An adaptive penalty based covariance matrix adaptation–evolution strategy

Although most of unconstrained optimization problems with moderate to high dimensions can be easily handled with Evolutionary Computation (EC) techniques, constraint optimization problems (COPs) with inequality and equality constraints are very hard to deal with. Despite the fact that only equality constraints can be used to eliminate a certain variable, both types of constraints implicitly enforce a relation between problem variables. Most conventional constraint handling methods in EC do not consider the correlations between problem variables imposed by the problem constraints. This paper relies on the idea that a proper genetic operator, which captures mentioned implicit correlations, can improve performance of evolutionary constrained optimization algorithms. With this in mind, we employ a (μ+λ)-Evolution Strategy with a simplified variant of Covariance Matrix Adaptation based mutation operator along an adaptive weight adjustment scheme. The proposed algorithm is tested on two test sets. The outperformance of the algorithm is significant on the first benchmark when compared with five conventional methods. The results on the second test set show that algorithm is highly competitive when benchmarked with three state-of-art algorithms. The main drawback of the algorithm is its slightly lower speed of convergence for problems with high dimension and/or large search domain.     

Multi-operator based evolutionary algorithms for solving constrained optimization problems

Over the last two decades, many sophisticated evolutionary algorithms have been introduced for solving constrained optimization problems. Due to the variability of characteristics in different COPs, no single algorithm performs consistently over a range of problems. In this paper, for a better coverage of the problem characteristics, we introduce an algorithm framework that uses multiple search operators in each generation. The appropriate mix of the search operators, for any given problem, is determined adaptively. The framework is tested by implementing two different algorithms. The performance of the algorithms is judged by solving 60 test instances taken from two constrained optimization benchmark sets from specialized literature. The first algorithm, which is a multi-operator based genetic algorithm (GA), shows a significant improvement over different versions of GA (each with a single one of these operators). The second algorithm, using differential evolution (DE), also confirms the benefit of the multi-operator algorithm by providing better and consistent solutions. The overall results demonstrated that both GA and DE based algorithms show competitive, if not better, performance as compared to the state of the art algorithms.     

AORCEA – An adaptive operator rate controlled evolutionary algorithm

When applying evolutionary algorithms to optimization problems many different strategy parameters have to be set to define the behavior of the evolutionary algorithm itself. To a certain extent these strategy parameter values determine whether the algorithm is capable of finding a near-optimum solution or not. In particular the choice of the different genetic operators and their relative rates is most often based on experience. Furthermore, the operator rates are defined before starting the optimization runs and remain unchanged until the stopping criterion is reached. Controlling the parameter values during the run has the potential of adjusting the algorithm to the problem while solving the problem. This paper investigates an adaptive strategy controlling the rates of arbitrary chosen genetic operators. The control mechanism is based on the state of the optimization by evaluating a success and a diversity measure for each operator. More efficient operators are favored in order to find better solutions with less evaluations. The algorithm is tested with constrained and unconstrained numerical examples and a concrete structural optimization problem is treated.     

基于交流的求解数值优化问题的混合演化算法

演化算法中有很多不同的演化算子,每一种算子对于不同的优化问题都有自己的优点和缺点。提出了一种基于交流模型的多算子混合演化算法。在该算法中,有两个种群,使用两种算子:多父体杂交算子和Cauchy变异算子。种群间的信息交换通过个体交流实现。对23个标准测试函数的数值仿真表明,该算法具有良好的全局收敛性和鲁棒性。     

A new evolutionary approach to cutting stock problems with and without contiguity

Evolutionary algorithms (EAs) have been applied to many optimization problems successfully in recent years. The genetic algorithm (GAs) and evolutionary programming (EP) are two different types of EAs. GAs use crossover as the primary search operator and mutation as a background operator, while EP uses mutation as the primary search operator and does not employ any crossover. This paper proposes a novel EP algorithm for cutting stock problems with and without contiguity. Two new mutation operators are proposed. Experimental studies have been carried out to examine the effectiveness of the EP algorithm. They show that EP can provide a simple yet more effective alternative to GAs in solving cutting stock problems with and without contiguity. The solutions found by EP are significantly better (in most cases) than or comparable to those found by GAs.Scope and purposeThe one-dimensional cutting stock problem (CSP) is one of the classical combinatorial optimization problems. While most previous work only considered minimizing trim loss, this paper considers CSPs with two objectives. One is the minimization of trim loss (i.e., wastage). The other is the minimization of the number of stocks with wastage, or the number of partially finished items (pattern sequencing or contiguity problem). Although some traditional OR techniques (e.g., programming based approaches) can find the global optimum for small CSPs, they are impractical to find the exact global optimum for large problems due to combinatorial explosion. Heuristic techniques (such as various hill-climbing algorithms) need to be used for large CSPs. One of the heuristic algorithms which have been applied to CSPs recently with success is the genetic algorithm (GA). This paper proposes a much simpler evolutionary algorithm than the GA, based on evolutionary programming (EP). The EP algorithm has been shown to perform significantly better than the GA for most benchmark problems we used and to be comparable to the GA for other problems.     

约束优化进化算法

约束优化问题是科学和工程应用领域经常会遇到的一类数学规划问题.近年来,约束优化问题求解已成为进化计算研究的一个重要方向.从约束优化进化算法=约束处理技术+进化算法的研究框架出发,从约束处理技术和进化算法两个基本方面对约束优化进化算法的研究及进展进行了综述.此外,对约束优化进化算法中的一些重要问题进行了探讨.最后进行了各种算法的比较性总结,深入分析了目前约束优化进化算法中亟待解决的问题,并指出了值得进一步研究的方向.     

A parallel boundary search particle swarm optimization algorithm for constrained optimization problems

During the past decade, considerable research has been conducted on constrained optimization problems (COPs) which are frequently encountered in practical engineering applications. By introducing resource limitations as constraints, the optimal solutions in COPs are generally located on boundaries of feasible design space, which leads to search difficulties when applying conventional optimization algorithms, especially for complex constraint problems. Even though penalty function method has been frequently used for handling the constraints, the adjustment of control parameters is often complicated and involves a trial-and-error approach. To overcome these difficulties, a modified particle swarm optimization (PSO) algorithm named parallel boundary search particle swarm optimization (PBSPSO) algorithm is proposed in this paper. Modified constrained PSO algorithm is adopted to conduct global search in one branch while Subset Constrained Boundary Narrower (SCBN) function and sequential quadratic programming (SQP) are applied to perform local boundary search in another branch. A cooperative mechanism of the two branches has been built in which locations of the particles near boundaries of constraints are selected as initial positions of local boundary search and the solutions of local boundary search will lead the global search direction to boundaries of active constraints. The cooperation behavior of the two branches effectively reinforces the optimization capability of the PSO algorithm. The optimization performance of PBSPSO algorithm is illustrated through 13 CEC06 test functions and 5 common engineering problems. The results are compared with other state-of-the-art algorithms and it is shown that the proposed algorithm possesses a competitive global search capability and is effective for constrained optimization problems in engineering applications.     

Multiple Elite Individual Guided Piecewise Search-Based Differential Evolution

The differential evolution (DE) algorithm relies mainly on mutation strategy and control parameters’ selection. To take full advantage of top elite individuals in terms of fitness and success rates, a new mutation operator is proposed. The control parameters such as scale factor and crossover rate are tuned based on their success rates recorded over past evolutionary stages. The proposed DE variant, MIDE, performs the evolution in a piecewise manner, i.e., after every predefined evolutionary stages, MIDE adjusts its settings to enrich its diversity skills. The performance of the MIDE is validated on two different sets of benchmarks: CEC 2014 and CEC 2017 (special sessions & competitions on real-parameter single objective optimization) using different performance measures. In the end, MIDE is also applied to solve constrained engineering problems. The efficiency and effectiveness of the MIDE are further confirmed by a set of experiments.      

Multi-center variable-scale search algorithm for combinatorial optimization problems with the multimodal property

Combinatorial optimization problems (COPs) are discrete problems arising from aerospace, bioinformatics, manufacturing, and other fields. One of the classic COPs is the scheduling problem. Moreover, these problems are usually multimodal optimization problems with a quantity of global and local optima. As a result, many search algorithms can easily become trapped into local optima. In this article, we propose a multi-center variable-scale search algorithm for solving both single-objective and multi-objective COPs. The algorithm consists of two distinct points. First, the multi-center strategy chooses several individuals with better performance as the only parents of the next generation, which means that there are a number of separate searching areas around the searching center. Second, the next generation of the population is produced by a variable-scale strategy with an exponential equation based on the searching center. The equation is designed to control the neighborhood scale, and adaptively realize the large-scale and small-scale searches at different search stages to balance the maintenance of diversity and convergence speed. In addition, an approach of adjusting centers is proposed concerning the number and distribution of centers for solving multi-objective COPs. Finally, the proposed algorithm is applied to three COPs, including the well-known flexible job shop scheduling problem, the unrelated parallel machine scheduling problem, and the test task scheduling problem. Both the single-objective optimization algorithm and the multi-objective optimization algorithm demonstrate competitive performance compared with existing methods.     

A decomposition-based hybrid multiobjective evolutionary algorithm with dynamic resource allocation

Different crossover operators suit different problems. It is, therefore, potentially problematic to chose the ideal crossover operator in an evolutionary optimization scheme. Using multiple crossover operators could be an effective way to address this issue. This paper reports on the implementation of this idea, i.e. the use of two crossover operators in a decomposition-based multi-objective evolutionary algorithm, but not simultaneously. After each cycle, the operator which has helped produce the better offspring is rewarded. This means that the overall algorithm uses a dynamic resource allocation to reward the better of the crossover operators in the optimization process. The operators used are the Simplex Crossover operator (SPX) and the Center of Mass Crossover operator (CMX). We report experimental results that show that this innovative use of two crossover operators improves the algorithm performance on standard test problems. Results on the sensitivity of the suggested algorithm to key parameters such as population size, neighborhood size and maximum number of solutions to be altered for a given subproblem in the the decomposition process are also included.     

A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization

A considerable number of constrained optimization evolutionary algorithms (COEAs) have been proposed due to increasing interest in solving constrained optimization problems (COPs) by evolutionary algorithms (EAs). In this paper, we first review existing COEAs. Then, a novel EA for constrained optimization is presented. In the process of population evolution, our algorithm is based on multiobjective optimization techniques, i.e., an individual in the parent population may be replaced if it is dominated by a nondominated individual in the offspring population. In addition, three models of a population-based algorithm-generator and an infeasible solution archiving and replacement mechanism are introduced. Furthermore, the simplex crossover is used as a recombination operator to enrich the exploration and exploitation abilities of the approach proposed. The new approach is tested on 13 well-known benchmark functions, and the empirical evidence suggests that it is robust, efficient, and generic when handling linear/nonlinear equality/inequality constraints. Compared with some other state-of-the-art algorithms, our algorithm remarkably outperforms them in terms of the best, mean, and worst objective function values and the standard deviations. It is noteworthy that our algorithm does not require the transformation of equality constraints into inequality constraints     

Evolution of Appropriate Crossover and Mutation Operators in a Genetic Process

Traditional genetic algorithms use only one crossover and one mutation operator to generate the next generation. The chosen crossover and mutation operators are critical to the success of genetic algorithms. Different crossover or mutation operators, however, are suitable for different problems, even for different stages of the genetic process in a problem. Determining which crossover and mutation operators should be used is quite difficult and is usually done by trial-and-error. In this paper, a new genetic algorithm, the dynamic genetic algorithm (DGA), is proposed to solve the problem. The dynamic genetic algorithm simultaneously uses more than one crossover and mutation operators to generate the next generation. The crossover and mutation ratios change along with the evaluation results of the respective offspring in the next generation. By this way, we expect that the really good operators will have an increasing effect in the genetic process. Experiments are also made, with results showing the proposed algorithm performs better than the algorithms with a single crossover and a single mutation operator.     

Engineering design optimization using an improved local search based epsilon differential evolution algorithm

Many engineering problems can be categorized into constrained optimization problems (COPs). The engineering design optimization problem is very important in engineering industries. Because of the complexities of mathematical models, it is difficult to find a perfect method to solve all the COPs very well. \(\varepsilon \) constrained differential evolution (\(\varepsilon \)DE) algorithm is an effective method in dealing with the COPs. However, \(\varepsilon \)DE still cannot obtain more precise solutions. The interaction between feasible and infeasible individuals can be enhanced, and the feasible individuals can lead the population finding optimum around it. Hence, in this paper we propose a new algorithm based on \(\varepsilon \) feasible individuals driven local search called as \(\varepsilon \) constrained differential evolution algorithm with a novel local search operator (\(\varepsilon \)DE-LS). The effectiveness of the proposed \(\varepsilon \)DE-LS algorithm is tested. Furthermore, four real-world engineering design problems and a case study have been studied. Experimental results show that the proposed algorithm is a very effective method for the presented engineering design optimization problems.     

An adaptive surrogate assisted differential evolutionary algorithm for high dimensional constrained problems

Differential evolution (DE) is a competitive algorithm for constrained optimization problems (COPs). In this study, in order to improve the efficiency and accuracy of the DE for high dimensional problems, an adaptive surrogate assisted DE algorithm, called ASA-DE is suggested. In the ASA, several kinds of surrogate modeling techniques are integrated. Furthermore, to avoid violate the constraints and obtain better solution simultaneously, adaptive strategies for population size and mutation are also suggested in this study. The suggested adaptive population strategy which controls the exploring and exploiting states according to whether algorithm find enough feasible solution is similar to a state switch. The mutation strategy is used to enhance the effect of state switch based on adaptive population size. Finally, the suggested ASA-DE is evaluated on the benchmark problems from congress on evolutionary computation (CEC) 2017 constrained real parameter optimization. The experimental results show the proposed algorithm is a competitive one compared to other state-of-the-art algorithms.     

时间序列相似模式的有效匹配

将经验模式分解和多层前向网络的交叉覆盖算法相结合,提出一种时间序列相似模式的匹配算法.先利用经验模式分解实现时问序列趋势的提取,再把所有的趋势序列分成训练集和测试集2个部分.通过训练为每个类别做出描述,根据测试集中的每个趋势序列和覆盖中心之间的距离把它们分配到与之最匹配的类别中.实验结果表明:该算法是一种较理想的序列模式匹配方法,更擅长于维数较高的序列的匹配.     

采用概率判定法的分组变异自适应差分进化算法

为了平衡差分进化算法(DE)的全局探索和局部开发过程,提高算法避免陷入局部最优的能力,文中提出采用概率判定法的分组变异自适应差分进化算法(GVADE).GVADE采用概率判定法判定个体进化状态为较好、较差或一般,并根据个体进化状态为个体选择合适的变异算子和控制参数组.同时,为了满足进化状态较差个体变异的需要,设计具有较强全局探索能力的变异算子.在CEC2005标准测试集合上的实验表明,GVADE优于现有的其它DE算法,可以更好地平衡全局探索和局部开发,具有更高的收敛精度.     

Active learning SVM with regularization path for image classification

In classification problems, many different active learning techniques are often adopted to find the most informative samples for labeling in order to save human labors. Among them, active learning support vector machine (SVM) is one of the most representative approaches, in which model parameter is usually set as a fixed default value during the whole learning process. Note that model parameter is closely related to the training set. Hence dynamic parameter is desirable to make a satisfactory learning performance. To target this issue, we proposed a novel algorithm, called active learning SVM with regularization path, which can fit the entire solution path of SVM for every value of model parameters. In this algorithm, we first traced the entire solution path of the current classifier to find a series of candidate model parameters, and then used unlabeled samples to select the best model parameter. Besides, in the initial phase of training, we constructed a training sample sets by using an improved K-medoids cluster algorithm. Experimental results conducted from real-world data sets showed the effectiveness of the proposed algorithm for image classification problems.     

Local search with quadratic approximations into memetic algorithms for optimization with multiple criteria

This paper proposes a local search optimizer that, employed as an additional operator in multiobjective evolutionary techniques, can help to find more precise estimates of the Pareto-optimal surface with a smaller cost of function evaluation. The new operator employs quadratic approximations of the objective functions and constraints, which are built using only the function samples already produced by the usual evolutionary algorithm function evaluations. The local search phase consists of solving the auxiliary multiobjective quadratic optimization problem defined from the quadratic approximations, scalarized via a goal attainment formulation using an LMI solver. As the determination of the new approximated solutions is performed without the need of any additional function evaluation, the proposed methodology is suitable for costly black-box optimization problems.     

基于改进遗传算法的无人机路径规划

针对传统遗传算法收敛速度慢、容易陷入局部最优、规划路径不够平滑、代价高等问题,提出了一种基于改进遗传算法的无人机（UAV）路径规划方法,该算法对遗传算法的选择算子、交叉算子和变异算子进行改进,从而规划出平滑、可飞的路径。首先,建立适合UAV田间信息获取的环境模型,并考虑UAV的目标函数与约束条件以建立适合本场景的更为复杂、精确的数学模型;然后,提出了混合无重串选择算子、非对称映射交叉算子和启发式多次变异算子,寻找最优路径以及扩大种群搜索范围;最后,采用三次B样条曲线对规划出的路径进行平滑,得到平滑的飞行路径,并且减少了算法的计算时间。实验结果表明,与传统遗传算法相比,所提算法的代价值降低了68%,收敛迭代次数减少了67%;相较蚁群优化（ACO）算法,其代价值降低了55%,收敛迭代次数减少了58%。通过大量对比实验得出,当交叉率的值为（1/染色体长度）时,算法的收敛效果最好。在不同环境下进行算法性能测试,结果表明所提算法具有很好的环境适应性,适合于复杂环境下的路径规划。     

On minimizing coding operations in network coding based multicast: an evolutionary algorithm

In telecommunications networks, to enable a valid data transmission based on network coding, any intermediate node within a given network is allowed, if necessary, to perform coding operations. The more coding operations needed, the more coding resources consumed and thus the more computational overhead and transmission delay incurred. This paper investigates an efficient evolutionary algorithm to minimize the amount of coding operations required in network coding based multicast. Based on genetic algorithms, we adapt two extensions in the proposed evolutionary algorithm, namely a new crossover operator and a neighbourhood search operator, to effectively solve the highly complex problem being concerned. The new crossover is based on logic OR operations to each pair of selected parent individuals, and the resulting offspring are more likely to become feasible. The aim of this operator is to intensify the search in regions with plenty of feasible individuals. The neighbourhood search consists of two moves which are based on greedy link removal and path reconstruction, respectively. Due to the specific problem feature, it is possible that each feasible individual corresponds to a number of, rather than a single, valid network coding based routing subgraphs. The neighbourhood search is applied to each feasible individual to find a better routing subgraph that consumes less coding resource. This operator not only improves solution quality but also accelerates the convergence. Experiments have been carried out on a number of fixed and randomly generated benchmark networks. The results demonstrate that with the two extensions, our evolutionary algorithm is effective and outperforms a number of state-of-the-art algorithms in terms of the ability of finding optimal solutions.