基于近似模型管理的汽车安全带约束系统优化设计

为提高汽车安全带约束系统的安全防护能力,通过实车碰撞实验对安全带约束系统数值模型进行校正;基于径向基函数建立安全带约束系统的近似模型,运用IP-GA遗传算法对安全带约束系统的动态特性参数进行优化。优化中为控制由近似模型所致误差,通过模型管理更新近似模型,并将误差达到允许范围内优化解作为实际问题的解。结果表明,该方法能快速有效获得安全带约束系统的最佳匹配参数,确保汽车乘员的安全性。     

基于动态加权系数和多目标进化的模型修正方法

建立准确的结构动力学模型是结构响应分析的基础,由于模型简化的不确切等因素,必然会带来一定的误差,为了获得高精度的动力学分析模型,需要结合试验数据对模型进行修正。模态试验结果中包含了试件不同状态不同阶次的频率和振型信息,模型修正时需要建立多个目标函数,提出了一种基于动态加权系数的多目标模型修正方法。通过对解的群体实施进化,在每一代非劣解中,挑选各个子目标函数的局部最优解,计算各个局部最优解与子目标期望值的差距,并根据差距对加权系数动态调整,从而在进化过程中对加权系数进行优化,避免维数灾难问题,实现各个子目标函数的快速收敛。采用该方法对导弹全弹动力学模型进行了修正,子目标函数个数达到16个,与基于Pareto最优的模型修正方法相比,用较少的代数实现了各个子目标函数的收敛,提高了群体搜索的效率,取得了较好的修正效果。     

熔融沉积快速成型零件成型方向的多目标优化

为了实现熔融沉积快速成型（FDM）中零件成型精度和成型效率的协同优化,基于零件成型方向对成型精度和成型效率的影响进行分析,以体积误差最小、零件成型方向上高度最低以及所需支撑体积最小为目标,建立了零件成型方向的多目标优化模型。设计了基于非支配排序遗传算法的智能求解算法,通过对模型的优化计算得到零件成型方向的Pareto解集,实现了FDM零件成型方向的智能优化。最后通过实例验证了所建模型的正确性与算法的有效性。     

双轴联动进给系统多目标优化设计与研究

为提高机床的加工精度,降低零件加工误差,以双轴联动进给系统的轮廓误差和Z轴、X轴的跟踪误差为优化目标,开展双轴联动进给系统的多目标优化设计与研究。首先,在前期研究的基础上,设置优化初始条件,并利用Box-Behnken方法获得试验样本点;其次,基于所建立的双轴联动进给系统的机电耦合动力学模型开展样本点运动轨迹仿真分析,得到轮廓误差和单轴跟踪误差数据,并采用灵敏度分析法获得对设计目标影响程度较大的设计变量;然后,基于仿真得到的数据,利用含交叉项的二次多项式拟合方法构建设计目标对设计变量的响应面模型;最后,利用NSGA-II （non-dominated sorting genetic algorithm-II,非支配排序遗传算法II）对双轴联动进给系统进行优化,得到双轴联动进给系统的Pareto最优解集,按照目标优先顺序从该解集中寻得最优解。从仿真结果可知,双轴联动进给系统的轮廓误差和Z轴、X轴的跟踪误差均明显降低,降幅超过30%,优化效果明显。该方法可为多轴联动进给系统的优化提供参考。     

一种快速构造非支配集的方法--擂台法则

多目标进化算法是用来解决多目标优化问题的,为了提高多目标算法的效率,提出了一种快速构造非支配集的方法——擂台法则。它的时间耗费要低于Deb和Jensen提出的构造非支配集的方法。在实验中将擂台法则同Deb和Jensen的方法进行了比较,最后实验结果证明前者在运行时间上要优于后两者。     

基于序贯层次Kriging模型的微型飞行器机身结构设计优化

在基于仿真模型的工程设计优化中,采用高精度、高成本的分析模型会导致计算量大,采用低精度、低成本的分析模型会导致设计优化结果的可信度低,难以满足实际工程的要求。为了有效平衡高精度与低成本之间的矛盾关系,通过建立序贯层次Kriging模型融合高/低精度数据,采用大量低成本、低精度的样本点反映高精度分析模型的变化趋势,并采用少量高成本、高精度的样本点对低精度分析模型进行校正,以实现对优化目标的高精度预测。为了避免层次Kriging模型误差对优化结果的影响,将层次Kriging模型与遗传算法相结合,根据6σ设计准则计算每一代最优解的预测区间,具有较大预测区间的当前最优解即为新的高精度样本点。同时,在优化过程中序贯更新层次Kriging模型,提高最优解附近的层次Kriging模型的预测精度,从而保证设计结果的可靠性。将所提出的方法应用于微型飞行器机身结构的设计优化中,以验证该方法的有效性和优越性。采用具有不同单元数的网格模型分别作为低精度分析模型和高精度分析模型,利用最优拉丁超立方设计分别选取60个低精度样本点和20个高精度样本点建立初始层次Kriging模型,采用本文方法求解并与直接采用高精度仿真模型求解的结果进行比较。结果表明,所提出的方法能够有效利用高/低精度样本点处的信息,建立高精度的层次Kriging模型;本文方法仅需要少量的计算成本就能求得近似最优解,有效提高了设计效率,为类似的结构设计优化问题提供了参考。     

电网停电后机组恢复优化方法研究

提出了机组恢复的多目标优化策略。以机组启动后提供的发电量尽可能大、已恢复的电源点尽量在网架层面铺开、有利于后续厂站层机组和重要负荷的恢复为优化目标,建立机组恢复的多目标优化模型。先将恢复过程划分为一系列顺序执行的恢复时步,再将每一时步的优化问题转化成多目标“0／1背包”问题;结合最短路径法为机组恢复方案搜索恢复路径,采用快速非支配排序遗传算法进行求解;最后对每时步的Pareto最优方案排序,确定最优解。算例结果验证了该方法的有效性。     

汽车车身耐撞性设计参数的区间稳健性优化

基于区间分析,提出了一种考虑公差的汽车车身耐撞性稳健优化设计模型,可在有效降低耐撞性能对设计参数波动敏感性的同时实现公差范围的最大化。该模型首先利用对称公差来描述汽车碰撞模型中车身关键耐撞部件的主要尺寸、位置和形状等设计参数本身的不确定性,然后将参数设计和公差设计相结合,建立了以稳健性评价指标和公差评价指标为优化目标,设计变量名义值和公差同步优化的多目标优化模型。再次,利用区间可能度处理不确定约束,将该优化模型转换为确定性多目标优化模型。最后,将该模型应用于两个汽车耐撞性优化设计问题,并通过序列二次规划法和改进的非支配排序遗传算法进行求解,结果表明该方法及稳健优化设计模型可行且实用。     

汽车乘员舱多层吸声材料的多目标优化

建立了汽车的统计能量分析模型,进行仿真与实验的误差分析,验证了所建模型的有效性,然后选取四层吸声材料布置于乘员舱顶棚,采用优化拉丁方法,以其厚度为设计变量,为降低驾驶员耳旁噪声和满足汽车结构轻量化和低成本的要求,以驾驶员头部声腔A声级降低幅度、吸声材料重量、降噪效率、材料价格和性价比为优化目标,选取30个样本点进行试验设计并通过计算得到全部响应值,之后建立了Kriging近似模型,为验证该近似模型模拟精度,任选三个新的样本点分析近似模型和仿真结果间的误差,最后以近似模型为基础执行多目标优化,与吸声材料初始组合相比,A声级降低幅度反而减小了0.289dB,但重量降低了54.8%,降噪效率提高了85.6%,材料价格降低了21.1%,性价比提高了6.0%。     

模型缩聚-模型修正迭代方法的研究

模型修正中通常需要解决自由度匹配问题,模型缩聚是解决这一问题的一种方法。当有限元建模误差较大时,模型缩聚的近似会大大降低模型修正的精度。针对这一问题,提出了模型缩聚-模型修正迭代方法,消除模型缩聚带来的误差。文中应用IRS缩聚和基于频响函数的模型修正方法对提出的迭代方法进行了具体讨论。通过板梁混合结构的数值模拟实验,比较了现有修正方法和迭代修正方法的修正精度。结果表明提出的迭代方法有效提高了修正精度,使修正后的模型频率和物理参数更逼近真实值。同时该方法具有较高的迭代收敛效率,符合实际工程应用的要求。     

Variation-aware clock network buffer sizing using robust multi-objective optimization

Many engineering optimization problems include unavoidable uncertainties in parameters or variables. Ignoring such uncertainties when solving the optimization problems may lead to inferior solutions that may even violate problem constraints. Another challenge in most engineering optimization problems is having different conflicting objectives that cannot be minimized simultaneously. Finding a balanced trade-off between these objectives is a complex and time-consuming task. In this paper, an optimization framework is proposed to address both of these challenges. First, we exploit a self-calibrating multi-objective framework to achieve a balanced trade-off between the conflicting objectives. Then, we develop the robust counterpart of the uncertainty-aware self-calibrating multi-objective optimization framework. The significance of this framework is that it does not need any manual tuning by the designer. We also develop a mathematical demonstration of the objective scale invariance property of the proposed framework. The engineering problem considered in this paper to illustrate the effectiveness of the proposed framework is a popular sizing problem in digital integrated circuit design. However, the proposed framework can be applied to any uncertain multi-objective optimization problem that can be formulated in the geometric programming format. We propose to consider variations in the sizes of circuit elements during the optimization process by employing ellipsoidal uncertainty model. For validation, several industrial clock networks are sized by the proposed framework. The results show a significant reduction in one objective (power, on average 38 %) as well as significant increase in the robustness of solutions to the variations. This is achieved with no significant degradation in the other objective (timing metrics of the circuit) or reduction in its standard deviation which demonstrates a more robust solution.     

A particle swarm optimizer for constrained multi-objective engineering design problems

This article presents a particle swarm optimizer (PSO) capable of handling constrained multi-objective optimization problems. The latter occur frequently in engineering design, especially when cost and performance are simultaneously optimized. The proposed algorithm combines the swarm intelligence fundamentals with elements from bio-inspired algorithms. A distinctive feature of the algorithm is the utilization of an arithmetic recombination operator, which allows interaction between non-dominated particles. Furthermore, there is no utilization of an external archive to store optimal solutions. The PSO algorithm is applied to multi-objective optimization benchmark problems and also to constrained multi-objective engineering design problems. The algorithmic effectiveness is demonstrated through comparisons of the PSO results with those obtained from other evolutionary optimization algorithms. The proposed particle swarm optimizer was able to perform in a very satisfactory manner in problems with multiple constraints and/or high dimensionality. Promising results were also obtained for a multi-objective engineering design problem with mixed variables.     

Performance-based multi-objective optimization of large steel structures

In recent years, the importance of economical considerations in the field of structures has motivated many researchers to propose new methods for minimizing the initial and life cycle cost of the structures subjected to seismic loading. In this paper, a new framework is presented to solve the performance-based multi-objective optimization problem considering the initial and life cycle cost of large structures. In order to solve this problem, a non-dominated sorting genetic algorithm (NSGA-II) using differential evolution operators is employed to solve the optimization problem, while a specific meta-model is utilized for reducing the number of fitness function evaluations. The required computational time for pushover analysis is decreased by a simple numerical method. The constraints of the optimization problem are based on the FEMA codes. The presented results for application of the proposed framework demonstrate its capability in solving the present complex multi-objective optimization problem.     

Multi-objective inventory control using electromagnetism-like meta-heuristic

Most of the works on multi-objective inventory control unify the various objectives into a single objective such that lead to a compromise solution whose non-dominance is not guaranteed. This paper presents an algorithm based on Electromagnetism-like Mechanism (EM) to solve a multi-objective inventory control problem with cost and shortage minimization objectives. EM is a new meta-heuristic originated from the electromagnetism theory in physics; it simulates attraction and repulsion of charged particles in order to move towards the optimum. A framework, so called Multi-Objective EM (MOEM), is proposed to approximate the well-known efficient solutions of order size and safety stock without using any surrogate measure (e.g. service level or shortage cost) and prior preference information from decision-makers. To give a specific compromise solution, any outranking method can be implemented to prioritize the non-dominated solutions for decision-makers. Finally, this could be the first attempt to apply EM to multi-objective inventory control, even the inventory control problems.     

Multi-objective feasibility enhanced particle swarm optimization

This article introduces a new method entitled multi-objective feasibility enhanced partical swarm optimization (MOFEPSO), to handle highly-constrained multi-objective optimization problems. MOFEPSO, which is based on the particle swarm optimization technique, employs repositories of non-dominated and feasible positions (or solutions) to guide feasible particle flight. Unlike its counterparts, MOFEPSO does not require any feasible solutions in the initialized swarm. Additionally, objective functions are not assessed for infeasible particles. Such particles can only fly along sensitive directions, and particles are not allowed to move to a position where any previously satisfied constraints become violated. These unique features help MOFEPSO gradually increase the overall feasibility of the swarm and to finally attain the optimal solution. In this study, multi-objective versions of a classical gear-train optimization problem are also described. For the given problems, the article comparatively evaluates the performance of MOFEPSO against several popular optimization algorithms found in the literature.     

An uncertain multidisciplinary design optimization method using interval convex models

This article proposes an uncertain multi-objective multidisciplinary design optimization methodology, which employs the interval model to represent the uncertainties of uncertain-but-bounded parameters. The interval number programming method is applied to transform each uncertain objective function into two deterministic objective functions, and a satisfaction degree of intervals is used to convert both the uncertain inequality and equality constraints to deterministic inequality constraints. In doing so, an unconstrained deterministic optimization problem will be constructed in association with the penalty function method. The design will be finally formulated as a nested three-loop optimization, a class of highly challenging problems in the area of engineering design optimization. An advanced hierarchical optimization scheme is developed to solve the proposed optimization problem based on the multidisciplinary feasible strategy, which is a well-studied method able to reduce the dimensions of multidisciplinary design optimization problems by using the design variables as independent optimization variables. In the hierarchical optimization system, the non-dominated sorting genetic algorithm II, sequential quadratic programming method and Gauss–Seidel iterative approach are applied to the outer, middle and inner loops of the optimization problem, respectively. Typical numerical examples are used to demonstrate the effectiveness of the proposed methodology.     

A multi-phase covering Pareto-optimal front method to multi-objective parallel machine scheduling

This paper considers the problem of parallel machine scheduling with sequence-dependent setup times to minimise both makespan and total earliness/tardiness in the due window. To tackle the problem considered, a multi-phase algorithm is proposed. The goal of the initial phase is to obtain a good approximation of the Pareto-front. In the second phase, to improve the Pareto-front, non-dominated solutions are unified to constitute a big population. In this phase, based on the local search in the Pareto space concept, three multi-objective hybrid metaheuristics are proposed. Covering the whole set of Pareto-optimal solutions is a desired task of multi-objective optimisation methods. So in the third phase, a new method using an e-constraint hybrid metaheuristic is proposed to cover the gaps between the non-dominated solutions and improve the Pareto-front. Appropriate combinations of multi-objective methods in various phases are considered to improve the total performance. The multi-phase algorithm iterates over a genetic algorithm in the first phase and three hybrid metaheuristics in the second and third phases. Experiments on the test problems with different structures show that the multi-phase method is a better tool to approximate the efficient set than the global archive sub-population genetic algorithm presented previously.     

An uncertain optimization method for overall ballistics based on stochastic programming and a neural network surrogate model

A nonlinear stochastic programming method is proposed in this article to deal with the uncertain optimization problems of overall ballistics. First, a general overall ballistic dynamics model is achieved based on classical interior ballistics, projectile initial disturbance calculation model, exterior ballistics and firing dispersion calculation model. Secondly, the random characteristics of uncertainties are simulated using a hybrid probabilistic and interval model. Then, a nonlinear stochastic programming method is put forward by integrating a back-propagation neural network with the Monte Carlo method. Thus, the uncertain optimization problem is transformed into a deterministic multi-objective optimization problem by employing the mean value, the standard deviation, the probability and the expected loss function, and then the sorting and optimizing of design vectors are realized by the non-dominated sorting genetic algorithm-II. Finally, two numerical examples in practical engineering are presented to demonstrate the effectiveness and robustness of the proposed method.     

Self-adaptive multi-objective harmony search for optimal design of water distribution networks

In multi-objective optimization computing, it is important to assign suitable parameters to each optimization problem to obtain better solutions. In this study, a self-adaptive multi-objective harmony search (SaMOHS) algorithm is developed to apply the parameter-setting-free technique, which is an example of a self-adaptive methodology. The SaMOHS algorithm attempts to remove some of the inconvenience from parameter setting and selects the most adaptive parameters during the iterative solution search process. To verify the proposed algorithm, an optimal least cost water distribution network design problem is applied to three different target networks. The results are compared with other well-known algorithms such as multi-objective harmony search and the non-dominated sorting genetic algorithm-II. The efficiency of the proposed algorithm is quantified by suitable performance indices. The results indicate that SaMOHS can be efficiently applied to the search for Pareto-optimal solutions in a multi-objective solution space.