Self-adaptive constrained artificial bee colony for constrained numerical optimization

The artificial bee colony is a simple and effective global optimization algorithm. It has been successfully applied to solve a wide range of real-world optimization problem, and later, it was extended to constrained design problems as well. This paper describes a self-adaptive constrained artificial bee colony algorithm for constrained optimization problem based on feasible rule method and multiobjective optimization method. The employed bee colony severs as the global search engine for each population based on feasible rule. Then, the onlooker bee colony can explore the new search space based on the multiobjective optimization. In order to enhance the convergence rate of the proposed algorithm, a self-adaptive modification rate is proposed to make the algorithm can change many parameters. To verify the performance of our approach, 24 well-known constrained problems from 2006 IEEE congress on Evolution Computation (CEC2006) are employed. Experimental results indicate that the proposed algorithm performs better than, or at least comparable to, state-of-the-art approaches in terms of the quality of the resulting solutions from literature.     

动态电源管理的随机切换模型与在线优化

考虑系统参数未知情况下的动态电源管理问题，提出一种基于强化学习的在线策略优化算法. 通过建立事件驱动的随机切换分析模型，将动态电源管理问题转化为带约束的Markov 决策过程的策略优化问题. 利用此模型的动态结构特性，结合在线学习估计梯度与随机逼近改进策略，提出动态电源管理策略的在线优化算法．随机切换模型对电源管理系统的动态特性描述精确，在线优化算法自适应性强，运算量小，精度高，具有较高的实际应用价值．     

Constrained structural design optimization via a parallel augmented Lagrangian particle swarm optimization approach

This paper presents an extension to the basic particle swarm optimization approach for the solution of constrained engineering design optimization problems. The approach takes advantage of the PSO ability to find global optimum in problems with complex design spaces while directly enforcing feasibility of constraints using an augmented Lagrange multiplier method. Details in the algorithm implementation and properties are presented and the effectiveness of the approach is illustrated in different benchmark structural optimization test cases. Results show the ability of the proposed methodology to find better solutions for structural optimization tasks as compared to other optimization algorithms.     

Mathematical programming models and algorithms for engineering design optimization

Mathematical programming provides general tools for engineering design optimization. We present numerical models for simultaneous analysis and design optimization (SAND) and multidisciplinary design optimization (MDO) represented by mathematical programs. These models are solved with numerical techniques based on the feasible arc interior point algorithm (FAIPA) for nonlinear constrained optimization. Even if MDO is a very large optimization problem, our approach reduces considerably the computer effort. Several tools for very large problems are also presented. The present approach is very strong and efficient for real industrial applications and can easily interact with existing simulation engineering codes.     

A hybrid evolutionary approach for solving constrained optimization problems over finite domains

A novel approach for the integration of evolution programs and constraint-solving techniques over finite domains is presented. This integration provides a problem-independent optimization strategy for large-scale constrained optimization problems over finite domains. In this approach, genetic operators are based on an arc-consistency algorithm, and chromosomes are arc-consistent portions of the search space of the problem. The paper describes the main issues arising in this integration: chromosome representation and evaluation, selection and replacement strategies, and the design of genetic operators. We also present a parallel execution model for a distributed memory architecture of the previous integration. We have adopted a global parallelization approach that preserves the properties, behavior, and fundamentals of the sequential algorithm. Linear speedup is achieved since genetic operators are coarse grained as they perform a search in a discrete space carrying out arc consistency. The implementation has been tested on a GRAY T3E multiprocessor using a complex constrained optimization problem.     

An interval space reducing method for constrained problems with particle swarm optimization

In this paper, we propose a method for solving constrained optimization problems using interval analysis combined with particle swarm optimization. A set inverter via interval analysis algorithm is used to handle constraints in order to reduce constrained optimization to quasi unconstrained one. The algorithm is useful in the detection of empty search spaces, preventing useless executions of the optimization process. To improve computational efficiency, a space cleaning algorithm is used to remove solutions that are certainly not optimal. As a result, the search space becomes smaller at each step of the optimization procedure. After completing pre-processing, a modified particle swarm optimization algorithm is applied to the reduced search space to find the global optimum. The efficiency of the proposed approach is demonstrated through comprehensive experimentation involving 100 000 runs on a set of well-known benchmark constrained engineering design problems. The computational efficiency of the new method is quantified by comparing its results with other PSO variants found in the literature.     

动态调整成长方式的郊狼优化算法及其应用

郊狼优化算法在迭代运行时种群多样性降低,收敛速度变慢,易陷入局部最优,并且在求解约束优化问题时难以获得可行解。提出一种动态调整成长方式的郊狼优化算法（DGCOA）。在狼群进化中引入变异交叉策略,增强种群多样性,基于郊狼成长策略加入全局最优个体指导搜索,使得每个子种群中的个体从不同的方向快速逼近最优解位置,并根据种群中个体相似度对郊狼位置更新方式进行调整,平衡算法的全局探索与局部开发能力。在求解约束优化问题时,利用自适应约束处理方法构建新的适应度函数,协调优化目标和约束违反度。基于CEC2006对22个测试函数和3个工程设计问题进行仿真,结果表明,与COA、ICTLBO、ODPSO等算法相比,DGCOA算法具有较高的收敛精度和稳定性,适用于求解复杂优化问题。     

Bilinear modeling via augmented Lagrange multipliers (BALM)

This paper presents a unified approach to solve different bilinear factorization problems in computer vision in the presence of missing data in the measurements. The problem is formulated as a constrained optimization where one of the factors must lie on a specific manifold. To achieve this, we introduce an equivalent reformulation of the bilinear factorization problem that decouples the core bilinear aspect from the manifold specificity. We then tackle the resulting constrained optimization problem via Augmented Lagrange Multipliers. The strength and the novelty of our approach is that this framework can seamlessly handle different computer vision problems. The algorithm is such that only a projector onto the manifold constraint is needed. We present experiments and results for some popular factorization problems in computer vision such as rigid, non-rigid, and articulated Structure from Motion, photometric stereo, and 2D-3D non-rigid registration.     

求解运输问题的GAPSO算法

运输问题是一个应用非常广泛的问题,传统方法对于大规模的运输问题求解比较复杂,而一些基于随机搜索算法的方法对于其约束条件的处理又比较困难.基于运输问题约束条件的特殊性,设计了一种产生可行解的方法,将对约束条件的处理转化到了算法设计之中.在此基础上,又设计了基于遗传算法和粒子群优化算法的求解运输问题的GAPSO算法,为避开对非可行解的处理,该算法对迭代过程也进行了特殊设计,从而简化了运用随机搜索算法解决运输问题的过程.最后给出了三个实例验证,通过对验证结果分析和比较,说明该算法在时间复杂度和收敛性方面都具有其优良性,是行之有效的.     

基于SQP和自适应搜索的混沌粒子群算法

针对基本粒子群优化算法（PSO）算法易陷入局部最优的缺点,提出混沌自适应粒子群-序列二次规划算法（CAPSO-SQP）。在基本PSO算法的基础上,加入混沌搜索和自适应惯性权重提高全局收敛能力,并在PSO算法每一代的迭代过程中,引入SQP策略,加快局部搜索并提高对约束优化问题的计算可靠性。测试函数仿真结果表明,CAPSO-SQP算法计算精度高,稳定性好,收敛速度快。将所提出算法应用于悬臂梁结构优化设计,求解结果表明算法在结构优化计算方面的可行性,而且相对于CPSO算法求解更加准确,具有较高的计算可靠性和实用价值。     

改进的约束优化多目标遗传算法及工程应用

利用多目标法处理约束条件,提出一种改进的基于多目标优化的遗传算法用于求解约束优化问题。该算法将约束优化问题转化为两个目标的多目标优化问题; 利用庄家法构造非劣个体,将种群分为支配子种群和非支配子种群,以一定概率分别从支配子种群和非支配子种群中选择个体进行算术交叉操作,引导个体逐步向极值点靠近,增强算法的局部搜索能力,对非支配子种群进行多样性变异操作。8个标准测试函数和3个工程应用的仿真实验结果表明了该算法的有效性。     

动态分级的并行约束优化进化算法

提出一种动态分级的并行进化算法用于求解约束优化问题。该算法首先利用佳点集方法初始化种群。在进化过程中,将种群个体分为两个子种群,分别用于全局和局部搜索,并根据不同的搜索阶段动态调整各种级别中并行变量的数目。标准测试问题的实验结果表明了该算法的可行性和有效性。     

Cam shape optimisation by genetic algorithm

This article overviews a genetic algorithm based computer-aided approach for preliminary design and shape optimisation of cam profiles for cam operated mechanisms. The primary objective of the work was to create a complete systematic approach for preliminary cam shape design including cam shape design automation and true cam shape optimisation with respect to the simulated computer models of cam mechanisms. Typically, shape optimisation of a cam cross-section is a multiobjective optimisation problem of two-dimensional geometric shape in a heavily constrained environment. In order to illustrate the genetic algorithm based cam shape optimisation approach, a cam shape design example is described, in which a cam shape designed by genetic algorithm is compared with its more conventionally designed counterpart.     

Particle swarm optimization for solving engineering problems: A new constraint-handling mechanism

This paper addresses constrained and optimal engineering problems solved using an adapted particle swarm optimization (PSO) algorithm. In fact, a specific constraint-handling mechanism is presented. It consists of a closeness evaluation of the solutions to the feasible region. The total constraints violation is introduced as an objective function to minimize. Interval arithmetic is used to normalize the total violations. The resulting objective problem is solved using a simple lexicographic method. The new algorithm is called CVI-PSO for constraint violation with interval arithmetic PSO. The paper provides numerous experimental results based on a well-known benchmark and comparisons with previously reported results. Finally, a case study of the optimal design of an electrical actuator with several model reformulations is detailed.     

A hybrid approach to constrained global optimization

In this paper, we propose a novel hybrid global optimization method to solve constrained optimization problems. An exact penalty function is first applied to approximate the original constrained optimization problem by a sequence of optimization problems with bound constraints. To solve each of these box constrained optimization problems, two hybrid methods are introduced, where two different strategies are used to combine limited memory BFGS (L-BFGS) with Greedy Diffusion Search (GDS). The convergence issue of the two hybrid methods is addressed. To evaluate the effectiveness of the proposed algorithm, 18 box constrained and 4 general constrained problems from the literature are tested. Numerical results obtained show that our proposed hybrid algorithm is more effective in obtaining more accurate solutions than those compared to.     

一种求解约束优化问题的混合算法

提出一种基于修改增广Lagrange函数和PSO的混合算法用于求解约束优化问题。将约束优化问题转化为界约束优化问题,混合算法由两层迭代结构组成,在内层迭代中,利用改进PSO算法求解界约束优化问题得到下一个迭代点。外层迭代主要修正Lagrange乘子和罚参数,检查收敛准则是否满足,重构下次迭代的界约束优化子问题,检查收敛准则是否满足。数值实验结果表明该混合算法的有效性。     

Method for solving nonlinear goal programming with interval coefficients using genetic algorithm

Traditional formulations on reliability optimization problems have assumed that the coefficients of models are known as fixed quantities and reliability design problem is treated as deterministic optimization problems. Because that the optimal design of system reliability is resolved in the same stage of overall system design, model coefficients are highly uncertainty and imprecision during design phase and it is usually very difficult to determine the precise values for them. However, these coefficients can be roughly given as the intervals of confidence.

In this paper, we formulated reliability optimization problem as nonlinear goal programming with interval coefficients and develop a genetic algorithm to solve it. The key point is how to evaluate each solution with interval data. We give a new definition on deviation variables which take interval relation into account. Numerical example is given to demonstrate the efficiency of the proposed approach.     

一种新的约束优化遗传算法及其工程应用

提出一种新的用于求解约束优化问题的遗传算法,该算法利用佳点集方法初始化个体以维持种群的多样性.在进化过程中,通过可行解与不可行解算术交叉对问题的决策空间进行搜索;对可行种群与不可行种群分别采用高斯变异和柯西变异,从而协调算法的勘探和开采能力.几个标准测试问题的实验结果表明该算法的有效性;应用新算法求解两个工程优化设计问题,结果表明该算法的可行性.     

多目标优化问题的蚁群算法研究

将离散空间问题求解的蚁群算法引入连续空间,针对多目标优化问题的特点,提出一种用于求解带有约束条件的多目标函数优化问题的蚁群算法.该方法定义了连续空间中信息量的留存方式和蚂蚁的行走策略,并将信息素交流和基于全局最优经验指导两种寻优方式相结合,用以加速算法收敛和维持群体的多样性.通过3组基准函数来测试算法性能,并与NSGAII算法进行了仿真比较.实验表明该方法搜索效率高,向真实Pareto前沿逼近的效果好,获得的解的散布范围广,是一种求解多目标优化问题的有效方法.     

基于状态空间模型的智能优化算法及其应用

针对城市公共交通系统中公交优化调度问题的具体特征,提出一种基于状态空间模型的实数编码智能优化算法(SIA)。SIA引入遗传算法(GA)的基本理念。通过构造状态进化矩阵来指导算法的搜索方向,再通过选种池的优胜劣汰的选择机理来实现算法朝最优解逼近。将该算法与GA分别应用到公交优化调度问题中,考虑发车时间间隔的约束,建立以企业和乘客的利益最大化为目标的数学模型。实例仿真结果表明,SIA在寻优精度和计算量方面优于GA,验证了该算法的有效性。