求解TSP问题的改进离散蝴蝶优化算法

针对离散蝴蝶优化算法求解TSP问题时精度低和收敛速度慢等问题,提出一种改进离散蝴蝶优化算法.为了提升搜索效率,利用贪婪机制初始化种群,同时结合2-opt算子、改进的2-opt算子和模拟退火等策略来提高寻优能力.通过标准TSPLIB数据库中几十个实例仿真实验,并与一些经典、新型的智能算法比较,结果表明提出的算法在寻优能力和鲁棒性方面表现优越.     

模拟退火猫群优化算法

猫群优化算法(Cat Swarm Optimization,CSO)是建立在猫的行为模式和群体智能基础上的一种新型群体智能优化算法。为提高猫群优化算法的性能,把模拟退火算法应用于猫群优化算法,提出模拟退火猫群优化算法(Simulated Annealing Cat Swarm Optimization,SACSO),通过变异算子调整所要优化的种群。其基本过程为先行产生随机初始种群,接着进行搜索,并设置初始温度,继而应用模拟退火算法获取全局最优替代值,再依据位置和速度公式更新新解,然后在个体较优位置再运用变异运算,进行进一步地搜索。然后分别将猫群优化算法、模拟退火粒子群算法(Simulated Annealing Particle Swarm Optimization,SAPSO)、模拟退火猫群优化算法在11个典型的基准测试函数下进行仿真对比,结果表明模拟退火猫群优化算法不仅增加了全局收敛性,而且在收敛速度和精度方面均优于其它两种算法。     

含有等式约束非线性规划的全局优化算法

针对含有多个等式约束的非线性规划问题,提出一个全局优化算法.该方法基于可行集策略把改进的模拟退火方法与确定的局部算法方法相结合.对算法的收敛性进行了证明,数值结果表明算法的有效性及正确性.     

改进的粒子群算法在桁架结构优化设计中的应用

应用改进的粒子群算法进行桁架结构优化设计。首先,在确定初始种群时用随机方向法产生一组适应环境值较高的初始种群,使算法快速收敛于全局最优解,降低了算法的时间复杂度;其次,将模糊推理应用于算法的参数动态调整中,提高种群的适应搜索空间环境的能力;最后,将改进的粒子群算法应用于桁架结构优化设计中.算例表明,改进后算法的搜索性能得到了一定改善,为其应用于大型复杂的工程结构优化设计提供了借鉴.     

基于改进模拟退火算法的推动式生产-配送协调优化

为减小物资生产与配送不协调造成的成本及生产资源浪费,建立了考虑推动式生产调度的物资配送优化模型,并针对标准模拟退火算法受随机因素影响易陷入局部最优的缺点,设计带有回火与缓冷操作的改进模拟退火算法对模型求解,确定了优化的车辆配送路线以及物资生产计划。对比实验结果表明:相对于单纯的物资配送优化模型,考虑推动式生产调度的配送优化模型,能够有效减小物资滞留时间以及配送延误成本;相较于标准模拟退火算法,改进算法搜索到了更优解,且计算结果的标准差减小了93.42%,稳定性更好;同时,改进模拟退火算法具有较低的偏差率,在中小规模算例中求解质量较高,平均偏差率在0.5%以内。     

函数优化的小生境蝙蝠算法

针对蝙蝠算法易陷入局部最优解的缺点,利用小生境技术对蝙蝠算法进行了改进,提出一种小生境蝙蝠优化算法.算法基于小生境技术的适应度共享来分隔种群,引入了小生境排挤机制来保持种群多样性,在延续蝙蝠算法原有并行搜索等优势的基础上,提高了算法的金局搜索能力和局部收敛速度,具有可在不同邻域内发现多个解的特点.通过对一系列经典函数测试,并与已有算法进行比较,结果表明该算法在函数优化问题的求解中具有较高的计算效率和精度,以及较好的全局寻优能力.     

自适应多种群回溯群居蜘蛛算法求解TSP问题

在群居蜘蛛优化算法中引入自适应决策半径,将蜘蛛种群动态地分成多个种群,种群内适应度不同的个体采取不同的更新方式.在筛选全局极值的基础上,根据进化程度执行回溯迭代更新,提出一种自适应多种群回溯群居蜘蛛优化算法,旨在提高种群样本多样性和算法全局寻优能力.函数寻优结果表明改进算法具有较快的收敛速度和较高的收敛精度.最后将其应用于TSP问题的求解.     

一类连续函数模拟退火算法及其收敛性分析

高维连续函数的全局优化问题普遍存在于计算生物学、计算化学等领域．针对这类问题和现有连续函数模拟退火算法的某些不足,本文给出了一类改进的模拟退火算法．采用一种简单的方法证明了算法的全局收敛性．数值结果表明,对于高维连续函数,该算法能够快速有效地收敛到全局最优点,比较了两种新解产生方法的试验结果。     

基于改进的旗鱼优化算法求解Sylvester问题

Sylvester问题又称最小包围圆问题,提出了一种改进的旗鱼优化算法(ISFO)对其进行求解.首先对旗鱼优化算法(SFO)的寻优策略进行分析;其次,针对旗鱼优化算法种群初始化依赖,容易陷入局部最优等问题,引入Arnold映射初始化种群,提高算法的寻优能力;引入反向学习与柯西变异算子策略对全局最优解进行扰动产生新解,平衡算法的开发与勘探能力,避免算法出现早熟现象;然后和基本SFO算法与PSO算法使用6个基准测试函数进行仿真实验对比,结果表明ISFO算法相对于SFO算法收敛速度更快、精度更高、有效避免了早熟现象.最后使用ISFO、SFO、PSO对三个规模案例的Sylvester问题进行求解,证明了ISFO算法求解Sylvester问题的可行性与优越性.     

改进种群多样性的双变异差分进化算法

差分进化算法(DE)是一种基于种群的启发式随机搜索技术,对于解决连续性优化问题具有较强的鲁棒性.然而传统差分进化算法存在种群多样性和收敛速度之间的矛盾,一种改进种群多样性的双变异差分进化算法(DADE),通过引入BFS-best机制(基于排序的可行解选取递减策略)改进变异算子"DE/current-to-best",将其与DE/rand/1构成双变异策略来改善DE算法中种群多样性减少的问题.同时,每个个体的控制参数基于排序自适应更新.最后,利用多个CEC2013标准测试函数对改进算法进行测试,实验结果表明,改进后的算法能有效改善种群多样性,较好地提高了算法的全局收敛能力和收敛速度.     

Distributed stochastic nonsmooth nonconvex optimization

Distributed consensus optimization has received considerable attention in recent years and several distributed consensus-based algorithms have been proposed for (nonsmooth) convex and (smooth) nonconvex objective functions. However, the behavior of these distributed algorithms on nonconvex, nonsmooth and stochastic objective functions is not understood. Such class of functions and distributed setting are motivated by several applications, including problems in machine learning and signal processing. This paper presents the first convergence analysis of the decentralized stochastic subgradient method for such classes of problems, over networks modeled as undirected, fixed, graphs.     

Inverse multi-objective combinatorial optimization

Inverse multi-objective combinatorial optimization consists of finding a minimal adjustment of the objective functions coefficients such that a given set of feasible solutions becomes efficient. An algorithm is proposed for rendering a given feasible solution into an efficient one. This is a simplified version of the inverse problem when the cardinality of the set is equal to one. The adjustment is measured by the Chebyshev distance. It is shown how to build an optimal adjustment in linear time based on this distance, and why it is right to perform a binary search for determining the optimal distance. These results led us to develop an approach based on the resolution of mixed-integer linear programs. A second approach based on a branch-and-bound is proposed to handle any distance function that can be linearized. Finally, the initial inverse problem is solved by a cutting plane algorithm.     

Hierarchically constrained blackbox optimization

In blackbox optimization, evaluation of the objective and constraint functions is time consuming. In some situations, constraint values may be evaluated independently or sequentially. The present work proposes and compares two strategies to define a hierarchical ordering of the constraints and to interrupt the evaluation process at a trial point when it is detected that it will not improve the current best solution. Numerical experiments are performed on a closed-form test problem.     

Vector Ordinal Optimization

Ordinal optimization is a tool to reduce the computational burden in simulation-based optimization problems. So far, the major effort in this field focuses on single-objective optimization. In this paper, we extend this to multiobjective optimization and develop vector ordinal optimization, which is different from the one introduced in Ref. 1. Alignment probability and ordered performance curve (OPC) are redefined for multiobjective optimization. Our results lead to quantifiable subset selection sizes in the multiobjective case, which supplies guidance in solving practical problems, as demonstrated by the examples in this paper.This paper was supported in part by Army Contract DAAD19-01-1-0610, AFOSR Contract F49620-01-1-0288, and a contract with United Technology Research Center (UTRC). The first author received additional funding from NSF of China Grants 60074012 and 60274011, Ministry of Education (China), and a Tsinghua University (Beijing, China) Fundamental Research Funding Grant, and the NCET program of China.The authors are grateful to and benefited from two rounds of reviews from three anonymous referees.     

Well-Posedness and Optimization under Perturbations

Estimates of the size of sets of approximate solutions are obtained for well-posed optimization problems in a Banach space, and extended to problems subject to perturbations of a general form. An estimate of the perturbations guaranteeing a prescribed level of suboptimality is presented.     

Hidden Convex Minimization

A class of nonconvex minimization problems can be classified as hidden convex minimization problems. A nonconvex minimization problem is called a hidden convex minimization problem if there exists an equivalent transformation such that the equivalent transformation of it is a convex minimization problem. Sufficient conditions that are independent of transformations are derived in this paper for identifying such a class of seemingly nonconvex minimization problems that are equivalent to convex minimization problems. Thus, a global optimality can be achieved for this class of hidden convex optimization problems by using local search methods. The results presented in this paper extend the reach of convex minimization by identifying its equivalent with a nonconvex representation.     

Two basic problems in reliability-based structural optimization

Optimization of structures with respect to performance, weight or cost is a well-known application of mathematical optimization theory. However optimization of structures with respect to weight or cost under probabilistic reliability constraints or optimization with respect to reliability under cost/weight constraints has been subject of only very few studies. The difficulty in using probabilistic constraints or reliability targets lies in the fact that modern reliability methods themselves are formulated as a problem of optimization. In this paper two special formulations based on the so-called first-order reliability method (FORM) are presented. It is demonstrated that both problems can be solved by a one-level optimization problem, at least for problems in which structural failure is characterized by a single failure criterion. Three examples demonstrate the algorithm indicating that the proposed formulations are comparable in numerical effort with an approach based on semi-infinite programming but are definitely superior to a two-level formulation.     

Towards global bilevel dynamic optimization

The global solution of bilevel dynamic optimization problems is discussed. An overview of a deterministic algorithm for bilevel programs with nonconvex functions participating is given, followed by a summary of deterministic algorithms for the global solution of optimization problems with nonlinear ordinary differential equations embedded. Improved formulations for scenario-integrated optimization are proposed as bilevel dynamic optimization problems. Solution procedures for some of the problems are given, while for others open challenges are discussed. Illustrative examples are given.     

Multicriteria Approach to Bilevel Optimization

In this paper, we study the relationship between bilevel optimization and multicriteria optimization. Given a bilevel optimization problem, we introduce an order relation such that the optimal solutions of the bilevel problem are the nondominated points with respect to the order relation. In the case where the lower-level problem of the bilevel optimization problem is convex and continuously differentiable in the lower-level variables, this order relation is equivalent to a second, more tractable order relation. Then, we show how to construct a (nonconvex) cone for which we can prove that the nondominated points with respect to the order relation induced by the cone are also nondominated points with respect to any of the two order relations mentioned before. We comment also on the practical and computational implications of our approach.     

Generalized pattern searches with derivative information

A common question asked by users of direct search algorithms is how to use derivative information at iterates where it is available. This paper addresses that question with respect to Generalized Pattern Search (GPS) methods for unconstrained and linearly constrained optimization. Specifically, this paper concentrates on the GPS pollstep. Polling is done to certify the need to refine the current mesh, and it requires O(n) function evaluations in the worst case. We show that the use of derivative information significantly reduces the maximum number of function evaluations necessary for pollsteps, even to a worst case of a single function evaluation with certain algorithmic choices given here. Furthermore, we show that rather rough approximations to the gradient are sufficient to reduce the pollstep to a single function evaluation. We prove that using these less expensive pollsteps does not weaken the known convergence properties of the method, all of which depend only on the pollstep.