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1.
    
For constrained multi-objective optimization problems (CMOPs), how to preserve infeasible individuals and make use of them is a problem to be solved. In this case, a modified objective function method with feasible-guiding strategy on the basis of NSGA-II is proposed to handle CMOPs in this paper. The main idea of proposed algorithm is to modify the objective function values of an individual with its constraint violation values and true objective function values, of which a feasibility ratio fed back from current population is used to keep the balance, and then the feasible-guiding strategy is adopted to make use of preserved infeasible individuals. In this way, non-dominated solutions, obtained from proposed algorithm, show superiority on convergence and diversity of distribution, which can be confirmed by the comparison experiment results with other two CMOEAs on commonly used constrained test problems.  相似文献   

2.
  总被引:1,自引:0,他引:1  
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.  相似文献   

3.
提出了一种求解约束优化问题的微分进化算法。该算法使得种群在演化过程中能保持较好的多样性,且参数设置简单,不容易陷入局部最优,并能在较短时间内找到问题的最优解。在对多个测试函数的数值模拟中都得到了较好的结果,体现了该算法的有效性、通用性和稳健性。  相似文献   

4.
    

Constrained multi-objective optimization problems (CMOPs) generally contain multiple constraints, which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions, thus they propose serious challenges for solvers. Among all constraints, some constraints are highly correlated with optimal feasible regions; thus they can provide effective help to find feasible Pareto front. However, most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints, and do not consider judging the relations among constraints and do not utilize the information from promising single constraints. Therefore, this paper attempts to identify promising single constraints and utilize them to help solve CMOPs. To be specific, a CMOP is transformed into a multitasking optimization problem, where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively. Besides, an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships. Moreover, an improved tentative method is designed to find and transfer useful knowledge among tasks. Experimental results on three benchmark test suites and 11 real-world problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.

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5.
Constraint handling is one of the major concerns when applying genetic algorithms (GAs) to solve constrained optimization problems. This paper proposes to use the gradient information derived from the constraint set to systematically repair infeasible solutions. The proposed repair procedure is embedded into a simple GA as a special operator. Experiments using 11 benchmark problems are presented and compared with the best known solutions reported in the literature. Our results are competitive, if not better, compared to the results reported using the homomorphous mapping method, the stochastic ranking method, and the self-adaptive fitness formulation method.  相似文献   

6.
操三强  雷德明 《信息与控制》2019,48(4):437-444,451
针对约束多目标优化问题,提出了一种基于约束违背程度和Pareto支配的有效约束处理策略,并设计了一种新型多目标帝国竞争算法(MOICA).该算法采用一种简化的初始帝国构建过程,在同化过程引入了向外部档案内非劣解学习的机制,并基于帝国势力新定义的帝国竞争新方法以获取问题高质量的解.选用了7个测试问题CF1~CF7进行计算实验并和多种算法进行对比.计算结果表明, MOICA在求解约束多目标优化问题方面具有较强的搜索能力和优势.  相似文献   

7.
为了制定合理高效的泊位岸桥联合分配方案,加快船舶周转,本文针对船舶动态到港的连续泊位建立了以船舶总在港时间最短为目标的泊位岸桥联合分配混合整数非线性模型.通过多目标约束处理策略将复杂约束的违反程度转化为另一个目标,从而将原单目标优化模型转化为双目标优化模型,并用基于快速非支配排序的多目标遗传算法(NSGA-II)对其进行求解.同时,针对问题特点,分别设计了基于调整、惩罚函数、可行解优先和综合约束处理策略的单目标遗传算法对原模型进行求解.通过多组不同规模的标准算例对本文的方法进行测试,验证了基于多目标约束处理策略的方法求解效果相较于单目标约束处理策略的方法更加高效和稳定.  相似文献   

8.
建立低碳疫苗冷链配送问题的约束多目标优化模型,在满足可用车数量、车辆容量约束和时间窗约束的条件下,考虑最小化碳排放的企业运输成本和客户不满意度。提出一种双档案协同进化的离散多目标烟花算法,采用消除车辆数量和容量约束的解码方式,设计了部分映射爆炸算子,设置可行解档案和不可行解档案协同进化,并对不可行解档案实施可行性搜索。实验结果表明,与已有算法相比,所提算法在低碳疫苗冷链配送问题上能高效地搜索到一组收敛精度和分布性能更优的Pareto非支配解。  相似文献   

9.
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.  相似文献   

10.
张凯  周德云  杨振  潘潜 《计算机应用》2020,40(3):902-911
面对未来作战中高密度、多方位的集群智能体,传统点对点饱和攻击已不是最佳策略,可通过选择合适的武器类型和作用点实现火力覆盖,达到武器数量小于目标数量的最大杀伤效果。综合考虑安全目标、毁伤门限、偏好指派等作战需求,首先,建立了多约束多目标武器-目标分配(CMWTA)数学模型;其次,设计了约束违反值的计算方法,并采用个体编码、检测修复和约束支配相结合的方式处理多约束;最后,设计了针对多目标武器-目标分配模型的收敛性度量指标,并基于多目标进化算法(MOEA)框架进行了仿真分析。其中在进化算法框架对比中,SPEA2下的Pareto集合容量主要分布于[21,25]区间内,NSGA-Ⅱ下的Pareto集合容量主要分布于[16,20],而MOEA/D下的Pareto集合容量均小于16;在修复算法验证中,修复算法将三种进化算法框架的Convergence指标提升了20%以上,且可将Pareto解集中不可行解的比例保持在0%。实验结果表明,在求解CMWTA模型中,SPEA2算法框架在分布性和收敛性上优于NSGA-Ⅱ和MOEA/D算法框架,且所提修复算法有效地提高了进化算法对非支配可行解的求解效率。  相似文献   

11.
    
Optimizing reactive power flow in electrical network is an important aspect of system study as the reactive power supports network voltage which needs to be maintained within desirable limits for system reliability. A network consisting of only conventional thermal generators has been extensively studied for optimal active and reactive power dispatch. However, increasing penetration of renewable sources into the grid necessitates power flow studies incorporating these sources. This paper presents a formulation and solution procedure for stochastic optimal reactive power dispatch (ORPD) problem with uncertainties in load demand, wind and solar power. Appropriate probability density functions (PDFs) are considered to model the stochastic load demand and the power generated from the renewable energy sources. Numerous scenarios are created running Monte-Carlo simulation and scenario reduction technique is implemented to deal with reduced number of scenarios. Real power loss and steady state voltage deviation of load buses in the network are set as the objectives of optimization. Success history based adaptive differential evolution (SHADE) is adopted as the basic search algorithm. SHADE has been successfully integrated with a constraint handling technique, called epsilon constraint (EC) handling, to handle constraints in ORPD problem. The effectiveness of a proper constraint handling technique is substantiated with case studies for deterministic ORPD on base configurations of IEEE 30-bus and 57-bus systems using SHADE-EC algorithm. The single-objective and multi-objective stochastic ORPD cases are also solved using the SHADE-EC algorithm. The results are discussed, compared and critically analyzed in this study.  相似文献   

12.
粒子群优化算法在多目标优化中的应用与仿真   总被引:3,自引:1,他引:3  
该文结合经济多目标优化的实际问题,对粒子群算法的初始化进行了改进,在给定范围内进行初始化,并且对于复杂域约束优化问题,给出了其实现与仿真。  相似文献   

13.
提出一种基于双局部最优的多目标粒子群优化算法,与可行解为优的约束处理方法相结合,来求解决非线性带约束的多目标电力系统环境经济调度问题。该算法针对传统多目标粒子群算法多样性低的局限性,通过对搜索空间的分割归类来增加帕累托最优解的多样性;并采用一种新的双局部最优来引导粒子的搜索,从而增强了算法的全局搜索能力。算法加入了可行解为优的约束处理方法对IEEE30节点六发电机电力系统环境经济负荷分配模型分别在几个不同复杂性问题的情况进行仿真测试,并与文献中的其他算法进行了比较。结果表明,改进的算法能够在保持帕累托最优解多样性的同时具有良好的收敛性能,更有效地解决电力系统环境经济调度问题。  相似文献   

14.
    
Over the last few decades, many different evolutionary algorithms have been introduced for solving constrained optimization problems. However, due to the variability of problem characteristics, no single algorithm performs consistently over a range of problems. In this paper, instead of introducing another such algorithm, we propose an evolutionary framework that utilizes existing knowledge to make logical changes for better performance. The algorithmic aspects considered here are: the way of using search operators, dealing with feasibility, setting parameters, and refining solutions. The combined impact of such modifications is significant as has been shown by solving two sets of test problems: (i) a set of 24 test problems that were used for the CEC2006 constrained optimization competition and (ii) a second set of 36 test instances introduced for the CEC2010 constrained optimization competition. The results demonstrate that the proposed algorithm shows better performance in comparison to the state-of-the-art algorithms.  相似文献   

15.
We present a new hybrid method for solving constrained numerical and engineering optimization problems in this paper. The proposed hybrid method takes advantage of the differential evolution (DE) ability to find global optimum in problems with complex design spaces while directly enforcing feasibility of constraints using a modified augmented Lagrangian multiplier method. The basic steps of the proposed method are comprised of an outer iteration, in which the Lagrangian multipliers and various penalty parameters are updated using a first-order update scheme, and an inner iteration, in which a nonlinear optimization of the modified augmented Lagrangian function with simple bound constraints is implemented by a modified differential evolution algorithm. Experimental results based on several well-known constrained numerical and engineering optimization problems demonstrate that the proposed method shows better performance in comparison to the state-of-the-art algorithms.  相似文献   

16.
The present paper proposes a double-multiplicative penalty strategy for constrained optimization by means of genetic algorithms (GAs). The aim of this research is to provide a simple and efficient way of handling constrained optimization problems in the GA framework without the need for tuning the values of penalty factors for any given optimization problem. After a short review on the most popular and effective exterior penalty formulations, the proposed penalty strategy is presented and tested on five different benchmark problems. The obtained results are compared with the best solutions provided in the literature, showing the effectiveness of the proposed approach.  相似文献   

17.
    
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.  相似文献   

18.
Penalty function approaches have been extensively applied to genetic algorithms for tackling constrained optimization problems. The effectiveness of the genetic searches to locate the global optimum on constrained optimization problems often relies on the proper selections of many parameters involved in the penalty function strategies. A successful genetic search is often completed after a number of genetic searches with varied combinations of penalty function related parameters. In order to provide a robust and effective penalty function strategy with which the design engineers use genetic algorithms to seek the optimum without the time-consuming tuning process, the self-organizing adaptive penalty strategy (SOAPS) for constrained genetic searches was proposed. This paper proposes the second generation of the self-organizing adaptive penalty strategy (SOAPS-II) to further improve the effectiveness and efficiency of the genetic searches on constrained optimization problems, especially when equality constraints are involved. The results of a number of illustrative testing problems show that the SOAPS-II consistently outperforms other penalty function approaches.  相似文献   

19.
This paper is the second one of the two papers entitled “Weighted Superposition Attraction (WSA) Algorithm”, which is about the performance evaluation of the WSA algorithm in solving the constrained global optimization problems. For this purpose, the well-known mechanical design optimization problems, design of a tension/compression coil spring, design of a pressure vessel, design of a welded beam and design of a speed reducer, are selected as test problems. Since all these problems were formulated as constrained global optimization problems, WSA algorithm requires a constraint handling method for tackling them. For this purpose we have selected 6 formerly developed constraint handling methods for adapting into WSA algorithm and analyze the effect of the used constraint handling method on the performance of the WSA algorithm. In other words, we have the aim of producing concluding remarks over the performance and robustness of the WSA algorithm through a set of computational study in solving the constrained global optimization problems. Computational study indicates the robustness and the effectiveness of the WSA in terms of obtained results, reached level of convergence and the capability of coping with the problems of premature convergence, trapping in a local optima and stagnation.  相似文献   

20.
One of the most important issues in developing an evolutionary optimization algorithm is the proper handling of any constraints on the problem. One must balance the objective function against the degree of constraint violation in such a way that neither is dominant. Common approaches to strike this balance include implementing a penalty function and the more recent stochastic ranking method, but these methods require an extra tuning parameter which must be chosen by the user. The present paper demonstrates that a proper balance can be achieved using an addition of ranking method. Through the ranking of the individuals with respect to the objective function and constraint violation independently, we convert these two properties into numerical values of the same order of magnitude. This removes the requirement of a user-specified penalty coefficient or any other tuning parameters. Direct addition of the ranking terms is then performed to integrate all information into a single decision variable. This approach is incorporated into a (μλ) evolution strategy and tested on thirteen benchmark problems, one engineering design problem, and five difficult problems with a high dimensionality or many constraints. The performance of the proposed strategy is similar to that of the stochastic ranking method when dealing with inequality constraints, but it has a much simpler ranking procedure and does not require any tuning parameters. A percentage-based tolerance value adjustment scheme is also proposed to enable feasible search when dealing with equality constraints.  相似文献   

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