求解约束优化问题的一种新算法

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。     

Constraint handling in genetic algorithms using a gradient-based repair method

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.     

一种新型约束多目标帝国竞争算法

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.     

多目标约束处理方法求解泊位岸桥联合分配问题

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.     

采用双档案协同进化离散多目标烟花算法的低碳疫苗冷链优化配送

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。     

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.     

多约束集群目标下武器-目标分配问题

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。     

粒子群优化算法在多目标优化中的应用与仿真

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。     

双局部粒子群算法解决环境经济调度问题

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。     

A hybrid differential evolution augmented Lagrangian method for constrained numerical and engineering optimization

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.     

A double-multiplicative dynamic penalty approach for constrained evolutionary optimization

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.     

The second generation of self-organizing adaptive penalty strategy for constrained genetic search

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.     

Weighted Superposition Attraction (WSA): A swarm intelligence algorithm for optimization problems – Part 2: Constrained optimization

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.     

Evolutionary constrained optimization using an addition of ranking method and a percentage-based tolerance value adjustment scheme

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 (μ, λ) 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.