Nonlinear model predictive control using deterministic global optimization

This paper presents a Nonlinear Model Predictive Control (NMPC) algorithm utilizing a deterministic global optimization method. Utilizing local techniques on nonlinear nonconvex problems leaves one susceptible to suboptimal solutions at each iteration. In complex problems, local solver reliability is difficult to predict and dependent upon the choice of initial guess. This paper demonstrates the application of a deterministic global solution technique to an example NMPC problem. A terminal state constraint is used in the example case study. In some cases the local solution method becomes infeasible, while the global solution correctly finds the feasible global solution. Increased computational burden is the most significant limitation for global optimization based online control techniques. This paper provides methods for improving the global optimization rates of convergence. This paper also shows that globally optimal NMPC methods can provide benefits over local techniques and can successfully be used for online control.     

Hybrid ant colony-genetic algorithm (GAAPI) for global continuous optimization

Many real-life optimization problems often face an increased rank of nonsmoothness (many local minima) which could prevent a search algorithm from moving toward the global solution. Evolution-based algorithms try to deal with this issue. The algorithm proposed in this paper is called GAAPI and is a hybridization between two optimization techniques: a special class of ant colony optimization for continuous domains entitled API and a genetic algorithm (GA). The algorithm adopts the downhill behavior of API (a key characteristic of optimization algorithms) and the good spreading in the solution space of the GA. A probabilistic approach and an empirical comparison study are presented to prove the convergence of the proposed method in solving different classes of complex global continuous optimization problems. Numerical results are reported and compared to the existing results in the literature to validate the feasibility and the effectiveness of the proposed method. The proposed algorithm is shown to be effective and efficient for most of the test functions.     

改进的人工蜂群算法在函数优化问题中的应用

人工蜂群算法是近年来新提出的一种优化算法。针对标准人工蜂群算法的局部搜索能力差,精度低的缺点,提出了一个改进的人工蜂群算法,利用全局最优解和个体极值的信息来改进人工蜂群算法中的搜索模式,并引入异步变化学习因子,保持全局搜索和局部搜索的平衡。将改进的人工蜂群算法在函数优化问题上进行测试,结果表明改进的人工蜂群算法优于原算法。     

基于改进细菌觅食算法的飞控系统多模态参数优化

针对飞控系统参数优化过程中存在的解空间非凸性问题,或由于多约束条件下导致的全局最优不可达问题,提出一种基于改进细菌觅食算法的多模态参数优化方法.采用基于格型准则的采样方法以尽可能广泛地搜索解空间,并利用K均值聚类的小生境技术使得多个细菌种群能够分别搜索各自的区域,以尽可能多地获得解空间中不同位置的可行解.同时研究一种自适应深度搜索策略,确保算法在整个寻优过程中的鲁棒性.所提出算法可以在完成对系统优化的基础上,探寻飞控系统中各参数本身的可行域及其在解空间中所处的位置,也能够在一定程度上揭示解空间本身的特性.仿真结果验证了所提出算法可以有效地简化系统调参的过程,更为快速地获得一个满足设计性能期望的飞控系统.     

基于越界重置和高斯变异的蝙蝠优化算法

针对蝙蝠算法个体越界、易早熟收敛的问题，提出一种基于越界重置和高斯变异的蝙蝠优化算法。新算法将飞越解空间边界的个体拉回解空间内，利用越界重置策略重新分配位置。通过高斯变异策略控制个体的搜索范围，使种群以最优解为中心向四周呈放射状搜索，增强了算法的局部搜索和全局寻优能力。蝙蝠算法在靠近目标解时响度和脉冲发射频率更新不协调，影响了算法的持续进化能力,通过线性渐变策略保证响度和脉冲发射频率的变化与算法持续进化相适应。研究了在解空间不同位置关系的情况下新算法和对比算法的优化能力，并结合实验数据对算法收敛稳定性进行分析。实验结果表明，提出的新算法具有较好的收敛速度和精度，其全局寻优能力和高维问题优化能力体现了很好的鲁棒性。     

A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice

Most engineering optimization algorithms are based on numerical linear and nonlinear programming methods that require substantial gradient information and usually seek to improve the solution in the neighborhood of a starting point. These algorithms, however, reveal a limited approach to complicated real-world optimization problems. If there is more than one local optimum in the problem, the result may depend on the selection of an initial point, and the obtained optimal solution may not necessarily be the global optimum. This paper describes a new harmony search (HS) meta-heuristic algorithm-based approach for engineering optimization problems with continuous design variables. This recently developed HS algorithm is conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. Various engineering optimization problems, including mathematical function minimization and structural engineering optimization problems, are presented to demonstrate the effectiveness and robustness of the HS algorithm. The results indicate that the proposed approach is a powerful search and optimization technique that may yield better solutions to engineering problems than those obtained using current algorithms.     

SSTT: Efficient local search for GSI global routing

In this paper, a novel global routing algorithm is presented for congestion opti-mization based on efficient local search, named SSTT (search space traversing technology). This method manages to traverse the whole search space. A hybrid optimization strategy is adopted,consisting of three optimization sub-strategies: stochastic optimization, deterministic optimiza-tion and local enumeration optimization, to dynamically reconstruct the problem structure. Thus,“transition” can be made from a local minimum point to reach other parts of the search space,traverse the whole search space, and obtain the global (approximate) optimal routing solution.Since any arbitrary initial routing solution can be used as the start point of the search, the initial-ization in SSTT algorithm is greatly simplified. SSTT algorithm has been tested on both MCNC benchmark circuits and industrial circuits, and the experimental results were compared with those of typical existing algorithms. The experimental results show that SSTT algorithm can obtain the global (approximate) optimal routing solution easily and quickly. Moreover, it can meet the needs of practical applications. The SSTT global routing algorithm gives a general-purpose routing solution.     

Advanced-step multistage nonlinear model predictive control: Robustness and stability

Nonlinear model predictive control (NMPC) has been popular in many applications, especially when constraint satisfaction is critical. However, due to plant-model mismatch and disturbances, robust NMPC generally faces three challenges: robust performance, real-time implementation, and stability. In this paper, we propose a parallelizable advanced-step multistage NMPC (as-msNMPC), which provides a non-conservative robust control solution that explicitly addresses two types of uncertainty: model parameters and unmeasured noise. The first type is attended to by incorporating scenario trees and the second by applying nonlinear programming (NLP) sensitivity. In addition, robust stability concepts have been discussed for both ideal multistage NMPC (ideal-msNMPC) and as-msNMPC. Under suitable assumptions, as-msNMPC has demonstrated input-to-state practical stability properties with the presence of two types of uncertainty. Lastly, the as-msNMPC framework has been applied to continuous stirred tank reactor (CSTR) and quad-tank case studies for tracking setpoints to demonstrate its performance in robustness and efficiency.     

一种基于云模型的改进型量子遗传算法*

针对量子遗传算法在函数优化中易陷入局部最优和早熟收敛等缺点,采用云模型对其进行改进,采用量子种群基因云对种群进化进行定性控制,采用基于云模型的量子旋转门自适应调整策略进行更新操作,使算法在定性知识的指导下能够自适应控制搜索空间范围,能在较大搜索空间条件下避开局部最优解。典型函数对比实验表明,该算法可以避免陷入局部最优解,能提高全局寻优能力,同时能以更快的速度收敛于全局最优解,优化质量和效率都要优于遗传算法和量子遗传算法。     

基于SQP/GA混合优化算法的双容水箱非线性预测控制

为了计算控制序列，非线性模型预测控制可以转换为一个带约束的非线性优化过程．本文分析了三种约束处理方案，根据遗传算法的特点，将等式约束用于状态量计算，在搜索空间降维的同时消除遗传算法难以求解的等式约束．对双容水箱进行遗传算法和序列二次规划仿真试验和实际控制，结果表明遗传算法对控制量的优化效果优于序列二次规划．为克服遗传算法耗时较长、优化结果存在随机抖动的缺点，结合序列二次规划提出一种混合优化算法，仿真和实控结果表明其可行性和有效性．     

FOA: fireworks optimization algorithm

In this paper, a novel meta-heuristic algorithm called Fireworks Optimization Algorithm (FOA) is introduced with few control parameters for discrete and continuous optimization problems. This algorithm is inspired from explosion pyrotechnic devices producing colorful spikes like red, blue and silver. By modelling the explosion behavior of the Fireworks in the sky, the search space can be swept efficiently to find the global optima. To improve the balance between the exploration and exploitation of individuals, three categories are defined to avoid local optimal traps and applied to the search agents. Each category has a different task and predefined updating position rules. A grouping strategy is considered to prevent the algorithm from premature convergence. The performance of FOA is demonstrated over 15 standard benchmarks in the continuous version and 30 images thresholding problems in the discrete version. The obtained results reveal the superiority of the proposed algorithm with fewer input parameters over other state-of-the-art optimization methods in most cases.

     

A novel hybrid adaptive collaborative approach based on particle swarm optimization and local search for dynamic optimization problems

This paper proposes a novel hybrid approach based on particle swarm optimization and local search, named PSOLS, for dynamic optimization problems. In the proposed approach, a swarm of particles with fuzzy social-only model is frequently applied to estimate the location of the peaks in the problem landscape. Upon convergence of the swarm to previously undetected positions in the search space, a local search agent (LSA) is created to exploit the respective region. Moreover, a density control mechanism is introduced to prevent too many LSAs crowding in the search space. Three adaptations to the basic approach are then proposed to manage the function evaluations in the way that are mostly allocated to the most promising areas of the search space. The first adapted algorithm, called HPSOLS, is aimed at improving PSOLS by stopping the local search in LSAs that are not contributing much to the search process. The second adapted, algorithm called CPSOLS, is a competitive algorithm which allocates extra function evaluations to the best performing LSA. The third adapted algorithm, called CHPSOLS, combines the fundamental ideas of HPSOLS and CPSOLS in a single algorithm. An extensive set of experiments is conducted on a variety of dynamic environments, generated by the moving peaks benchmark, to evaluate the performance of the proposed approach. Results are also compared with those of other state-of-the-art algorithms from the literature. The experimental results indicate the superiority of the proposed approach.     

遗传算法计算效率的改进

根据适应值的分布, 采用缩小、移动搜索区间的方法, 将整体和局部寻优能力有机地结合起来, 明显地提高了遗传算法的收敛速度和解的精度. 本文提出的方法对大范围、高精度寻优尤其适合. 最后以连续函数为例, 说明了算法的有效性.     

基于云模型的量子免疫优化算法

采用云模型对量子免疫算法进行了改进,采用量子种群基因云对种群进化进行定性控制,基于云模型的量子旋转门自适应调整策略进行更新操作,使算法在定性知识的指导下能够自适应控制搜索空间范围,使其能在较大搜索空间条件下避开局部最优解。典型函数对比实验表明该算法可以避免陷入局部最优解,能提高全局寻优能力,能以更快的速度收敛于全局最优解,具有较好的应用价值。     

A direct search variant of the simulated annealing algorithm for optimization involving continuous variables

A memory-based simulated annealing algorithm is proposed which fundamentally differs from the previously developed simulated annealing algorithms for continuous variables by the fact that a set of points rather than a single working point is used. The implementation of the new method does not need differentiability properties of the function being optimized. The method is well tested on a range of problems classified as easy, moderately difficult and difficult. The new algorithm is compared with other simulated annealing methods on both test problems and practical problems. Results showing an improved performance in finding the global minimum are given.Scope and purposeThe inherent difficulty of global optimization problems lies in finding the very best optimum (maximum or minimum) from a multitude of local optima. Many practical global optimization problems of continuous variables are non-differentiable and noisy and even the function evaluation may involve simulation of some process. For such optimization problems direct search approaches are the methods of choice. Simulated annealing is a stochastic global optimization algorithm, initially designed for combinatorial (discrete) optimization problems. The algorithm that we propose here is a simulated annealing algorithm for optimization problems involving continuous variables. It is a direct search method. The strengths of the new algorithm are: it does not require differentiability or any other properties of the function being optimized and it is memory-based. Therefore, the algorithm can be applied to noisy and/or not exactly known functions. Although the algorithm is stochastic in nature, it can memorise the best solution. The new simulated annealing algorithm has been shown to be reliable, fast, general purpose and efficient for solving some difficult global optimization problems.     

一种带规范知识引导的改进人工蜂群算法

针对数值函数优化问题,提出一种改进的人工蜂群算法.受文化算法双层进化空间的启发,利用信度空间中的规范知识引导搜索区域,自适应调整算法的搜索范围,提高算法的收敛速度和勘探能力.为保持种群多样性,设计一种种群分散策略,平衡群体的全局探索和局部开采能力,并且在各个进化阶段采用不同的方式探索新的位置.通过对多种标准测试函数进行实验并与多个近期提出的人工蜂群算法比较,结果表明该算法在收敛速度和求解质量上均取得较好的改进效果.     

Fast shape matching and retrieval based on approximate dynamic space warping

Dynamic space warping (DSW) has emerged as a very effective tool for matching shapes. However, a central computational difficulty associated with DSW arises when a boundary’s starting point (or rotation angle) is unknown. In this article, the HopDSW algorithm is proposed to speed up the starting point computation. Rather than performing an exhaustive search for the correct starting point as in classical approaches, the proposed algorithm operates in a coarse-to-fine manner. The coarse search is global and uses a hopping step to exclude points from the search. Then the search is refined in the neighborhood of the solution of the coarse search. A criterion that governs selecting the hopping step parameter is given, which reduces the number of starting point computations by an order. For shape representation, a triangle area signature (TAS) is computed from triangles formed by the boundary points. Experimental results on the MPEG-7 CE-1 database of 1400 shapes show that the proposed algorithm returns the solution to an exhaustive search with a high degree of accuracy and a considerable reduction in the number of computations.     

Learning the Search Range for Evolutionary Optimization in Dynamic Environments

Conventional evolutionary algorithms operate in a fixed search space with limiting parameter range, which is often predefined via a priori knowledge or trial and error in order to ‘guess’ a suitable region comprising the global optimal solution. This requirement is hard, if not impossible, to fulfil in many real-world optimization problems since there is often no clue of where the desired solutions are located in these problems. Thus, this paper proposes an inductive–deductive learning approach for single- and multi-objective evolutionary optimization. The method is capable of directing evolution towards more promising search regions even if these regions are outside the initial predefined space. For problems where the global optimum is included in the initial search space, it is capable of shrinking the search space dynamically for better resolution in genetic representation to facilitate the evolutionary search towards more accurate optimal solutions. Validation results based on benchmark optimization problems show that the proposed inductive–deductive learning is capable of handling different fitness landscapes as well as distributing nondominated solutions uniformly along the final trade-offs in multi-objective optimization, even if there exist many local optima in a high-dimensional search space or the global optimum is outside the predefined search region. Received 15 January 2001 / Revised 8 June 2001 / Accepted in revised form 24 July 2001     

Boundary Search for Constrained Numerical Optimization Problems With an Algorithm Inspired by the Ant Colony Metaphor

This paper presents a novel boundary approach that is included as a constraint-handling technique in an algorithm inspired by the ant colony metaphor. The necessity of approaching the boundary between the feasible and infeasible search space for many constrained optimization problems is a paramount challenge for every constraint-handling technique. Our proposed technique precisely focuses the search on the boundary region and can be either used alone or in combination with other constraint-handling techniques depending on the type and number of problem constraints. For validation purposes, an algorithm inspired by the ant colony metaphor is adopted as our search engine that works following one of the principles of the ant colony approach, i.e., a population of agents iteratively, cooperatively, and independently search for a solution. Each ant in the distributed algorithm applies a simple mutation-like operator, which explores the neighborhood region of a particular point in the search space (individual search level). The operator is designed for exploring the boundary between the feasible and infeasible search space. In addition, each ant obtains global information from the colony in order to exploit the most promising regions of the search space (cooperation level). We compare our proposed approach with respect to a well-known constraint-handling technique that is representative of the state-of-the-art in the area, using a set of standard test functions.     

基于IWOA算法求解并联冷机负荷分配问题

中央空调系统并联冷水机组系统能耗非常大,如果操作不当,能耗会大大增加。针对OCL问题提出了一种求解连续非线性优化问题的改进鲸群优化算法,首先,为使后续迭代寻优的搜索空间更精确,运用混沌映射初始化种群,使初始解均匀遍布解空间。其次引入变异指数对收敛因子进行改进,平衡了局部勘探和全局勘探的关系。之后引入正弦和余弦使算法收敛到全局最优解,防止了算法过早收敛,提高了算法的收敛精度。最后,通过两个典型的案例来评估IWOA算法的性能,并将其与应用于OCL问题的其他优化算法进行了比较。结果表明,IWOA算法是解决OCL问题的有效方法。此外,算法性能的比较显示,IWOA算法在收敛速度和电能消耗方面相比于其他应用于OCL问题的优化方法提供了更好的解决方案。