A new optimization algorithm for solving complex constrained design optimization problems

This article presents the performance of a very recently proposed Jaya algorithm on a class of constrained design optimization problems. The distinct feature of this algorithm is that it does not have any algorithm-specific control parameters and hence the burden of tuning the control parameters is minimized. The performance of the proposed Jaya algorithm is tested on 21 benchmark problems related to constrained design optimization. In addition to the 21 benchmark problems, the performance of the algorithm is investigated on four constrained mechanical design problems, i.e. robot gripper, multiple disc clutch brake, hydrostatic thrust bearing and rolling element bearing. The computational results reveal that the Jaya algorithm is superior to or competitive with other optimization algorithms for the problems considered.     

Constrained multi-objective optimization using constrained non-dominated sorting combined with an improved hybrid multi-objective evolutionary algorithm

Constrained multi-objective optimization problems (cMOPs) are complex because the optimizer should balance not only between exploration and exploitation, but also between feasibility and optimality. This article suggests a parameter-free constraint handling approach called constrained non-dominated sorting (CNS). In CNS, each solution in a population is assigned a constrained non-dominated rank based on its constraint violation degree and Pareto rank. An improved hybrid multi-objective optimization algorithm called cMOEA/H for solving cMOPs is proposed. Additionally, a dynamic resource allocation mechanism is adopted by cMOEA/H to spare more computational efforts for those relatively hard sub-problems. cMOEA/H is first compared with the baseline algorithm using an existing constraint handling mechanism, verifying the advantages of the proposed constraint handling mechanism. Then cMOEA/H is compared with some classic constrained multi-objective optimizers, experimental results indicating that cMOEA/H could be a competitive alternative for solving cMOPs. Finally, the characteristics of cMOEA/H are studied.     

An effective hybrid cuckoo search and genetic algorithm for constrained engineering design optimization

This article presents an effective hybrid cuckoo search and genetic algorithm (HCSGA) for solving engineering design optimization problems involving problem-specific constraints and mixed variables such as integer, discrete and continuous variables. The proposed algorithm, HCSGA, is first applied to 13 standard benchmark constrained optimization functions and subsequently used to solve three well-known design problems reported in the literature. The numerical results obtained by HCSGA show competitive performance with respect to recent algorithms for constrained design optimization problems.     

An evolutionary algorithm for global optimization based on self-organizing maps

In this article, a new population-based algorithm for real-parameter global optimization is presented, which is denoted as self-organizing centroids optimization (SOC-opt). The proposed method uses a stochastic approach which is based on the sequential learning paradigm for self-organizing maps (SOMs). A modified version of the SOM is proposed where each cell contains an individual, which performs a search for a locally optimal solution and it is affected by the search for a global optimum. The movement of the individuals in the search space is based on a discrete-time dynamic filter, and various choices of this filter are possible to obtain different dynamics of the centroids. In this way, a general framework is defined where well-known algorithms represent a particular case. The proposed algorithm is validated through a set of problems, which include non-separable problems, and compared with state-of-the-art algorithms for global optimization.     

Optimization of constrained multiple-objective reliability problems using evolutionary algorithms

This paper illustrates the use of multi-objective optimization to solve three types of reliability optimization problems: to find the optimal number of redundant components, find the reliability of components, and determine both their redundancy and reliability. In general, these problems have been formulated as single objective mixed-integer non-linear programming problems with one or several constraints and solved by using mathematical programming techniques or special heuristics. In this work, these problems are reformulated as multiple-objective problems (MOP) and then solved by using a second-generation Multiple-Objective Evolutionary Algorithm (MOEA) that allows handling constraints. The MOEA used in this paper (NSGA-II) demonstrates the ability to identify a set of optimal solutions (Pareto front), which provides the Decision Maker with a complete picture of the optimal solution space. Finally, the advantages of both MOP and MOEA approaches are illustrated by solving four redundancy problems taken from the literature.     

An optimization design of vehicle axle system based on multiobjective cooperative optimization algorithm

ABSTRACT

To address multiobjective, multi constraint and time-consuming structural optimization problems in a vehicle axle system, a multiobjective cooperative optimization model of a vehicle axle structure is established. In light of the difficulty in the nondominated sorting of the NSGA-II algorithm caused by inconsistent effects of the uniformity objective function and physical objective function, this paper combines a multiobjective genetic algorithm with cooperative optimization and presents a strategy for handling the optimization of a vehicle axle structure. The uniformity objective function of the sub discipline is transformed to its self-constraint. Taking the multiobjective optimization of a vehicle axle system as an example, a multiobjective cooperative optimization design for the system is carried out in ISIGHT. The results show that the multiobjective cooperative optimization strategy can simplify the complexity of optimization problems and that the multiobjective cooperative optimization method based on an approximate model is favorable for accuracy and efficiency, thereby providing a theoretical basis for the optimization of similar complex structures in practical engineering.     

RDS-NSGA-II: a memetic algorithm for reference point based multi-objective optimization

Reference point based optimization offers tools for the effective treatment of preference based multi-objective optimization problems, e.g. when the decision-maker has a rough idea about the target objective values. For the numerical solution of such problems, specialized evolutionary strategies have become popular, despite their possible slow convergence rates. Hybridizing such evolutionary algorithms with local search techniques have been shown to produce faster and more reliable algorithms. In this article, the directed search (DS) method is adapted to the context of reference point optimization problems, making this variant, called RDS, a well-suited option for integration into evolutionary algorithms. Numerical results on academic test problems with up to five objectives demonstrate the benefit of the novel hybrid (i.e. the same approximation quality can be obtained more efficiently by the new algorithm), using the state-of-the-art algorithm R-NSGA-II for this coupling. This represents an advantage when treating costly-to-evaluate real-world engineering design problems.     

A constrained optimization algorithm based on the simplex search method

In this article, a robust method is presented for handling constraints with the Nelder and Mead simplex search method, which is a direct search algorithm for multidimensional unconstrained optimization. The proposed method is free from the limitations of previous attempts that demand the initial simplex to be feasible or a projection of infeasible points to the nonlinear constraint boundaries. The method is tested on several benchmark problems and the results are compared with various evolutionary algorithms available in the literature. The proposed method is found to be competitive with respect to the existing algorithms in terms of effectiveness and efficiency.     

压电智能连续体结构/控制一体化广义拓扑优化

对于以往较少涉及到的同时考虑结构拓扑、作动器位置与数目和控制器参数等多种优化设计变量参与的压电智能板结构的一体化优化设计问题,研究了结构/控制一体化广义拓扑优化设计的方法。提出采用基于耦合模态空间的二次型最优控制系统设计与基于遗传算法和数学形态学处理的策略进行一体化拓扑优化设计实现。数值算例的结果表明,所提方法合理、有效,能够得到清晰的结构拓扑和良好的可控性。     

基于进化算法的产品造型创新设计方法研究

为了满足用户多样化的产品造型需求,模拟设计师的设计思维特性,提出了应用元胞遗传算法和标准遗传算法的产品造型创新设计新方法.首先收集产品样本,经聚类分析、设计师聚焦等确定代表性产品样本,再利用形态分析法得到产品造型元素并定量描述设计参数;其次,以代表性产品样本为初始种群,应用元胞遗传算法建立产品造型初始设计系统,实现了以少量原型生成大量创新性方案的智能设计进程;最后,应用标准遗传算法建立产品造型细化设计系统,进一步优化初始设计方案,快速实现方案的细化智能设计进程.卡通表情造型设计实例表明,该方法可为创新设计提供有效的辅助与支持.     

A surrogate-model based multi-modal optimization algorithm

In this article a new algorithm for optimization of multi-modal, nonlinear, black-box objective functions is introduced. It extends the recently-introduced adaptive multi-modal optimization by incorporating surrogate modelling features similar to response surface methods. The resulting algorithm has reduced computational intensity and is well-suited for optimization of expensive objective functions. It relies on an adaptive, multi-resolution mesh to obtain an initial estimation of the objective function surface. Local surrogate models are then constructed and used to generate additional trial points around the local minima discovered. The steps of mesh refinement and surrogate modelling continue until convergence is achieved. The algorithm produces progressively accurate surrogate models, which can be used for post-optimization studies such as sensitivity and tolerance analyses with minimal computational effort. This article demonstrates the effectiveness of the algorithm using comparative optimization of several multi-modal objective functions, and shows an engineering application of the design of a power electronic converter.     

Multi-objective robust design optimization of fatigue life for a welded box girder

To reduce the scatter of fatigue life for welded structures, a robust optimization method is presented in this study based on a dual surrogate modelling and multi-objective particle swam optimization algorithm. Considering the perturbations of material parameters and environment variables, the mean and standard deviation of fatigue life are fitted using dual surrogate modelling and selected as the objective function to be minimized. As an example, a welded box girder is presented to reduce the standard deviation of fatigue life. A set of non-dominated solutions is produced through a multi-objective particle swam optimization algorithm. A cognitive approach is used to select the optimum solution from the Pareto sets. As a comparative study, traditional single objective optimizations are also presented in this study. The results reduced the standard deviation of the fatigue life by about 16.5%, which indicated that the procedure improved the robustness of the fatigue life.     

Solving constrained optimization problems with a hybrid particle swarm optimization algorithm

This article presents a particle swarm optimization algorithm for solving general constrained optimization problems. The proposed approach introduces different methods to update the particle's information, as well as the use of a double population and a special shake mechanism designed to avoid premature convergence. It also incorporates a simple constraint-handling technique. Twenty-four constrained optimization problems commonly adopted in the evolutionary optimization literature, as well as some structural optimization problems are adopted to validate the proposed approach. The results obtained by the proposed approach are compared with respect to those generated by algorithms representative of the state of the art in the area.     

二维正交柱透镜列阵光学系统及优化设计

提出二维正交凸柱透镜列阵光学系统,可实现靶面光强二维均匀辐照,应用矩阵光学和衍射积分理论,详细分析了工作原理、焦斑强度分布特性,并从衍射、干涉等角度分析了系统参数与强度分布的关系,给出了详细的系统优化设计参数和数值计算结果。     

Systematic design optimization of grabs considering bulk cargo variability

Ship unloader grabs are usually designed using the manufacturer’s in-house knowledge based on a traditional physical prototyping approach. The grab performance depends greatly on the properties of the bulk material being handled. By considering the bulk cargo variability in the design process, the grab performance can be improved significantly. A multi-objective simulation-based optimization framework is therefore established to include bulk cargo variability in the design process of grabs. The primary objective is to reach a maximized and consistent performance in handling a variety of iron ore cargoes. First, a range of bulk materials is created by varying levels of cohesive forces and plasticity in the elasto-plastic adhesive DEM contact model. The sensitivity analysis of the grabbing process to the bulk variability allowed three classes of iron ore materials to be selected that have significant influence on the product performance. Second, 25 different grab designs are generated using a random sampling method, Latin Hypercube Design, to be assessed as to their handling of the three classes of iron ore materials. Of this range of grab designs, optimal solutions are found using surrogate modelling-based optimization and the NSGA-II genetic algorithm. The optimization outcome is verified by comparing predictions of the optimization algorithm and results of DEM-MBD co-simulation. The established optimization framework offers a straightforward and reliable tool for designing grabs and other similar equipment.     

Particle swarm optimization approach for multi-objective composite box-beam design

This paper presents a multi-agent search technique to design an optimal composite box-beam helicopter rotor blade. The search technique is called particle swarm optimization (‘inspired by the choreography of a bird flock’). The continuous geometry parameters (cross-sectional dimensions) and discrete ply angles of the box-beams are considered as design variables. The objective of the design problem is to achieve (a) specified stiffness value and (b) maximum elastic coupling. The presence of maximum elastic coupling in the composite box-beam increases the aero-elastic stability of the helicopter rotor blade. The multi-objective design problem is formulated as a combinatorial optimization problem and solved collectively using particle swarm optimization technique. The optimal geometry and ply angles are obtained for a composite box-beam design with ply angle discretizations of 10°, 15° and 45°. The performance and computational efficiency of the proposed particle swarm optimization approach is compared with various genetic algorithm based design approaches. The simulation results clearly show that the particle swarm optimization algorithm provides better solutions in terms of performance and computational time than the genetic algorithm based approaches.     

Improved genetic algorithm for mixed-discrete-continuous design optimization problems

An improved genetic algorithm (IGA) is presented to solve the mixed-discrete-continuous design optimization problems. The IGA approach combines the traditional genetic algorithm with the experimental design method. The experimental design method is incorporated in the crossover operations to systematically select better genes to tailor the crossover operations in order to find the representative chromosomes to be the new potential offspring, so that the IGA approach possesses the merit of global exploration and obtains better solutions. The presented IGA approach is effectively applied to solve one structural and five mechanical engineering problems. The computational results show that the presented IGA approach can obtain better solutions than both the GA-based and the particle-swarm-optimizer-based methods reported recently.     

混沌优化法在机械设计中的应用

针对一般的二次载波的混沌优化方法收敛慢的弱点,提出了一些改进的方法.主要是利用当前解的信息,自动改变最优点的搜索路径,能明显提高首次载波寻找最佳点大概位置的速度和效能;同时能更快更精确实现二次载波的精细搜索.将该算法用于一机械设计问题———箱形盖板优化设计计算之中,取得了优于常规方法———Powell法的结果,说明该方法在机械优化设计中具有较好的应用价值.     

Practical solutions for multi-objective optimization: An application to system reliability design problems

For multiple-objective optimization problems, a common solution methodology is to determine a Pareto optimal set. Unfortunately, these sets are often large and can become difficult to comprehend and consider. Two methods are presented as practical approaches to reduce the size of the Pareto optimal set for multiple-objective system reliability design problems. The first method is a pseudo-ranking scheme that helps the decision maker select solutions that reflect his/her objective function priorities. In the second approach, we used data mining clustering techniques to group the data by using the k-means algorithm to find clusters of similar solutions. This provides the decision maker with just k general solutions to choose from. With this second method, from the clustered Pareto optimal set, we attempted to find solutions which are likely to be more relevant to the decision maker. These are solutions where a small improvement in one objective would lead to a large deterioration in at least one other objective. To demonstrate how these methods work, the well-known redundancy allocation problem was solved as a multiple objective problem by using the NSGA genetic algorithm to initially find the Pareto optimal solutions, and then, the two proposed methods are applied to prune the Pareto set.