A framework for self-tuning optimization algorithm

The performance of any algorithm will largely depend on the setting of its algorithm-dependent parameters. The optimal setting should allow the algorithm to achieve the best performance for solving a range of optimization problems. However, such parameter tuning itself is a tough optimization problem. In this paper, we present a framework for self-tuning algorithms so that an algorithm to be tuned can be used to tune the algorithm itself. Using the firefly algorithm as an example, we show that this framework works well. It is also found that different parameters may have different sensitivities and thus require different degrees of tuning. Parameters with high sensitivities require fine-tuning to achieve optimality.     

A framework for the application of metaheuristics to?tasks-to-processors assignation problems

The optimization of the execution time of a parallel algorithm can be achieved through the use of an analytical cost model function representing the running time. Typically the cost function includes a set of parameters that model the behavior of the system and the algorithm. In order to reach an optimal execution, some of these parameters must be fitted according to the input problem and to the target architecture. An optimization problem can be stated where the modeled execution time for the algorithm is used to estimate the parameters. Due to the large number of variable parameters in the model, analytical minimization techniques are discarded. Exhaustive search techniques can be used to solve the optimization problem, but when the number of parameters or the size of the computational system increases, the method is impracticable due to time restrictions. The use of approximation methods to guide the search is also an alternative. However, the dependence on the algorithm modeled and the bad quality of the solutions as a result of the presence of many local optima values in the objective functions are also drawbacks to these techniques. The problem becomes particularly difficult in complex systems hosting a large number of heterogeneous processors solving non-trivial scientific applications. The use of metaheuristics allows for the development of valid approaches to solve general problems with a large number of parameters. A well-known advantage of metaheuristic methods is the ability to obtain high-quality solutions at low running times while maintaining generality. We propose combining the parameterized analytical cost model function and metaheuristic minimization methods, which contributes to a novel real alternative to minimize the parallel execution time in complex systems. The success of the proposed approach is shown with two different algorithmic schemes on parallel heterogeneous systems. Furthermore, the development of a general framework allows us to easily develop and experiment with different metaheuristics to adjust them to particular problems.     

基于微粒群优化算法的间歇过程迭代学习

在实际的间歇过程优化控制中面临着模型参数不确定性的问题,并且基于梯度的优化控制技术在处理具有多个局部极值的目标函数时,往往会陷入局部极值点.针对该问题,提出一种基于微粒群优化算法的间歇过程产品质量迭代学习策略.结合间歇过程产品质量控制问题的特点和各种约束条件,利用微粒群优化算法在非线性问题求解及大尺度空间搜索上的优势,...     

Robust design of non-linear structures using optimization methods

The robust design of non-linear structures with path-dependent response is stated as a two-criteria optimization problem and is solved by the method of mathematical programming. To this end, the perturbation technique is applied in conjunction with the incremental loading procedure for the response moment analysis of path-dependent non-linear structural systems with random parameters. Furthermore, the sensitivities of mean and variance of the structural performance function are evaluated using direct differentiation in the framework of perturbation based stochastic finite element analysis. By introducing a weighting factor in the compound objective––resp. desirability function, and feasibility indices in the constraints, the mathematical model of structural robust design problem is formulated and is solved with a gradient-based algorithm. Numerical examples demonstrate the applicability of the presented method.     

Joint optimization for area traffic control and network flow

A joint optimization problem for solving area traffic control and network flow is investigated. A bilevel programming is used to formulate this joint optimization problem where the network flow following Wardrop's principles can be obtained by solving traffic assignment problems. In this paper, we present a solution approach for jointly optimizing the area traffic control and network flow on the basis of a newly presented algorithm for concurrent flow (Comput. Oper. Res. (2004) in press). We propose three kinds of formulations for this joint optimization problem and present a gradient-based method to effectively solve this problem via a mixture of locally optimal search and global search heuristic where a near global optimum may be found. Numerical comparisons are made for the values of performance index achieved by the joint optimization problem with system optimal flow and those did by equilibrium flow at various sets of initial signal settings. Substantially good results have demonstrated the robustness of the proposed algorithm in solving both system optimal and user equilibrium flow for the joint optimization problem at large-scale networks.     

生化途径参数估计的QPSO-MGbest算法

讨论了非线性动力生化过程的参数估计（反问题）,描述为受一组非线性代数-微分方程约束的非线性规划问题,由于频繁的病态和多峰值,传统的算法（如梯度算法）并不能得到满意的解。提出了一种改进的量子行为粒子群优化算法求解代谢途径的参数估计,该算法采用基于全局最好位置的变异操作以提高算法的非线性逼近能力和较好的全局搜索能力。以一个三阶段代谢途径为研究对象,建立参数估计的算法模型,以实验值和预测值的误差平方加权的和为目标优化函数。实验表明改进量子行为粒子群优化算法能够较好求解该问题。     

Parameter and shape sensitivity of thermo-viscoelastic response

Gradient-based optimization methods are still most efficient methods for solving structural optimization problems. The sensitivity formulation has been one of the central issues in the gradient-based optimization algorithm. Thermo-viscoelastic constitutive and parameter sensitivity formulation are presented in this paper. The model considered is composed of two coupled subproblems: the transient heat transfer problem and a rheological, viscoelastic material model known in literature as the standard model. Design variables considered are with material and shape-defining parameters. The investigation includes a finite element formulation and implementation in an object-oriented finite element environment. Results of numerical analysis are presented.     

A parallel membrane inspired harmony search for optimization problems: A case study based on a flexible job shop scheduling problem

Harmony search is an emerging meta-heuristic optimization algorithm that is inspired by musical improvisation processes, and it can solve various optimization problems. Membrane computing is a distributed and parallel model for solving hard optimization problems. First, we employed some previously proposed approaches to improve standard harmony search by allowing its parameters to be adaptive during the processing steps. Information from the best solutions was used to improve the speed of convergence while preventing premature convergence to a local minimum. Second, we introduced a parallel framework based on membrane computing to improve the harmony search. Our approach utilized the parallel membrane computing model to execute parallelized harmony search efficiently on different cores, where the membrane computing communication characteristics were used to exchange information between the solutions on different cores, thereby increasing the diversity of harmony search and improving the performance of harmony search. Our simulation results showed that the application of the proposed approach to different variants of harmony search yielded better performance than previous approaches. Furthermore, we applied the parallel membrane inspired harmony search to the flexible job shop scheduling problem. Experiments using well-known benchmark instances showed the effectiveness of the algorithm.     

蚁群算法在求解旅行商问题中的应用综述

旅行商问题作为组合优化研究中最具挑战的问题之一, 自被提出以来就引起了学术界的广泛关注并提出了大量的方法来解决它. 蚁群算法是求解复杂组合优化问题的一种启发式仿生进化算法, 是求解旅行商问题的有效手段. 本文分别介绍蚁群算法中几个有代表性的算法, 综述了蚁群算法的改进、融合和应用的文献研究进展, 以评价近年来不同版本的蚁群算法为解决旅行商问题的发展和研究成果, 并针对改进蚁群算法结构框架、算法参数的设置及优化、信息素优化和混合算法等方面, 对现被提出的改进算法进行了分类综述. 对蚁群算法在未来对旅行商问题及其他不同领域的研究内容和研究热点的进一步发展提供了展望和依据.     

蚁群优化算法在物流车辆调度系统中的应用

根据对蚁群算法进行的深入研究,指出了蚁群算法在解决大型非线性系统优化问题时的优越性。通过仔细分析遗传算法和粒子群算法在解决物流车辆调度系统问题的不足之处,基于蚁群算法的优点,并根据物流车辆调度系统自身的特点,对基本蚁群算法进行适当的改进,给出算法框架。并且以线性规划理论为基础,建立物流车辆系统的数学模型,给出调度目标与约束条件,用改进后的蚁群算法求解物流车辆调度系统的问题,求得最优解,根据最优解和调度准则进行实时调度。使用Java语言编写模拟程序对比基于改进粒子群算法和改进蚁群算法的调度程序。通过对比证明了所提出的改进蚁群算法解决物流车辆调度优化问题的正确性和有效性     

An augmented Lagrangian decomposition method for quasi-separable problems in MDO

Several decomposition methods have been proposed for the distributed optimal design of quasi-separable problems encountered in Multidisciplinary Design Optimization (MDO). Some of these methods are known to have numerical convergence difficulties that can be explained theoretically. We propose a new decomposition algorithm for quasi-separable MDO problems. In particular, we propose a decomposed problem formulation based on the augmented Lagrangian penalty function and the block coordinate descent algorithm. The proposed solution algorithm consists of inner and outer loops. In the outer loop, the augmented Lagrangian penalty parameters are updated. In the inner loop, our method alternates between solving an optimization master problem and solving disciplinary optimization subproblems. The coordinating master problem can be solved analytically; the disciplinary subproblems can be solved using commonly available gradient-based optimization algorithms. The augmented Lagrangian decomposition method is derived such that existing proofs can be used to show convergence of the decomposition algorithm to Karush–Kuhn–Tucker points of the original problem under mild assumptions. We investigate the numerical performance of the proposed method on two example problems.     

An Iterative local-search framework for solving constraint satisfaction problem

In this article, we introduce a new solving framework based on using alternatively two local-search algorithms to solve constraint satisfaction and optimization problems. The technique presented is based on the integration of local-search algorithm as a mechanism to diversify the search instead of using a build on diversification mechanisms. Thus, we avoid tuning the multiple parameters to escape from a local optimum. This technique improves the existing methods: it is generic especially when the given problem can be expressed as a constraint satisfaction problem. We present the way the local-search algorithm can be used to diversify the search in order to solve real examination timetabling problems. We describe how the local-search algorithm can be used to assist any other specific local-search algorithm to escape from local optimality. We showed that such framework is efficient on real benchmarks for timetabling problems.     

平衡装载约束下的车辆路径问题研究

针对车辆三维装载约束下的车辆路径问题（3L-VRP）进行研究,引进车辆的平衡装载约束,综合考虑传统的先进后出、局部支撑、脆弱性等约束,构建平衡装载约束下的车辆路径问题（BL-VRP）模型。针对模型中的平衡约束,提出一种接触面积的装载算法。在此基础上,构建以回溯遗传算法（B-GA）为骨架的多阶段算法框架,对车辆路径优化进行求解。研究结果表明,多阶段算法不仅在解决3L-VRP上好于目前已有算法,同时对BL-VRP表现优秀。提出的多阶段算法为解决BL-VRP问题提供一条参考思路,但在时效性上需要进一步完善。     

Topology optimization of channel flow problems

This paper describes a topology design method for simple two-dimensional flow problems. We consider steady, incompressible laminar viscous flows at low-to-moderate Reynolds numbers. This makes the flow problem nonlinear and hence a nontrivial extension of the work of Borrvall and Petersson (2003).Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity-driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost function which measures either some local aspect of the velocity field or a global quantity, such as the rate of energy dissipation. We use the finite element method to model the flow, and we solve the optimization problem with a gradient-based math-programming algorithm that is driven by analytical sensitivities. Our target application is optimal layout design of channels in fluid network systems. Using concepts borrowed from topology optimization of compliant mechanisms in solid mechanics, we introduce a method for the synthesis of fluidic components, such as switches, diodes, etc.     

Group Search Optimizer: An Optimization Algorithm Inspired by Animal Searching Behavior

Nature-inspired optimization algorithms, notably evolutionary algorithms (EAs), have been widely used to solve various scientific and engineering problems because of to their simplicity and flexibility. Here we report a novel optimization algorithm, group search optimizer (GSO), which is inspired by animal behavior, especially animal searching behavior. The framework is mainly based on the producer-scrounger model, which assumes that group members search either for ldquofindingrdquo (producer) or for ldquojoiningrdquo (scrounger) opportunities. Based on this framework, concepts from animal searching behavior, e.g., animal scanning mechanisms, are employed metaphorically to design optimum searching strategies for solving continuous optimization problems. When tested against benchmark functions, in low and high dimensions, the GSO algorithm has competitive performance to other EAs in terms of accuracy and convergence speed, especially on high-dimensional multimodal problems. The GSO algorithm is also applied to train artificial neural networks. The promising results on three real-world benchmark problems show the applicability of GSO for problem solving.     

一种基于区间优化的神经网络学习算法

神经网络的学习算法通常是采用梯度下降法,此方法容易陷入局部极小而得到次最优解。另外,对于有些应用来说,用于训练网络的样本的输入／输出数据无法精确给出,而只能以一定的范围的形式给出,这就给传统的神经网络带来了困难。该文提出了一种基于区间优化的神经网络学习算法,可以很好地解决上面所提到的传统神经网络学习算法的缺点。     

Non-probabilistic reliability-based topology optimization with multidimensional parallelepiped convex model

In this paper, a new non-probabilistic reliability-based topology optimization (NRBTO) method is proposed to account for interval uncertainties considering parametric correlations. Firstly, a reliability index is defined based on a newly developed multidimensional parallelepiped (MP) convex model, and the reliability-based topology optimization problem is formulated to optimize the topology of the structure, to minimize material volume under displacement constraints. Secondly, an efficient decoupling scheme is applied to transform the double-loop NRBTO into a sequential optimization process, using the sequential optimization & reliability assessment (SORA) method associated with the performance measurement approach (PMA). Thirdly, the adjoint variable method is used to obtain the sensitivity information for both uncertain and design variables, and a gradient-based algorithm is employed to solve the optimization problem. Finally, typical numerical examples are used to demonstrate the effectiveness of the proposed topology optimization method.     

二次分配问题的改进粒子群优化算法

粒子群优化算法已经成功地应用于求解连续域问题,但是对于离散域问题的求解,尤其涉及组合优化问题的研究和应用还很少。二次分配问题本身是一个离散域问题,因此,使用粒子群算法求解二次分配问题是一个新的研究方向。文章引入交叉策略和变异策略对粒子群优化算法进行改造,使得粒子群优化算法可以用来解决二次分配问题。     

改进粒子群优化算法求解任务指派问题

任务指派问题是典型NP难题,引入粒子群优化算法对其进行求解。建立了任务指派问题的数学模型,给出了粒子群优化算法求解任务指派问题的具体方案。为提高其优化求解效果,引入变异机制及局部更新机制对粒子群优化算法进行改进。实例及数字仿真验证了改进粒子群优化算法的有效性。     

An immersed boundary approach for shape and topology optimization of stationary fluid-structure interaction problems

This paper presents an approach to shape and topology optimization of fluid-structure interaction (FSI) problems at steady state. The overall approach builds on an immersed boundary method that couples a Lagrangian formulation of the structure to an Eulerian fluid model, discretized on a deforming mesh. The geometry of the fluid-structure boundary is manipulated by varying the nodal parameters of a discretized level set field. This approach allows for topological changes of the fluid-structure interface, but free-floating volumes of solid material can emerge in the course of the optimization process. The free-floating volumes are tracked and modeled as fluid in the FSI analysis. To sense the isolated solid volumes, an indicator field described by linear, isotropic diffusion is computed prior to analyzing the FSI response of a design. The fluid is modeled with the incompressible Navier-Stokes equations, and the structure is assumed linear elastic. The FSI model is discretized by an extended finite element method, and the fluid-structure coupling conditions are enforced weakly. The resulting nonlinear system of equations is solved monolithically with Newton’s method. The design sensitivities are computed by the adjoint method and the optimization problem is solved by a gradient-based algorithm. The characteristics of this optimization framework are studied with two-dimensional problems at steady state. Numerical results indicate that the proposed treatment of free-floating volumes introduces a discontinuity in the design evolution, yet the method is still successful in converging to meaningful designs.