遗传算法的机理与收敛性研究

采用一种新的基于解空间分解的定量分析方法,对遗传算法的种群进化过程进行分析,阐明了选择、交叉和变异操作的寻优机理,给出了子代种群在解空间上的概率分布情况;理论上,证明了遗传算法具备寻找全局最优解的能力,并给出了具备寻找全局最优解能力的充分必要条件,即证明了积木块假设的结论是成立的.同时,建立了二进制编码有限群体的M arkov链模型,计算出在用于静态优化问题的交叉和变异操作下,种群在解空间上概率分布情况以及收敛到最优解的概率,并讨论了产生早熟现象和GA-欺骗问题的原因.     

停车场中车辆最佳间距的确定

通过分析车辆从停车位转出的过程,计算其在此过程中所占用的面积.调整停车时的车辆间距,应用遗传算法,求得车辆转出的最佳运动方案及其在此运动方案下所占用的最小面积.综合考虑各种因素,得到使停车场面积利用率最大的停车间距.     

Variational principle for magnetostatic potential

The magnetostatic potential due to the magnetization existing in the magnetic media is characterized by a variational principle defined in the whole space. Representing the magnetostatic potential in the exterior of the magnetic media by its values on the boundary of an unbounded exterior space, the variational principle may be re-defined in a finite solution space. Alternatively, if one is willing to determine the potential solution on certain prescribed boundary of a finite space, the variational principle may also be re-defined in the prescribed space. The cost for the savings in the solution space is the representation of the potential in the exterior space for the former case, or the determination of the potential solution on certain prescribed boundary for the second case.     

Output feedback controller for polytopic systems exploiting the direct searching of the design space

This paper deals with the problem of designing a robust static output feedback controller for polytopic systems. The current research that tackled this problem is mainly based on LMI method, which is conservative by nature. In this paper, a novel approach is proposed, which considers the design space of the controller parameters and iteratively partitions the space to small simplexes. Then, by assessing the stability in each simplex, the solution space for design parameters is directly determined. It has been theoretically proved that, if there exists a feasible solution in the design space, the algorithm can find it. To validate the result of the proposed approach, comparative simulation examples are given to illustrate the performance of the design methodology as compared to those of previous approaches.     

图的顶点着色问题的一种DNA算法

在构造了一种新型的“类发夹”式探针的基础上,给出了图的顶点着色问题的一种DNA算法。利用顶点的适当编码,该算法直接生成可满足解空间,无须在全体解空间中进行各种过滤过程,使用常规的生物操作完成可满足解空间的产生及最终解的分离。     

基于自组织映射的遗传聚类算法

遗传聚类算法往往需要较大的种群规模才能得到最优解,导致收敛速度慢,针对这一问题,本文提出一种基于自组织映射的超启发遗传聚类算法。首先利用自组织映射把数据空间转换到特征空间,再在特征空间里利用遗传算法进行搜索,然后进行反映射,即把聚类结果在数据空间里表现,从而得到一组解,同时利用K-means算法在数据空间里进行粗聚类,获得另一组解,最后比较2组解的聚类结果,相同的样本保留,不同的再次聚类,进而有效地保证了最优解的获得。计算机仿真实验验证了所提算法在种群规模较小的情况下,可以获得较高的准确率。      

Modelling and estimating the pose of a human arm

Pose estimation of 3-D objects based on monocular computer vision is an ill-posed problem. To ease matters a model-based approach can be applied. Such an approach usually relies on iterating when matching the model and the image data. In this paper we estimate the 3-D pose of a human arm from a monocular image. To avoid the inherent problems when iterating, we apply an exhaustive matching strategy. To make this plausible, we reduce the size of the solution space through a very compact model representation of the arm and prune the solution space. The model is developed through a detailed investigation of the functionality and structure of the arm and the shoulder complex. The model consists of just two parameters and is based on the screw-axis representation together with image measurements. The pruning is achieved through kinematic constraints and it turns out that the solution space of the compact model can be pruned , on average. Altogether, the compact representation and the constraints reduce the solution space significantly and, therefore, allow for an exhaustive matching procedure. The approach is tested in a model-based silhouette framework, and tests show promising results.Published online: 8 August 2003Correspondence to: Thomas B. Moeslund     

Analytical solution of the linear fractional system of commensurate order

A useful representation of fractional order systems is the state space representation. For the linear fractional systems of commensurate order, the state space representation is defined as for regular integer state space representation with the state vector differentiated to a real order. This paper presents a solution of the linear fractional order systems of commensurate order in the state space. The solution is obtained using a technique based on functions of square matrices and the Cayley-Hamilton theorem. The technique developed for linear systems of integer order is extended to derive analytical solutions of linear fractional systems of commensurate order. The basic ideas and the derived formulations of the technique are presented. Both, homogeneous and inhomogeneous cases with usual input functions are solved. The solution is calculated in the form of a linear combination of suitable fundamental functions. The presented results are illustrated by analyzing some examples to demonstrate the effectiveness of the presented analytical approach.     

遗传算法对解空间搜索比例的递减性评估

遗传算法在搜索最优解方面具有很高的效率，根据模式定理，我们推断，在保证基本精度的前提下，我们只要搜索解空间的很小一部分就能够搜索到最优解或次优解，并且随着解空间的扩大，对解空间的搜索比例呈显著下降趋势，本文利用旅行商问题对这一推论加以验证，其验证方法对于用遗传算法求解的其它问题了值得借鉴。     

A coevolutionary approach to adapt the genotype-phenotype map in genetic algorithms

This article introduces a coevolutionary approach to genetic algorithms (GAs) for exploring not only within a part of the solution space defined by the genotype-pheno-type map, but also the map itself. In canonical GAs with a fixed map, how large an area of the solution space can be covered by possible genomes, and consequently how better solutions can be found by a GA, rely on how well the geotype-phenotype map in designed, but it is difficult for designers of the algorithms to design the map without a priori knowledge of the solution space. In the proposed algorithm, the genotype-phenotype map is improved adaptively during the search process for solution candidates. It is applied to 3-bit deceptive problems such as of typical combinatorial optimazation problems. These are well known because their difficulty for GAs can be controlled by the genotype-phenotype map, and this shows a fairly good performance compared with a conventional GA. This work was presented in part at the Sixth International Symposium on Artificial Life and Robotics, Tokyo, January 15–17, 2001.     

Local solutions of the Hamilton-Jacobi-Bellman equation for some stochastic problems

Consideration is given to the control problem of motion of a linear oscillator, which is subject to the external Gaussian and Poisson random actions, with the aim to minimize the mean energy with the aid of the external bounded control force. The hybrid solution method is suggested for the solution of the stated problem. This method relies on the search in a portion of the phase space for the exact analytical solution of the appropriate Hamilton-Jacobi-Bellman (HJB) equation and the numerical solution of this equation in the remaining (bounded) portion of the space. It is proved that the found analytical solutions represent the asymptotics of solutions of the Hamilton-Jacobi-Bellman equation. With the aid of the decomposition method, the obtained results are applied to the problem for the suppression with the aid of the actuator of vibrations of an elastic rod (plate) that is found to be under the action of Gaussian random actions. Results of the numerical modeling are given.     

遗传算法中群体多样性的研究与应用

遗传算法中,初始群体的特性对计算结果和计算效率均有重要影响,要实现全局最优解,初始群体在解空间中应尽量分散,标准遗传算法是按预定或随机方法产生一组初始群体,这样就导致初始群体在解空间中分布不均匀。本文阐述了用相似度和适应度值对群体中每两个个体进行逐位比较,剔除相似个体,选择不同模式的个体组成新的群体,增加了群体的多样性,尤其在计算初期,能够有效的避免早熟问题的产生。最后,通过实例应用matlab7.0编程测试说明了这种方法的可行性。     

一种新的项目调度解表示方法

基于解集合的准启发式方法是解决资源约束下项目调度问题的有效方法，解的表示形式一直是这种方法的一个重要研究问题。只有充分利用解的形式和目标函数之间的联系，才可能达到在少数枚举下得到尽可能好的解。详细分析了解空间性质，提出了用额外关系表示一个可行解的方法，给出了这种表示方法的理论依据。并介绍了用该方法产生邻域的方法。     

The optimal determination of the space requirement and the number of transfer cranes for import containers

It is discussed how to determine the optimal amount of storage space and the optimal number of transfer cranes for import containers. A cost model is developed for the decision making. It includes the space cost, the fixed cost of transfer cranes which corresponds to the investment cost, the variable cost of transfer cranes and outside trucks which is related to the time spent for the transfer of containers. A simple solution procedure for the optimal solution is provided. The solution procedure is illustrated using a numerical example.     

搜索空间边界连接的微粒群优化算法

针对粒子出界问题对微粒群优化算法收敛性能产生的不利影响,本文提出一种搜索空间边界连接的边界处理算法。该算法首先将搜索空间每一维的上下边界连接,形成一个逻辑上闭合的搜索空间,然后通过调整该空间中粒子位置的更新策略以及粒子速度更新公式中个体认知和社会认知差分向量的计算方法,消除了边界对飞行粒子的不利影响,使粒子在可行解空间中能够更加高效且均匀地搜索。实验结果表明,无论全局最优解位于搜索空间的边界区域还是中心区域,本文方法的全局搜索性能均优于现有的粒子边界处理方法。     

Direct computation of solution spaces

In engineering, it is often desirable to find a subset of the set of feasible designs, a solution space, rather than a single solution. A feasible design is defined as a design which does not violate any constraints and has a performance value below a desired threshold. Performance measure, threshold value and constraints depend on the specific problem. For evaluation of a design with respect to feasibility, a model is required which maps the design parameters from the input space onto the performance measures in the output space. In state-of-the-art methodology, iterative sampling is used to generate an estimate of the frontier between feasible and infeasible regions in the input space. By evaluating each sample point with respect to feasibility, areas which contain a large fraction of feasible designs are identified and subsequently resampled. The largest hypercube containing only feasible designs is sought, because this results in independent intervals for each design parameter. Estimating this hypercube with sufficient precision may require a large number of model evaluations, depending on the dimensionality of the input space. In this paper, a novel approach is proposed for modeling the inequality constraints and an objective function in a way for which a linear formulation can be used, independently of the dimensionality of the problem. Thereby the exact solution for the largest feasible hypercube can be calculated at much lower cost than with stochastic sampling as described above, as the problem is reduced to solving a linear system of equations. The method is applied to structural design with respect to the US-NCAP frontal impact. The obtained solution is compared to numerical solutions of an identical system, which are computed using reduced order models and stochastic methods. By this example, the high potential of the new direct method for solution space computation is shown.     

Optimal base-stock policy of the assemble-to-order systems

In this work, an ordinal optimization-based evolution algorithm (OOEA) is proposed to solve a problem for a good enough target inventory level of the assemble-to-order (ATO) system. First, the ATO system is formulated as a combinatorial optimization problem with integer variables that possesses a huge solution space. Next, the genetic algorithm is used to select N excellent solutions from the solution space, where the fitness is evaluated with the radial basis function network. Finally, we proceed with the optimal computing budget allocation technique to search for a good enough solution. The proposed OOEA is applied to an ATO system comprising 10 items on 6 products. The solution quality is demonstrated by comparing with those obtained by two competing methods. The good enough target inventory level obtained by the OOEA is promising in the aspects of solution quality and computational efficiency.     

Solving systems of equations with multi-stage Monte Carlo optimization

Dantzig (1963), Orchard-Hays (1968) and other pioneers have helped to develop linear programming theory and applications. Additionally an elegant solution technique is available for linear systems of equations. However there is a need to be able to solve the general non-linear model and non-linear systems of equations. Multi-stage Monte Carlo optimization along with the absolute value transformations presented here show some promise in solving difficult non-linear problems. They also perform well on many linear problems and tend to streamline the solution process and give the practitioner more freedom to develop accurate non-linear models and systems. The fundamental theorem of linear programming tells us that the optimal solution is at a ‘corner point’ of the n-dimensional constrained solution space. The simplex technique goes along the edges of the constrained region from corner point to corner point until it finds the optimal solution. However, with multistage Monte Carlo for non-linear problems, the solution could be anywhere in the constrained or unconstrained solution space. Preliminary Bayesian discovery samples are thus taken to help to locate the optimal solution region or regions and n-dimensional geometric shapes will then go straight across the region in pursuit of the solution area. These geometric shapes slowly close in and find the solution, making considerable use of the law of large numbers and the relatively compact nature of n-dimensional space. An example is presented here.     

A multi-restart iterated local search algorithm for the permutation flow shop problem minimizing total flow time

A variety of metaheuristics have been developed to solve the permutation flow shop problem minimizing total flow time. Iterated local search (ILS) is a simple but powerful metaheuristic used to solve this problem. Fundamentally, ILS is a procedure that needs to be restarted from another solution when it is trapped in a local optimum. A new solution is often generated by only slightly perturbing the best known solution, narrowing the search space and leading to a stagnant state. In this paper, a strategy is proposed to allow the restart solution to be generated from a group of solutions drawn from local optima. This allows an extension of the search space, while maintaining the quality of the restart solution. A multi-restart ILS (MRSILS) is proposed, with the performance evaluated on a set of benchmark instances and compared with six state of the art metaheuristics. The results show that the easily implementable MRSILS is significantly better than five of the other metaheuristics and comparable to or slightly better than the remaining one.     

对于NEH启发式方法搜索邻域的研究

综合考虑所需的计算时间和最终获得的解的质量,研究了NEH启发式方法在以Makespan为目标的置换流水车间调度问题(PFSP)中的应用。由于NEH算法取得成功的一个重要原因在于其迭代式插入邻域搜索过程,因此,着重从它的邻域搜索空间入手,用精简或增强邻域的方法,给出了几种不同的空间结构。实验结果表明,给出的两种增强的结构能取得比以往算法更优的解,即利用这两种算法可以大大缩短完工时间,获得更有效的调度。