临界层中根据最大拥挤距离或生存值选择所需个体,最终形成新种群,实现种群快速接近Pareto前沿并具有良好分布性.为验证所提出算法的性能,对近期提出的一组DOC基准函数进行仿真计算,采用反世代距离(IGD)和超体积(HV)两个通用评价指标,与NSGA-II-CDP、C-TAEA、PPS、ToP、A-NSGA-III、AGE-MOEA约束多目标算法进行比较分析,实验结果证明ConMOEA具有更优的收敛性和多样性.     

A linear programming algorithm for optimal portfolio selection with transaction costs

We study the optimal portfolio selection problem with transaction costs. In general, the efficient frontier can be determined by solving a parametric non-quadratic programming problem. In a general setting, the transaction cost is a V-shaped function of difference between the existing and the new portfolio. We show how to transform this problem into a quadratic programming model. Hence a linear programming algorithm is applicable by establishing a linear approximation on the utility function of return and variance.     

DEMORS: A hybrid multi-objective optimization algorithm using differential evolution and rough set theory for constrained problems

The aim of this paper is to show how the hybridization of a multi-objective evolutionary algorithm (MOEA) and a local search method based on the use of rough set theory is a viable alternative to obtain a robust algorithm able to solve difficult constrained multi-objective optimization problems at a moderate computational cost. This paper extends a previously published MOEA [Hernández-Díaz AG, Santana-Quintero LV, Coello Coello C, Caballero R, Molina J. A new proposal for multi-objective optimization using differential evolution and rough set theory. In: 2006 genetic and evolutionary computation conference (GECCO’2006). Seattle, Washington, USA: ACM Press; July 2006], which was limited to unconstrained multi-objective optimization problems. Here, the main idea is to use this sort of hybrid approach to approximate the Pareto front of a constrained multi-objective optimization problem while performing a relatively low number of fitness function evaluations. Since in real-world problems the cost of evaluating the objective functions is the most significant, our underlying assumption is that, by aiming to minimize the number of such evaluations, our MOEA can be considered efficient. As in its previous version, our hybrid approach operates in two stages: in the first one, a multi-objective version of differential evolution is used to generate an initial approximation of the Pareto front. Then, in the second stage, rough set theory is used to improve the spread and quality of this initial approximation. To assess the performance of our proposed approach, we adopt, on the one hand, a set of standard bi-objective constrained test problems and, on the other hand, a large real-world problem with eight objective functions and 160 decision variables. The first set of problems are solved performing 10,000 fitness function evaluations, which is a competitive value compared to the number of evaluations previously reported in the specialized literature for such problems. The real-world problem is solved performing 250,000 fitness function evaluations, mainly because of its high dimensionality. Our results are compared with respect to those generated by NSGA-II, which is a MOEA representative of the state-of-the-art in the area.     

Fuzzy portfolio selection using genetic algorithm

This paper presents the development of fuzzy portfolio selection model in investment. Fuzzy logic is utilized in the estimation of expected return and risk. Using fuzzy logic, managers can extract useful information and estimate expected return by using not only statistical data, but also economical and financial behaviors of the companies and their business strategies. In the formulated fuzzy portfolio model, fuzzy set theory provides the possibility of trade-off between risk and return. This is obtained by assigning a satisfaction degree between criteria and constraints. Using the formulated fuzzy portfolio model, a Genetic Algorithm (GA) is applied to find optimal values of risky securities. Numerical examples are given to demonstrate the effectiveness of proposed method.     

Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems.

This paper presents a novel evolutionary algorithm (EA) for constrained optimization problems, i.e., the hybrid constrained optimization EA (HCOEA). This algorithm effectively combines multiobjective optimization with global and local search models. In performing the global search, a niching genetic algorithm based on tournament selection is proposed. Also, HCOEA has adopted a parallel local search operator that implements a clustering partition of the population and multiparent crossover to generate the offspring population. Then, nondominated individuals in the offspring population are used to replace the dominated individuals in the parent population. Meanwhile, the best infeasible individual replacement scheme is devised for the purpose of rapidly guiding the population toward the feasible region of the search space. During the evolutionary process, the global search model effectively promotes high population diversity, and the local search model remarkably accelerates the convergence speed. HCOEA is tested on 13 well-known benchmark functions, and the experimental results suggest that it is more robust and efficient than other state-of-the-art algorithms from the literature in terms of the selected performance metrics, such as the best, median, mean, and worst objective function values and the standard deviations.     

一种求解约束优化问题的混沌文化算法*

在求解约束优化问题时,为了有效处理约束条件,克服文化算法易陷入局部极值点、混沌搜索优化初值敏感、搜索效率低等缺陷,将混沌搜索优化嵌入至文化算法框架,提出一种求解约束优化问题的混沌文化算法。该模型由基于混沌的群体空间和存储知识的信念空间组成,利用地形知识表达约束条件,标准知识和地形知识共同引导混沌搜索,并利用形势知识引导混沌扰动。实例表明,该算法具有较优良的搜索性能,尤其能有效处理高维复杂约束优化问题。     

一种求解约束优化问题的混合算法

提出一种基于修改增广Lagrange函数和PSO的混合算法用于求解约束优化问题。将约束优化问题转化为界约束优化问题,混合算法由两层迭代结构组成,在内层迭代中,利用改进PSO算法求解界约束优化问题得到下一个迭代点。外层迭代主要修正Lagrange乘子和罚参数,检查收敛准则是否满足,重构下次迭代的界约束优化子问题,检查收敛准则是否满足。数值实验结果表明该混合算法的有效性。     

A novel modified differential evolution algorithm for constrained optimization problems

A novel modified differential evolution algorithm (NMDE) is proposed to solve constrained optimization problems in this paper. The NMDE algorithm modifies scale factor and crossover rate using an adaptive strategy. For any solution, if it is at a standstill, its own scale factor and crossover rate will be adjusted in terms of the information of all successful solutions. We can obtain satisfactory feasible solutions for constrained optimization problems by combining the NMDE algorithm and a common penalty function method. Experimental results show that the proposed algorithm can yield better solutions than those reported in the literature for most problems, and it can be an efficient alternative to solving constrained optimization problems.