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.     

MULTIOBJECTIVE DESIGN OPTIMIZATION BY AN EVOLUTIONARY ALGORITHM

This paper presents an evolutionary algorithm for generic multiobjective design optimization problems. The algorithm is based on nondominance of solutions in the objective and constraint space and uses effective mating strategies to improve solutions that are weak in either. Since the methodology is based on nondominance, scaling and aggregation affecting conventional penalty function methods for constraint handling does not arise. The algorithm incorporates intelligent partner selection for cooperative mating. The diversification strategy is based on niching which results in a wide spread of solutions in the parametric space. Results of the algorithm for the design examples clearly illustrate the efficiency of the algorithm in solving multidisciplinary design optimization problems.     

Ant algorithm for single and multiobjective reliability optimization problems

The paper illustrates the application of the ant colony optimization algorithm to solve both continuous function and combinatorial optimization problems in reliability engineering. The ant algorithm is combined with the strength Pareto fitness assignment procedure to handle multiobjective problems. Further, a clustering procedure has been applied to prune the Pareto set and to maintain diversity. Benchmark case examples show the superiority of the ant algorithm to such problems. Copyright © 2002 John Wiley & Sons, Ltd.     

Cost effective simulation-based multiobjective optimization in the performance of an internal combustion engine

Solving real-life engineering problems can be difficult because they often have multiple conflicting objectives, the objective functions involved are highly nonlinear and they contain multiple local minima. Furthermore, function values are often produced via a time-consuming simulation process. These facts suggest the need for an automated optimization tool that is efficient (in terms of number of objective function evaluations) and capable of solving global and multiobjective optimization problems. In this article, the requirements on a general simulation-based optimization system are discussed and such a system is applied to optimize the performance of a two-stroke combustion engine. In the example of a simulation-based optimization problem, the dimensions and shape of the exhaust pipe of a two-stroke engine are altered, and values of three conflicting objective functions are optimized. These values are derived from power output characteristics of the engine. The optimization approach involves interactive multiobjective optimization and provides a convenient tool to balance between conflicting objectives and to find good solutions.     

Non-convex multiobjective optimization under uncertainty: a descent algorithm. Application to sandwich plate design and reliability

In this paper a novel algorithm for solving multiobjective design optimization problems with non-smooth objective functions and uncertain parameters is presented. The algorithm is based on the existence of a common descent vector for each sample of the random objective functions and on an extension of the stochastic gradient algorithm. The proposed algorithm is applied to the optimal design of sandwich material. Comparisons with the genetic algorithm NSGA-II and the DMS solver are given and show that it is numerically more efficient due to the fact that it does not necessitate the objective function expectation evaluation. It can moreover be entirely parallelizable. Another simple illustration highlights its potential for solving general reliability problems, replacing each probability constraint by a new objective written in terms of an expectation. Moreover, for this last application, the proposed algorithm does not necessitate the computation of the (small) probability of failure.     

MULTIOBJECTIVE DESIGN OF A MARINE VEHICLE WITH AID OF DESIGN KNOWLEDGE

To generate the Pareto optimal set efficiently in multiobjective optimization, a hybrid optimizer is developed by coupling the genetic algorithm and the direct search method. This method determines a candidate region around the global optimum point by using the genetic algorithm, then searches the global optimum point by the direct search method concentrating in this region, thus reducing calculation time and increasing search efficiency. Although the hybrid optimizer provides cost-effectiveness, the design optimization process involves a number of tasks which require human expertise and experience. Therefore, methods of optimization and associated programs have been used mostly by experts in the real design world. Hence, this hybrid optimizer incorporates a knowledge-based system with heuristic and analytic knowledge, thereby narrowing the feasible space of the objective function. Some domain knowledge is retrieved from database and design experts. The obtained knowledge is stored in the knowledge base. The results of this paper, through application to marine vehicle design with multiobjective optimization, show that the hybrid optimizer with aid of design knowledge can be a useful tool for multiobjective optimum design. © 1997 John Wiley & Sons, Ltd.     

结构减振设计的协同优化分析

建立一种适用于工程结构减振设计的协同优化模型。在学科级优化子模型中,分别使用了不同的目标函数;在系统级优化子模型中,以如何获得尽可能接近于子学科独立优化的最优解为目标函数。系统级目标函数消除了量纲和数量级的影响。该模型采用分布协同的双层结构,允许在每一级优化中使用不同的优化策略。以减速器和板梁柱混合结构为例,对其进行了单学科和多学科优化分析。实例结果表明,在结构减振设计时,采用协同优化模型进行优化设计,不仅可以有效的降低结构动力特性参数,而且优化后结构的综合性能更佳,说明该模型能应用于实际工程结构的减振设计。     

Enhanced multiobjective particle swarm optimization in combination with adaptive weighted gradient-based searching

This article proposes a new multiobjective optimization method for structural problems based on multiobjective particle swarm optimization (MOPSO). A gradient-based optimization method is combined with MOPSO to alleviate constraint-handling difficulties. In this method, a group of particles is divided into two groups—a dominated solution group and a non-dominated solution group. The gradient-based method, utilizing a weighting coefficient method, is applied to the latter to conduct local searching that yields superior non-dominated solutions. In order to enhance the efficiency of exploration in a multiple objective function space, the weighting coefficients are adaptively assigned considering the distribution of non-dominated solutions. A linear optimization problem is solved to determine the optimal weighting coefficients for each non-dominated solution at each iteration. Finally, numerical and structural optimization problems are solved by the proposed method to verify the optimization efficiency.     

Reliability optimization using multiobjective ant colony system approaches

The multiobjective ant colony system (ACS) meta-heuristic has been developed to provide solutions for the reliability optimization problem of series-parallel systems. This type of problems involves selection of components with multiple choices and redundancy levels that produce maximum benefits, and is subject to the cost and weight constraints at the system level. These are very common and realistic problems encountered in conceptual design of many engineering systems. It is becoming increasingly important to develop efficient solutions to these problems because many mechanical and electrical systems are becoming more complex, even as development schedules get shorter and reliability requirements become very stringent. The multiobjective ACS algorithm offers distinct advantages to these problems compared with alternative optimization methods, and can be applied to a more diverse problem domain with respect to the type or size of the problems. Through the combination of probabilistic search, multiobjective formulation of local moves and the dynamic penalty method, the multiobjective ACSRAP, allows us to obtain an optimal design solution very frequently and more quickly than with some other heuristic approaches. The proposed algorithm was successfully applied to an engineering design problem of gearbox with multiple stages.     

A method for simulation based optimization using radial basis functions

We propose an algorithm for the global optimization of expensive and noisy black box functions using a surrogate model based on radial basis functions (RBFs). A method for RBF-based approximation is introduced in order to handle noise. New points are selected to minimize the total model uncertainty weighted against the surrogate function value. The algorithm is extended to multiple objective functions by instead weighting against the distance to the surrogate Pareto front; it therefore constitutes the first algorithm for expensive, noisy and multiobjective problems in the literature. Numerical results on analytical test functions show promise in comparison to other (commercial) algorithms, as well as results from a simulation based optimization problem.     

Intelligent interactive multiobjective optimization method and its application to reliability optimization

In most practical situations involving reliability optimization, there are several mutually conflicting goals such as maximizing the system reliability and minimizing the cost, weight and volume. This paper develops an effective multiobjective optimization method, the Intelligent Interactive Multiobjective Optimization Method (IIMOM). In IIMOM, the general concept of the model parameter vector is proposed. From a practical point of view, a designer's preference structure model is built using Artificial Neural Networks (ANNs) with the model parameter vector as the input and the preference information articulated by the designer over representative samples from the Pareto frontier as the desired output. Then with the ANN model of the designer's preference structure as the objective, an optimization problem is solved to search for improved solutions and guide the interactive optimization process intelligently. IIMOM is applied to the reliability optimization problem of a multi-stage mixed system with five different value functions simulating the designer in the solution evaluation process. The results illustrate that IIMOM is effective in capturing different kinds of preference structures of the designer, and it provides a complete and effective solution for medium- and small-scale multiobjective optimization problems.     

Reliability and cost optimization of electronic devices considering the component failure rate uncertainty

The objective of this paper is to present an efficient computational methodology to obtain the optimal system structure of electronic devices by using either a single or a multiobjective optimization approach, while considering the constraints on reliability and cost. The component failure rate uncertainty is taken under consideration and it is modeled with two alternative probability distribution functions. The Latin hypercube sampling method is used to simulate the probability distributions. An optimization approach was developed using the simulated annealing algorithm because of its flexibility to be applied in various system types with several constraints and its efficiency in computational time. This optimization approach can handle efficiently either the single or the multiobjective optimization modeling of the system design. The developed methodology was applied to a power electronic device and the results were compared with the results of the complete enumeration of the solution space. The stochastic nature of the best solutions for the single objective optimization modeling of the system design was sampled extensively and the robustness of the developed optimization approach was demonstrated.     

A splitting algorithm for simulation-based optimization problems with categorical variables

In the design of complex products, some product components can only be chosen from a finite set of options. Each option then corresponds to a multidimensional point representing the specifications of the chosen components. A splitting algorithm that explores the resulting discrete search space and is suitable for optimization problems with simulation-based objective functions is presented. The splitting rule is based on the representation of a convex relaxation of the search space in terms of a minimum spanning tree and adopts ideas from multilevel coordinate search. The objective function is underestimated on its domain by a convex quadratic function. The main motivation is the aim to find—for a vehicle and environment specification—a configuration of the tyres such that the energy losses caused by them are minimized. Numerical tests on a set of optimization problems are presented to compare the performance of the algorithm developed with that of other existing algorithms.     

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.     

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.     

Flower pollination algorithm: A novel approach for multiobjective optimization

Multiobjective design optimization problems require multiobjective optimization techniques to solve, and it is often very challenging to obtain high-quality Pareto fronts accurately. In this article, the recently developed flower pollination algorithm (FPA) is extended to solve multiobjective optimization problems. The proposed method is used to solve a set of multiobjective test functions and two bi-objective design benchmarks, and a comparison of the proposed algorithm with other algorithms has been made, which shows that the FPA is efficient with a good convergence rate. Finally, the importance for further parametric studies and theoretical analysis is highlighted and discussed.     

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.     

Topology optimization of fluid problems using genetic algorithm assisted by the Kriging model

A non‐gradient‐based approach for topology optimization using a genetic algorithm is proposed in this paper. The genetic algorithm used in this paper is assisted by the Kriging surrogate model to reduce computational cost required for function evaluation. To validate the non‐gradient‐based topology optimization method in flow problems, this research focuses on two single‐objective optimization problems, where the objective functions are to minimize pressure loss and to maximize heat transfer of flow channels, and one multi‐objective optimization problem, which combines earlier two single‐objective optimization problems. The shape of flow channels is represented by the level set function. The pressure loss and the heat transfer performance of the channels are evaluated by the Building‐Cube Method code, which is a Cartesian‐mesh CFD solver. The proposed method resulted in an agreement with previous study in the single‐objective problems in its topology and achieved global exploration of non‐dominated solutions in the multi‐objective problems. © 2016 The Authors International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd     

A multiobjective mesh optimization framework for mesh quality improvement and mesh untangling

We propose a multiobjective mesh optimization framework for mesh quality improvement and mesh untangling. Our framework combines two or more competing objective functions into a single objective function to be solved using one of various multiobjective optimization methods. Methods within our framework are able to optimize various aspects of the mesh such as the element shape, element size, associated PDE interpolation error, and number of inverted elements, but the improvement is not limited to these categories. The strength of our multiobjective mesh optimization framework lies in its ability to be extended to simultaneously optimize any aspects of the mesh and to optimize meshes with different element types. We propose the exponential sum, objective product, and equal sum multiobjective mesh optimization methods within our framework; these methods do not require articulation of preferences. However, the solutions obtained satisfy a sufficient condition of weak Pareto optimality. Experimental results show that our multiobjective mesh optimization methods are able to simultaneously optimize two or more aspects of the mesh and also are able to improve mesh qualities while eliminating inverted elements. We successfully apply our methods to real‐world applications such as hydrocephalus treatment and shape optimization. Copyright © 2013 John Wiley & Sons, Ltd.     

MISO: mixed-integer surrogate optimization framework

We introduce MISO, the mixed-integer surrogate optimization framework. MISO aims at solving computationally expensive black-box optimization problems with mixed-integer variables. This type of optimization problem is encountered in many applications for which time consuming simulation codes must be run in order to obtain an objective function value. Examples include optimal reliability design and structural optimization. A single objective function evaluation may take from several minutes to hours or even days. Thus, only very few objective function evaluations are allowable during the optimization. The development of algorithms for this type of optimization problems has, however, rarely been addressed in the literature. Because the objective function is black-box, derivatives are not available and numerically approximating the derivatives requires a prohibitively large number of function evaluations. Therefore, we use computationally cheap surrogate models to approximate the expensive objective function and to decide at which points in the variable domain the expensive objective function should be evaluated. We develop a general surrogate model framework and show how sampling strategies of well-known surrogate model algorithms for continuous optimization can be modified for mixed-integer variables. We introduce two new algorithms that combine different sampling strategies and local search to obtain high-accuracy solutions. We compare MISO in numerical experiments to a genetic algorithm, NOMAD version 3.6.2, and SO-MI. The results show that MISO is in general more efficient than NOMAD and the genetic algorithm with respect to finding improved solutions within a limited budget of allowable evaluations. The performance of MISO depends on the chosen sampling strategy. The MISO algorithm that combines a coordinate perturbation search with a target value strategy and a local search performs best among all algorithms.