On three new approaches to handle constraints within evolution strategies

Evolutionary algorithms with a self-adaptive step control mechanism like evolution strategies (ES) often suffer from premature fitness stagnation on constrained numerical optimization problems. When the optimum lies on the constraint boundary or even in a vertex of the feasible search space, a disadvantageous success probability results in premature step size reduction. We introduce three new constraint-handling methods for ES on constrained continuous search spaces. The death penalty step control evolution strategy (DSES) is based on the controlled reduction of a minimum step size depending on the distance to the infeasible search space. The two sexes evolution strategy (TSES) is inspired by the biological concept of sexual selection and pairing. At last, the nested angle evolution strategy (NAES) is an approach in which the angles of the correlated mutation of the inner ES are adapted by the outer ES. All methods are experimentally evaluated on four selected test problems and compared with existing penalty-based constraint-handling methods.     

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.     

Ant colony optimization combined with taboo search for the job shop scheduling problem

In this paper, we present a hybrid algorithm combining ant colony optimization algorithm with the taboo search algorithm for the classical job shop scheduling problem. Instead of using the conventional construction approach to construct feasible schedules, the proposed ant colony optimization algorithm employs a novel decomposition method inspired by the shifting bottleneck procedure, and a mechanism of occasional reoptimizations of partial schedules. Besides, a taboo search algorithm is embedded to improve the solution quality. We run the proposed algorithm on 101 benchmark instances and obtain competitive results and a new best upper bound for one open benchmark instance is found.     

聚类佳点集交叉的约束优化混合进化算法

提出一种基于聚类佳点集多父代交叉和自适应约束处理技术的混合进化算法用于求解约束优化问题.新算法的主要特点是:在搜索机制方面,利用佳点集方法构造初始化种群,使个体能够均匀地分布在整个搜索空间.然后根据父代个体的相似度将种群个体进行聚类分析,从聚类中随机选择个体进行佳点集多父代交叉操作,利用多个父代个体所携带的信息产生新的具有代表性的子代个体,能够维持和增加种群的多样性.另外,引入局部搜索策略以提高算法局部搜索能力和收敛速度.在约束处理技术上,新算法引入了一个自适应约束处理技术,即根据当前种群中可行解的比例自适应选择不同的个体比较准则.通过15个标准测试函数验证了新算法的有效性.     

改进蚁群算法在路径规划中的应用

针对传统蚁群算法在机器人路径规划时存在收敛速度慢、易陷入局部最优等问题,提出了一种基于自适应归档更新的蚁群算法。根据路径性能指标建立多目标性能评估模型,对最优路径进行多指标优化;采用路径方案归档更新策略进行路径方案的更新和筛选,提高算法的收敛速度;当搜索路径进入不可行区域时,采用自适应路径补偿策略转移不可行路径节点,构造可行路径,减少死锁蚂蚁数量;若算法无法避开障碍或者进入停滞状态,则进行种群重新初始化,增加物种多样性,避免算法陷入局部最优。仿真实验表明,改进后的算法收敛速度更快、收敛精度更高、稳定性更好。     

A simple multimembered evolution strategy to solve constrained optimization problems

This work presents a simple multimembered evolution strategy to solve global nonlinear optimization problems. The approach does not require the use of a penalty function. Instead, it uses a simple diversity mechanism based on allowing infeasible solutions to remain in the population. This technique helps the algorithm to find the global optimum despite reaching reasonably fast the feasible region of the search space. A simple feasibility-based comparison mechanism is used to guide the process toward the feasible region of the search space. Also, the initial stepsize of the evolution strategy is reduced in order to perform a finer search and a combined (discrete/intermediate) panmictic recombination technique improves its exploitation capabilities. The approach was tested with a well-known benchmark. The results obtained are very competitive when comparing the proposed approach against other state-of-the art techniques and its computational cost (measured by the number of fitness function evaluations) is lower than the cost required by the other techniques compared.     

一个蚁群优化模型的期望性能分析

用蚁群优化求解组合优化问题时, 信息素模型及其规则可能使问题的各组件之间的竞争失衡, 从而有可能使蚁群搜索停滞在最差解。 研究了蚁群优化求解k-最小生成树问题时的信息素模型及其更新规则对性能的影响,对原有的信息素模型作出了新的解释:直接表示k-最小生成树问题的边被选择的概率。基于新的信息素模型设计了一种新的解的构造过程,这种过程不仅产生可行解, 也产生不可行解;同时研究了使用可行解和全部解更新信息素模型时算法的迭代期望质量随时间的增减情况,其结果表明, 只使用可行解时迭代期望质量随时间连续降低, 而使用全     

基于改进蚁群算法的无人飞行器航迹规划

无人飞行器航迹规划是现代战争中实施远程精确打击,提高飞行器实际作战效能的关键技术。蚁群算法作为一种启发式仿生优化算法,能够有效应用于航迹规划中。针对基本蚁群算法在应用中容易过早陷入局部最优解这一缺点,提出自适应动态双种群蚁群算法的改进策略,通过信息素的震荡变化和挥发系数的自适应调整,扩大搜索空间,提高算法搜索的全局性。并将改进后的算法应用于无人飞行器航迹规划,通过实验仿真,证明了此改进算法在航迹规划应用中的可行性和有效性。     

Particle swarm optimizer,ant colony strategy and harmony search scheme hybridized for optimization of truss structures

A heuristic particle swarm ant colony optimization (HPSACO) is presented for optimum design of trusses. The algorithm is based on the particle swarm optimizer with passive congregation (PSOPC), ant colony optimization and harmony search scheme. HPSACO applies PSOPC for global optimization and the ant colony approach is used to update positions of particles to attain the feasible solution space. HPSACO handles the problem-specific constraints using a fly-back mechanism, and harmony search scheme deals with variable constraints. Results demonstrate the efficiency and robustness of HPSACO, which performs better than the other PSO-based algorithms having higher converges rate than PSO and PSOPC.     

自适应约束优化混合粒子群算法

提出一种混合粒子群优化算法用于求解约束优化问题。新算法的主要特点是：在搜索机制方面,利用混沌初始化种群以提高初始群体的质量。为了扩大粒子的搜索范围,引入柯西变异算子。利用单形交叉算子对种群进行局部搜索。在约束处理技术方面,根据当前种群中可行解比例自适应地选择不同的个体比较准则。数值实验结果表明了该算法的有效性。     

A multi-objective differential evolutionary algorithm for constrained multi-objective optimization problems with low feasible ratio

Most current evolutionary multi-objective optimization (EMO) algorithms perform well on multi-objective optimization problems without constraints, but they encounter difficulties in their ability for constrained multi-objective optimization problems (CMOPs) with low feasible ratio. To tackle this problem, this paper proposes a multi-objective differential evolutionary algorithm named MODE-SaE based on an improved epsilon constraint-handling method. Firstly, MODE-SaE self-adaptively adjusts the epsilon level in line with the maximum and minimum constraint violation values of infeasible individuals. It can prevent epsilon level setting from being unreasonable. Then, the feasible solutions are saved to the external archive and take part in the population evolution by a co-evolution strategy. Finally, MODE-SaE switches the global search and local search by self-switching parameters of search engine to balance the convergence and distribution. With the aim of evaluating the performance of MODE-SaE, a real-world problem with low feasible ratio in decision space and fourteen bench-mark test problems, are used to test MODE-SaE and five other state-of-the-art constrained multi-objective evolution algorithms. The experimental results fully demonstrate the superiority of MODE-SaE on all mentioned test problems, which indicates the effectiveness of the proposed algorithm for CMOPs which have low feasible ratio in search space.     

Constrained global optimization via a DIRECT-type constraint-handling technique and an adaptive metamodeling strategy

Recent metamodel-based global optimization algorithms are very promising for box-constrained expensive optimization problems. However, few of them can tackle constrained optimization problems. This article presents an improved constrained optimization algorithm, called eDIRECT-C, for expensive constrained optimization problems. In the eDIRECT-C algorithm, we present a novel DIRECT-type constraint-handling technique that separately handles feasible and infeasible cells. This technique has no user-defined parameter and is beneficial for exploring the undetected feasible regions and boundary of feasible regions. We also employ an adaptive metamodeling strategy to build appropriate metamodel types for objective and constraints respectively. This strategy yields more accurate predictions and therefore significantly speeds up the convergence. To assess the performance of eDIRECT-C, we compare it with some state-of-the-art metamodel-based constrained optimization algorithms and the original DIRECT algorithm on 13 benchmark problems and 4 engineering examples. The comparative results imply that the proposed algorithm is very promising for constrained problems in terms of the convergence speed, quality of final solutions and success rate.     

Parametric reconfiguration improvement in non-iterative concurrent mechatronic design using an evolutionary-based approach

Parametric reconfiguration plays a key role in non-iterative concurrent design of mechatronic systems. This is because it allows the designer to select, among different competitive solutions, the most suitable without sacrificing sub-optimal characteristics. This paper presents a method based on an evolutionary algorithm to improve the parametric reconfiguration feature in the optimal design of a continuously variable transmission and a five-bar parallel robot. The approach considers a solution-diversity mechanism coupled with a memory of those sub-optimal solutions found during the process. Furthermore, a constraint-handling mechanism is added to bias the search to the feasible region of the search space. Differential Evolution is utilized as the search algorithm. The results obtained in a set of five experiments performed per each mechatronic system show the effectiveness of the proposed approach.     

Fusing ant colony optimization with Lagrangian relaxation for the multiple-choice multidimensional knapsack problem

The multiple-choice multidimensional knapsack problem (MMKP) concerns a wide variety of practical problems. It is strongly constrained and NP-hard; thus searching for an efficient heuristic approach for MMKP is of great significance. In this study, we attempt to solve MMKP by fusing ant colony optimization (ACO) with Lagrangian relaxation (LR). The algorithm used here follows the algorithmic scheme of max–min ant system for its outstanding performance in solving many other combinatorial optimization problems. The Lagrangian value of the item in MMKP, obtained from LR, is used as the heuristic factor in ACO since it performs best among the six domain-based heuristic factors we define. Furthermore, a novel infeasibility index is proposed for the development of a new repair operator, which converts possibly infeasible solutions into feasible ones. The proposed algorithm was compared with four existing algorithms by applying them to three groups of instances. Computational results demonstrate that the proposed algorithm is capable of producing competitive solutions.     

Subdomain generation using emergent ant colony optimization

Finite elements mesh decomposition is a well known optimization problem and is used to split a computationally expensive finite elements mesh into smaller subdomains for parallel finite elements analysis.The ant colony optimization is a type of algorithm that seeks to model the emergent behaviour observed in ant colonies and utilize this behaviour to solve combinatorial problems. This technique has been applied to several problems, most of which are graph related because the ant colony metaphor can be most easily applied to such types of problems. This paper examines the application of ant colony optimization algorithm to the partitioning of unstructured adaptive meshes for parallel explicit time-stepping finite elements analysis.The concept of ant colony optimization technique in addition to the notion of swarm intelligence for finding approximate solutions to combinatorial optimization problems is described. This algorithm combines the features of the classical ant colony optimization technique with swarm intelligence to form a model which is an artificial system designed to perform a certain task.The application of the ant colony optimization for partitioning finite elements meshes based on triangular elements using the swarm intelligence concept is described. A recursive greedy algorithm optimization method is also presented as a local optimization technique to improve the quality of the solutions given by the ant colony optimization algorithm. The partitioning is based on the recursive bisection approach.The mesh partitioning is carried out using normal and predictive modes for which the predictive mode uses a trained multi-layered feedforward neural network that estimates the number of triangular elements that will be generated after finite elements mesh generation is carried out.The performance of the proposed hybrid approach for the recursive bisection of finite elements meshes is examined by decomposing two mesh examples and comparing them with a well known finite elements domain decomposer.     

基于改进型蚁群算法的MFJSSP研究*

为了对MFJSSP进行优化,给出了改进的基于蚁群算法的MFJSSP解决方法。改进后的算法根据工件数量确定子集数量。给出了可选工作集的构建方法及在寻优过程中的邻域搜索策略,并对蚁群算法的参数选择问题进行了讨论。完成了MFJSSP中蚁群算法的改进,并将改进后的蚁群算法应用于解决4×5问题和8×8问题,取得了较理想结果。实验结果证明所提出的算法在解决MFJSSP上是一种可行、有效的解决方法。     

基于蚁群算法的多目标网页综合评价策略

蚁群算法是Marco和Dorigo等学者在真实蚂蚁觅食行为的启发下提出的一种群智能优化算法。为了提高搜索引擎系统中的查全率和查准率,采用理论分析和实验相结合的方式,研究了蚁群算法在搜索引擎系统中的应用。引用蚁群算法量化用户偏爱度,提出了一种基于网页的链接结构、内容关联度和用户偏爱度三个指标的多目标优化模型的网页价值综合评价体系。从理论上阐述了蚁群算法应用于搜索引擎系统的可行性及适应性。最后实验仿真证明了该网页价值综合评价策略的有效性和优越性。     

含维变异算子的连续域蚁群算法

针对在连续优化中,蚁群算法(ACO)存在的收敛速度慢和易陷入局部最优的问题,提出了一种新的含维变异算子的连续域蚁群算法(DMCACO)。该算法采用动态随机抽取的方法来确定目标个体,引导蚁群进行全局的快速搜索,同时在当前最优蚂蚁邻域内进行小步长的局部搜索。在定义了维多样性概念的基础上,引入维变异算子对维多样性最差的维进行变异：让所有蚂蚁在该维上的位置重新均匀分布在可行区域上。对测试函数所做的仿真实验表明,该算法具有优良的全局寻优能力和快速的收敛能力。     

基于自适应蚁群聚类的入侵检测

针对蚁群聚类算法在聚类结果中出现部分数据划分不够准确的问题,提出一种基于信息熵调整的自适应混沌蚁群聚类改进算法。该算法通过优化过程中种群的信息熵来衡量演化的程度,自适应地调整信息素更新策略。每一次迭代结束时,使用混沌搜索算子在当前全局最优解附近搜索更好的解。而随着算法的进行,混沌算子搜索范围逐渐缩小,这样混沌算子在蚁群搜索的初期起到防止陷入局部最优的作用,在蚁群搜索后期起到提高搜索精度的作用,从而得到更好的聚类结果。使用KDD Cup 1999入侵检测数据集所作的仿真实验结果表明,聚类效果改进明显,并能有效提高入侵检测的检测率、降低误检率。     

Chemical reaction optimization with greedy strategy for the 0–1 knapsack problem

The 0–1 knapsack problem (KP01) is a well-known combinatorial optimization problem. It is an NP-hard problem which plays important roles in computing theory and in many real life applications. Chemical reaction optimization (CRO) is a new optimization framework, inspired by the nature of chemical reactions. CRO has demonstrated excellent performance in solving many engineering problems such as the quadratic assignment problem, neural network training, multimodal continuous problems, etc. This paper proposes a new chemical reaction optimization with greedy strategy algorithm (CROG) to solve KP01. The paper also explains the operator design and parameter turning methods for CROG. A new repair function integrating a greedy strategy and random selection is used to repair the infeasible solutions. The experimental results have proven the superior performance of CROG compared to genetic algorithm (GA), ant colony optimization (ACO) and quantum-inspired evolutionary algorithm (QEA).