混合离散变量模拟退火方法及其应用

基于海洋工程中存在的设计变量为离散型和连续型的混合离散变量的情况,探讨了一种优化设计问题的方法———混合离散模拟退火法.该方法相对常规模拟退火方法有一定改进并且针对混合离散变量进行了特定处理.实际算例计算表明,该方法可用于海洋工程优化设计中,其结果不需圆整,而且其解题可靠性和效率相当高.     

基于遗传算法的混合离散变量结构优化设计

本文研究了适于解决混合离散变量结构优化设计的遗传算法，给出了混合离散变量的遗传基因表达模式和适值函数建立的简便方法，计算实例表明该算法是有效的。     

铺设角度与铺层顺序对层合板稳定性的影响

以层合板结构的临界屈曲载荷系数最大化为优化目标,基于改进型模拟退火算法对层合板结构铺设角度和铺层顺序进行优化。由于层合板结构的铺层角度是离散变量,模拟退火算法适合求解离散变量的优化问题。利用模拟退火算法优化层合板铺层,在算法内采用并行计算、引入记忆功能同时设置双阈值终止准则,有效地提高了优化过程的收敛速度,同时避免优化过程中出现局部最优解。以临界屈曲载荷系数作为目标函数,选取复合材料层合板的铺设角度顺序为设计变量,采用改进的模拟退火算法得出复合材料层合板的最优铺设角度以及铺层顺序。     

基于SA算法的行星齿轮减速器离散变量优化设计

 考虑制造工艺要求，将所有设计变量均视为离散变量，包括一般离散变量和伪离散变量，并就这两种情况下状态产生函数的设计原理进行深入研究，解决了将模拟退火算法用于离散变量函数优化的关键技术问题，介绍了一种基于模拟退火算法的离散变量函数优化的新方法。行星齿轮传动中各齿轮的齿数受传动比条件、同轴条件和装配条件的限制而不能任意取值，齿轮的模数也要受国家标准的制约只能取一些离散值，用以数学规划理论为基础的经典约束优化方法求解效果很差，用基于模拟退火算法的离散变量优化设计方法则可以方便快捷地获得满足各方面要求的最优设计方案。     

全船结构静动态优化设计

在采用归一化灵敏度分析方法对全船结构众多设计变量进行必要取舍的基础上，建立全船结构优化模型。通过优化板材厚度和骨材型号等离散变量，使结构在满足相应的频率、强度、变形约束和几何限制等条件下，达到全船结构重量最小化的优化目标。以某自航绞吸挖泥船为研究对象，建立优化模型，采用iSIGHT中集成的自适应模拟退火算法进行静力学、动力学特性的计算分析和优化设计。优化结果表明：优化后的全船结构在满足强度和刚度要求下，不仅具有更轻的结构质量，而且具有更高的固有频率储备，更低的振动水平，较好的实现了全船结构的优化设计。     

离散变量结构优化设计的拟满应力遗传算法

以力学准则法为基础,提出了一种求解离散变量结构优化设计的拟满应力方法;这种方法能直接求解具有应力约束和几何约束的离散变量结构优化设计问题。通过在遗传算法中定义拟满应力算子,建立了一种离散变量结构优化设计的混合遗传算法拟满应力遗传算法。算例表明:这种混合遗传算法对于离散变量结构优化设计问题具有较高的计算效率。     

离散变量桁架结构拓扑优化设计的混合算法

将相对差商法和混沌优化结合起来,形成求解离散变量桁架结构拓扑优化设计的混合算法。利用相对差商法可以对离散变量快速寻优的特点,及混沌变量的全局遍历性,可以有效地跳出局部最优解,达到拓扑优化全局寻优的目的。通过采用和准最优解的对比及几何稳定性的判断等辅助性技术,降低了重分析次数。同时,高效的重分析方法的结合,提高了求解的效率,也避免了拓扑优化问题中求解的一些困难。算例表明,该算法对于离散变量的拓扑优化设计问题是快速有效的。     

离散变量结构优化的拟满应力设计方法

本文以满应力设计思想为基础,提出了适用于离散变量结构优化设计计算的拟满应力设计方法。该方法能直接计算具有应力约束和截面尺寸约柬的离散变量结构优化设计问题,也能处理同时具有稳定性约束和位移约束的多工况、多约束、多变量的离散变量结构优化设计问题。算例结果表明,拟满应力设计方法对于离散变量结构优化计算是非常有效的。     

混合离散变量多目标结构模糊优化及FD解法

本文建立了混合离散变量多目标结构模糊优化设计的数学模型：提出了模糊寻优区间、模糊优越混合离散解集和模糊可行集的概念；     

桁架结构布局优化的并行子空间方法

由于结构布局优化存在设计变量类型众多和变量耦合等问题,采取合适的优化方法获得满足结构设计要求的最小质量的结构具有重要的工程意义.基于多学科设计优化方法中的并行子空间优化法,提出一种桁架结构布局优化的并行子空间优化方法.将结构布局设计问题按设计变量类型分为布局、形状和尺寸三个并行的子空间,设计变量在各自的子空间内单独优化,各子空间优化结束后,在系统级中协调3类设计变量,保持最小质量的子空间的优化设计变量不变,采用近似一维搜索的方法协调其他子空间的设计变量,然后进行下一次迭代直至收敛.2个算例表明该方法能够取得较好的优化结果,具有实际工程应用价值.     

Single and multiobjective structural optimization in discrete-continuous variables using simulated annealing

A multivariable optimization technique based on the Monte-Carlo method used in statistical mechanics studies of condensed systems is adapted for solving single and multiobjective structural optimization problems. This procedure, known as simulated annealing, draws an analogy between energy minimization in physical systems and objective function minimization in structural systems. The search for a minimum is simulated by a relaxation of the statistical mechanical system where a probabilistic acceptance criterion is used to accept or reject candidate designs. To model the multiple objective functions in the problem formulation, a cooperative game theoretic approach is used. Numerical results obtained using three different annealing strategies for the single and multiobjective design of structures with discrete-continuous variables are presented. The influence of cooling schedule parameters on the optimum solutions obtained is discussed. Simulation results indicate that, in several instances, the optimum solutions obtained using simulated annealing outperform the optimum solutions obtained using some gradient-based and discrete optimization techniques. The results also indicate that simulated annealing has substantial potential for additional applications in optimization, especially for problems with mixed discrete-continuous variables.     

A deterministic global approach for mixed-discrete structural optimization

This study proposes a novel approach for finding the exact global optimum of a mixed-discrete structural optimization problem. Although many approaches have been developed to solve the mixed-discrete structural optimization problem, they cannot guarantee finding a global solution or they adopt too many extra binary variables and constraints in reformulating the problem. The proposed deterministic method uses convexification strategies and linearization techniques to convert a structural optimization problem into a convex mixed-integer nonlinear programming problem solvable to obtain a global optimum. To enhance the computational efficiency in treating complicated problems, the range reduction technique is also applied to tighten variable bounds. Several numerical experiments drawn from practical structural design problems are presented to demonstrate the effectiveness of the proposed method.     

Engineering optimization using a real-parameter genetic-algorithm-based hybrid method

A hybrid optimization algorithm which combines the respective merits of the genetic algorithm and the simulated annealing algorithm is proposed. The proposed algorithm incorporates adaptive mechanisms designed to adjust the probabilities of the cross-over and mutation operators such that its hill-climbing ability towards the optimum solution is improved. The algorithm is used to optimize the weight of four planar or space truss structures and the results are compared with those obtained using other well-known optimization schemes. The evaluation trials investigate the performance of the algorithm in optimizing over discrete sizing variables only and over both discrete sizing variables and continuous configuration variables. The results show that the proposed algorithm consistently outperforms the other optimization methods in terms of its weight-saving capabilities. It is also shown that the global searching ability and convergence speed of the proposed algorithm are significantly improved by the inclusion of adaptive mechanisms to adjust the values of the genetic operators. Hence the hybrid algorithm provides an efficient and robust technique for solving engineering design optimization problems.     

Novel orthogonal simulated annealing with fractional factorial analysis to solve global optimization problems

A classical simulated annealing (SA) method is a generic probabilistic and heuristic approach to solving global optimization problems. It uses a stochastic process based on probability, rather than a deterministic procedure, to seek the minima or maxima in the solution space. Although the classical SA method can find the optimal solution to most linear and nonlinear optimization problems, the algorithm always requires numerous numerical iterations to yield a good solution. The method also usually fails to achieve optimal solutions to large parameter optimization problems. This study incorporates well-known fractional factorial analysis, which involves several factorial experiments based on orthogonal tables to extract intelligently the best combination of factors, with the classical SA to enhance the numerical convergence and optimal solution. The novel combination of the classical SA and fractional factorial analysis is termed the orthogonal SA herein. This study also introduces a dynamic penalty function to handle constrained optimization problems. The performance of the proposed orthogonal SA method is evaluated by computing several representative global optimization problems such as multi-modal functions, noise-corrupted data fitting, nonlinear dynamic control, and large parameter optimization problems. The numerical results show that the proposed orthogonal SA method markedly outperforms the classical SA in solving global optimization problems with linear or nonlinear objective functions. Additionally, this study addressed two widely used nonlinear functions, proposed by Keane and Himmelblau to examine the effectiveness of the orthogonal SA method and the presented penalty function when applied to the constrained problems. Moreover, the orthogonal SA method is applied to two engineering optimization design problems, including the designs of a welded beam and a coil compression spring, to evaluate the capacity of the method for practical engineering design. The computational results show that the proposed orthogonal SA method is effective in determining the optimal design variables and the value of objective function.     

基于改进模拟退火算法的复合材料层合板频率优化

针对复合材料层合板频率优化问题,结合可行规则法和直接搜索模拟退化算法,提出了一种自适应模拟退火(SA)改进算法。层合板优化目标是基频、频率带隙以及给定基频和带隙约束的层合板厚度。设计变量包括铺层角度和铺层数两种离散变量。改进算法的自适应新点产生模块采用依赖温度的动态调整搜索半径,改善了直接搜索模拟退化(DSA)算法易陷入局部极值的缺陷,而可行规则法的引入提高了SA算法求解约束问题的效率和简易性。采用Ritz法进行频率响应分析以考虑弯扭耦合影响。不同铺层数、角度增量和长宽比时的层合板3类算例结果显示:改进算法能有效求解层合板频率优化,可获得更多或更好的铺层顺序全局优化解。     

Multi-stage optimization method for air-intake system of hovercraft based on autonomous optimization

Abstract

In this study, an optimal structural design program was designed and developed for Computational Fluid Dynamics based on self-optimization, effectively reducing the time required for structural optimization. Through experimental design using this program, the effects of various design variables on the optimization objectives were evaluated, and an adaptive simulated annealing algorithm was used for global optimization. Furthermore, response surface methodology and a nonlinear quadratic programming algorithm were utilized to obtain a global optimum solution after repeated iterations. Moreover, using a hovercraft air-intake system as the optimized object, the total pressure loss of the system was completely optimized by using a porous medium model and Matlab analysis program, and the accuracy of the structural design optimization program was validated. After the global optimization, the total pressure loss of the air-intake system was reduced by 20.5% compared to the original model. An average nonuniformity of 4.36% of engine inlet speed and 5% local nonuniformity of 11.19% satisfy the design requirements of the hovercraft engine. This method can be directly applied to engineering optimization problems as well as multiobjective optimization tasks after improving the relevant methodologies.     

Multidisciplinary design and optimization of an air launched satellite launch vehicle using a hybrid heuristic search algorithm

A multidisciplinary design and optimization strategy for a multistage air launched satellite launch vehicle comprising of a solid propulsion system to low earth orbit with the implementation of a hybrid heuristic search algorithm is proposed in this article. The proposed approach integrated the search properties of a genetic algorithm and simulated annealing, thus achieving an optimal solution while satisfying the design objectives and performance constraints. The genetic algorithm identified the feasible region of solutions and simulated annealing exploited the identified feasible region in search of optimality. The proposed methodology coupled with design space reduction allows the designer to explore promising regions of optimality. Modules for mass properties, propulsion characteristics, aerodynamics, and flight dynamics are integrated to produce a high-fidelity model of the vehicle. The objective of this article is to develop a design strategy that more efficiently and effectively facilitates multidisciplinary design analysis and optimization for an air launched satellite launch vehicle.     

一种混合优化策略在工步排序中的应用

结合创成式ＣＡＰＰ系统中工步优化问题，介绍了由遗传算法（ＧｅｎｅｔｉｃＡｌｇｏｒｉｔｈｍｓ，ＧＡ）和模拟退火算法（ＳｉｍｕｌａｔｅｄＡｎｎｅａｌｉｎｇＡｌｇｏｒｉｔｈｍｓ，ＳＡ）构成的混合寻优策略。最后以一箱体的工艺规划过程为例，将基于混合寻优策略的工步排序融入以加工中心为主要加工设备的ＣＡＰＰ工艺决策过程。