求解约束优化问题的退火遗传算法

针对基于罚函数遗传算法求解实际约束优化问题的困难与缺点,提出了求解约束优化问题的退火遗传算法。对种群中的个体定义了不可行度,并设计退火遗传选择操作。算法分三阶段进行,首先用退火算法搜索产生初始种群体,随后利用遗传算法使搜索逐渐收敛于可行的全局最优解或较优解,最后用退火优化算法对解进行局部优化。两个典型的仿真例子计算结果证明该算法能极大地提高计算稳定性和精度。     

一种改进的视频序列超分辨率重建算法及应用

在凸集优化基础上,充分利用最大后验概率和凸集投影技术,提出了一种高效强鲁棒性视频序列分辨率提升算法。首先,在空域设计一个简单的预处理共轭梯度估计器,预测原始高分辨率图像;然后,在小波域分别创建帧间和帧内两个不同的凸集,并实施不同的投影运算,提取出隐含在相邻低分辨率图像中的细节信息;最后,利用空域估计器中相邻因子间的关系约束凸集投影解的可行域,保证快速获得图像重建的唯一最优解。仿真实验和实际交通监测系统应用结果均表明,该方法较其他方法不仅可获得更高的峰值信噪比和更好的可视化效果,而且收敛更快,鲁棒性更强。     

遗传算法与惩罚函数法在机械优化设计中的应用

提出了应用于机械优化设计的"遗传算法+惩罚函数法"的通用算法.它非常适合求解复杂的非线性约束优化问题.本通用算法既克服了传统优化方法的缺点,得到了一个较为理想的全域最优解;同时也改善了遗传算法的局限性.     

改进的蚂蚁算法在几何约束求解中的应用

将几何约束问题转化为数值优化问题。把蚂蚁算法引入几何约束求解中。在所有的操作中,由于没有涉及到在 Newton-Raphson 中遇到的矩阵求逆操作,因此蚂蚁算法具有很强的鲁棒性。笔者在基本蚂蚁算中混入局部优化算法,对每代的最优解进行改进,进一步加快蚂蚁算法的收敛速度。为了避免蚂蚁一开始就失去解的多样性,笔者改进了选择策略。为了克服蚂蚁算法计算时间较长的缺陷,这里引入遗传算法中的变异算子,经过局部优化后,整个群体的性能会有明显改善,使得算法保持更好的多样性。由于该算法对方程的个数和变量的个数没有什么特殊的要求,因此可以处理欠约束问题。     

基于并行混沌和复合形法的桁架结构形状优化

针对多工况下受应力、位移和局部稳定性约束的桁架形状优化问题,提出了基于并行混沌优化算法和复合形法的混合优化算法。该算法综合利用了并行混沌的全局搜索能力,复合形法的快速局部搜索能力和混沌细搜索。首先,利用并行混沌优化算法快速搜索到全局最优解附近,然后应用改进复合形法以并行混沌的优化解为初始复形进行搜索,提高了最优解的搜索速度,最后应用混沌细搜索策略提高最优解的精度。两个典型数值算例验证了该混合优化方法对桁架形状优化问题的有效性和稳定性。     

带非凸二次约束的二次规划问题的全局优化方法

利用二次函数的线形下界函数对带有非凸二次约束的二次规划(QP)提出一种新的求其全局最优解的分支定界算法.为改进算法的收敛性,根据问题的最优性和可行性提出一新的区域剪枝准则以排除(QP)的可行域中不存在全局解的部分.数值算例表明该准则能有效地加速算法的收敛性.     

带约束二进制矩阵编码染色体及遗传算子设计

提出了一类带约束的二进制矩阵型染色体的编码方法.相对于传统向量型染色体编码方法而言,该方法可以通过在矩阵中设置"禁止位"将复杂优化问题的若干约束条件在编码中体现出来.此类染色体的交叉和变异操作不能采用传统方法,否则子代染色体可能成为问题的非法解.设计了一种针对此类型染色体的巡回变换操作,基于该操作可以实现用于带约束二进制矩阵编码染色体的交叉和变异算子.仿真实例表明,此类染色体及遗传算子的设计对于遗传算法用于复杂优化问题的求解,具有一定意义.     

求解一类非线性双层规划问题的混合遗传算法

本文研究下层目标函数为拟凹函数的非线性双层规划问题。利用下层目标的最优值能在可行域极点上达到的性质,将求极点的方法引入遗传算法,提出了一种混合遗传算法。为了提高该算法的效率,结合种群最优个体,给出了有利于产生高质量后代的杂交和变异算子。对于下层问题存在多个最优解的情况,证明了其最优解可表示为极点最优解的凸组合,并利用这一结论修正了算法,使得该算法也能求解下层多解的情形。数值结果表明本文提出的算法是有效的。     

一种基于PSO算法的非线性模型预测控制方法

将微粒群优化(PSO)算法用于输入受限非线性系统,提出了一种基于PSO的非线性模型预测控制算法.该算法采用双模控制策略,将保证预测控制稳定性的终端等式约束转化为终端不等式约束,推导出使系统稳定的不变可行集.在不变集外,利用PSO算法优化求解预测控制律,使系统状态进入不变集;在不变集内,利用线性状态反馈使系统状态渐近稳定.同时对算法的稳定性进行了分析.仿真结果证明了该算法的可行性和有效性.     

进化策略实现圆度误差的统一评定研究

圆度误差的评定有最小区域法、最小外接圆法、最大内接圆法和最小二乘法4种方法,文中提出了将进化策略用于上述多种圆度误差的统一评定.该算法基于实数编码,采用(μ λ)选择策略和高斯变异算子,即父代种群参与竞争,算法简单、鲁棒性强,优化效率高.同时建立了进化策略评定上述圆度误差时目标函数的数学模型.最后,通过不同评价方法对圆度误差进行评定,结果证明该方法不仅能快速收敛到全局最优解,而且计算结果的稳定性好,易于在工程计量中推广使用.     

A global single-loop deterministic approach for reliability-based design optimization of truss structures with continuous and discrete design variables

A single-loop deterministic method (SLDM) has previously been proposed for solving reliability-based design optimization (RBDO) problems. In SLDM, probabilistic constraints are converted to approximate deterministic constraints. Consequently, RBDO problems can be transformed into approximate deterministic optimization problems, and hence the computational cost of solving such problems is reduced significantly. However, SLDM is limited to continuous design variables, and the obtained solutions are often trapped into local extrema. To overcome these two disadvantages, a global single-loop deterministic approach is developed in this article, and then it is applied to solve the RBDO problems of truss structures with both continuous and discrete design variables. The proposed approach is a combination of SLDM and improved differential evolution (IDE). The IDE algorithm is an improved version of the original differential evolution (DE) algorithm with two improvements: a roulette wheel selection with stochastic acceptance and an elitist selection technique. These improvements are applied to the mutation and selection phases of DE to enhance its convergence rate and accuracy. To demonstrate the reliability, efficiency and applicability of the proposed method, three numerical examples are executed, and the obtained results are compared with those available in the literature.     

Improved artificial bee colony algorithm for crack identification in beam using natural frequencies only

An improved artificial bee colony algorithm (I-ABC) is proposed for crack identification in beam structures. ABC is a heuristic algorithm and swarm technique with simple structure, which is easy to implement but with slow convergence rate. In the I-ABC, the differential evolution (DE) mechanism is introduced to employed bee phase, roulette selection strategy is replaced by tournament selection strategy and a new formula is used to simulate onlooker bee’s behaviour. A discrete open crack is used for vibration analysis of the cracked beam and only the changes in the first few natural frequencies are utilized to establish the objective function of the optimization problem for crack identification. A numerical simulation and an experimental work are studied to illustrate the efficiency of the proposed method. Studies show that the present techniques can produce more accurate damage identification results when compared with original ABC, DE algorithm, particle swarm optimization and genetic algorithm.     

An adaptive constraint handling technique for?differential evolution with dynamic use of variants in?engineering optimization

Differential Evolution is a simple and efficient stochastic population-based heuristics for global optimization over continuous spaces. As with other nature inspired techniques, there is no provision for constraint handling in its original formulation, and a few possibilities have been proposed in the literature. In this paper an adaptive penalty technique (APM), which has been shown to be quite effective within genetic algorithms, is adopted for constraint handling within differential evolution. The technique, which requires no extra parameters, is based on feedback obtained from the current status of the population of candidate solutions, and automatically defines, for each constraint, its corresponding penalty coefficient. Equality as well as inequality constraints can be dealt with. In this paper we additionally introduce a mechanism for dynamically selecting the mutation operator, according to its performance, among several variants commonly used in the literature. In order to assess the applicability and performance of the proposed procedure, several test-problems from the structural and mechanical engineering optimization literature are considered.     

Chemical process dynamic optimization based on the differential evolution algorithm with an adaptive scheduling mutation strategy

To solve chemical process dynamic optimization problems, a differential evolution algorithm integrated with adaptive scheduling mutation strategy (ASDE) is proposed. According to the evolution feedback information, ASDE, with adaptive control parameters, adopts the round-robin scheduling algorithm to adaptively schedule different mutation strategies. By employing an adaptive mutation strategy and control parameters, the real-time optimal control parameters and mutation strategy are obtained to improve the optimization performance. The performance of ASDE is evaluated using a suite of 14 benchmark functions. The results demonstrate that ASDE performs better than four conventional differential evolution (DE) algorithm variants with different mutation strategies, and that the whole performance of ASDE is equivalent to a self-adaptive DE algorithm variant and better than five conventional DE algorithm variants. Furthermore, ASDE was applied to solve a typical dynamic optimization problem of a chemical process. The obtained results indicate that ASDE is a feasible and competitive optimizer for this kind of problem.     

Solving initial and boundary value problems using learning automata particle swarm optimization

In this article, the particle swarm optimization (PSO) algorithm is modified to use the learning automata (LA) technique for solving initial and boundary value problems. A constrained problem is converted into an unconstrained problem using a penalty method to define an appropriate fitness function, which is optimized using the LA-PSO method. This method analyses a large number of candidate solutions of the unconstrained problem with the LA-PSO algorithm to minimize an error measure, which quantifies how well a candidate solution satisfies the governing ordinary differential equations (ODEs) or partial differential equations (PDEs) and the boundary conditions. This approach is very capable of solving linear and nonlinear ODEs, systems of ordinary differential equations, and linear and nonlinear PDEs. The computational efficiency and accuracy of the PSO algorithm combined with the LA technique for solving initial and boundary value problems were improved. Numerical results demonstrate the high accuracy and efficiency of the proposed method.     

Unequal-area facility layout by genetic search

This paper applies genetic optimization with an adaptive penalty function to the shape-constrained unequal-area facility layout problem. We implement a genetic search for unequal-area facility layout, and show how optimal solutions are affected by constraints on permitted department shapes, as specified by a maximum allowable aspect ratio for each department. We show how an adaptive penalty function can be used to find good feasible solutions to even the most highly constrained problems. We describe our genetic encoding, reproduction and mutation operators, and penalty evolution strategy. We provide results from several test problems that demonstrate the robustness of this approach across different problems and parameter settings.     

基于离散差分进化算法的随机车辆路径问题

针对差分进化算法求解组合优化问题存在的局限性,引入计算机语言中的2种按位运算符,对差分进化算法的变异算子进行重新设计,用来求解不确定需求和旅行时间下同时取货和送货的随机车辆路径问题（SVRPSPD）。通过对车辆路径问题的benchmark问题和SVRPSPD问题进行路径优化,并同差分进化算法和遗传算法的计算结果进行比较,验证了离散差分进化算法的性能。结果表明,离散差分进化算法在解决复杂的SVRPSPD问题时,具有较好的优化性能,不仅能得到更好的优化结果,而且具有更快的收敛速度。     

An Evolutionary Lagrange Method For Mixed-Integer Constrained Optimization Problems

This study proposes a method for solving mixed-integer constrained optimization problems using an evolutionary Lagrange method. In this approach, an augmented Lagrange function is used to transform the mixed-integer constrained optimization problem into an unconstrained min—max problem with decision-variable minimization and Lagrange-multiplier maximization. The mixed-integer hybrid differential evolution (MIHDE) is introduced into the evolutionary min—max algorithm to accomplish the implementation of the evolutionary Lagrange method. MIHDE provides a mixed coding to denote genetic representations of teal and integer variables, and a rounding operation is used to guide the genetic evolution of integer variables. To fulfill global convergence, self-adaptation for penalty parameters is involved in the evolutionary min—max algorithm so that small penalty parameters can be used, not affecting the final search results. Some numerical experiments are tested to evacuate the performance of the proposed method. Numerical experiments demonstrate that the proposed method converges to better solutions than the conventional penalty function method     

Two enhanced differential evolution algorithms for job shop scheduling problems

This paper proposes two new differential evolution algorithms (DE) for solving the job shop scheduling problem (JSP) that minimises two single objective functions: makespan and total weighted tardiness. The proposed algorithms aim to enhance the efficiency of the search by dynamically balancing exploration and exploitation ability in DE and avoiding the problem of premature convergence. The first algorithm allows DE population to simultaneously perform different mutation strategies in order to extract the strengths of various strategies and compensate for the weaknesses of each individual strategy to enhance the overall performance. The second algorithm allows the whole DE population to change the search behaviour whenever the solutions do not improve. This study also introduces a modified local mutation operation embedded in the two proposed DE algorithms to promote exploitation in different areas of the search space. In addition, a local search technique, called Critical Block (CB) neighbourhood, is applied to enhance the quality of solutions. The performances of the proposed algorithms are evaluated on a set of benchmark problems and compared with results obtained from an efficient existing Particle Swarm Optimisation (PSO) algorithm. The numerical results demonstrate that the proposed DE algorithms yield promising results while using shorter computing times and fewer numbers of function evaluations.     

基于改进蝗虫优化算法的光伏电池模型参数辨识

针对蝗虫优化算法容易陷入局部最优、收敛精度不足等缺点,提出一种改进蝗虫优化算法。将混沌算法与蝗虫优化算法融合,对蝗虫优化算法进行混沌初始化,改善初始种群质量;再引入差分进化算法的差分策略,通过变异、交叉和选择过程,维持种群的多样性,增大算法跳出局部最优的可能性,从而使算法能搜索到更好的解;在个体更新部分引入了粒子群算法的思想,以当前的最优个体为目标进行个体位置更新,加快算法寻优速度。将改进蝗虫优化算法用于多晶硅太阳能电池模型参数的辨识中,并通过与其它智能优化算法的比较,验证了改进蝗虫算法辨识太阳能电池参数的有效性和优越性。通过实验验证了改进蝗虫优化算法在不同光照下对太阳能电池参数的辨识效果。