Developments in the use of the genetic algorithm in engineering design

The adaptive search technique known as the genetic algorithm is described and research into its application within the fields of civil, structural and mechanical engineering discussed. Attention is drawn to the potential of the structured genetic algorithm both as a high-level decision support technique during the preliminary stages of the design process and as a powerful tool for the detailed design of complex components. Problems associated with the search for global optimum solutions and design sensitivity are outlined. Increasingly efficient and cost effective hybrid approaches are envisaged which incorporate a range of adaptive search and knowledge-based techniques.     

Dynamic selective pressure using hybrid evolutionary and ant system strategies for structural optimization

Genetic algorithms have already been applied to various fields of engineering problems as a general optimization tool in charge of expensive sampling of the coded design space. In order to reduce such a computational cost in practice, application of evolutionary strategies is growing rapidly in the adaptive use of problem‐specific information. This paper proposes a hybrid strategy to utilize a cooperative dynamic memory of more competitive solutions combining indirect information share in ant systems with direct constructive genetic search. Some proper coding techniques are employed to enable testing the method with various sets of control parameters. As a challenging field of interest, its application to structural layout optimization is considered while an example of a traveling salesman problem is also treated as a combinatorial benchmark. Copyright © 2007 John Wiley & Sons, Ltd.     

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 hybrid genetic based optimization procedure for aircraft conceptual analysis

The problem to define a methodology for the analysis of aircraft performances, in the phase of conceptual design, is addressed. The proposed approach is based on a numerical optimization procedure where a scalar objective function, the take-off weight, is minimized. Deterministic and stochastic approaches as well as hybridizations between these two search techniques are considered. More precisely, we consider two-stage strategies where the optimum localization is performed by a genetic algorithm, while a gradient-based method is used to terminate the optimization process. Also, another type of hybridization strategy is investigated where a partially converged gradient-based method is incorporated in the genetic algorithm as a new operator. A detailed discussion is made and various different solutions are critically compared. The proposed methodology is consistent and capable of giving fundamental information to the designer for further investigating towards the directions identified by the procedure. A basic example is described, and the use of the methodology to establish the effects of different geometrical and technological parameters is discussed.     

Handling constraints using multiobjective optimization concepts

In this paper, we propose a new constraint‐handling technique for evolutionary algorithms which we call inverted‐shrinkable PAES (IS‐PAES). This approach combines the use of multiobjective optimization concepts with a mechanism that focuses the search effort onto specific areas of the feasible region by shrinking the constrained search space. IS‐PAES also uses an adaptive grid to store the solutions found, but has a more efficient memory‐management scheme than its ancestor (the Pareto archived evolution strategy for multiobjective optimization). The proposed approach is validated using several examples taken from the standard evolutionary and engineering optimization literature. Comparisons are provided with respect to the stochastic ranking method (one of the most competitive constraint‐handling approaches used with evolutionary algorithms currently available) and with respect to other four multiobjective‐based constraint‐handling techniques. Copyright© 2004 John Wiley & Sons, Ltd.     

A transformation system for interactive reformulation of design optimization strategies

Automatic design optimization is highly sensitive to problem formulation. The choice of objective function, constraints and design parameters can dramatically impact on the computational cost of optimization and the quality of the resulting design. The best formulation varies from one application to another. A design engineer will usually not know the best formulation in advance. To address this problem, we have developed a system that supports interactive formulation, testing and reformulation of design optimization strategies. Our system includes an executable, data-flow language for representing optimization strategies. The language allows an engineer to define multiple stages of optimization, each using different approximations of the objective and constraints or different abstractions of the design space. We have also developed a set of transformations that reformulate strategies represented in our language. The transformations can approximate objective and constraint functions, abstract or reparameterize search spaces, or divide an optimization process into multiple stages. The system is applicable in principle to any design problem that can be expressed in terms of constrained optimization; however, we expect the system to be most useful when the design artifact is governed by algebraic and ordinary differential equations. We have tested the system on problems of racing yacht design and jet engine nozzle design. We report experimental results demonstrating that our reformulation techniques can significantly improve the performance of automatic design optimization. Our research demonstrates the viability of a reformulation methodology that combines symbolic program transformation with numerical experimentation. It is an important first step in a research program aimed at automating the entire strategy formulation process.     

Customized evolutionary optimization procedure for generating minimum weight compliant mechanisms

In this article, a customized evolutionary optimization procedure is developed for generating minimum weight compliant mechanisms. A previously-suggested concept of multi-objectivization in which a helper objective is introduced in addition to the primary objective of the original single-objective optimization problem (SOOP) is used here. The helper objective is chosen in a way such that it is in conflict with the primary objective, thereby causing an evolutionary multi-objective optimization algorithm to maintain diversity in its population from one generation to another. The elitist non-dominated sorting genetic algorithm (NSGA-II) is customized with a domain-specific initialization strategy, a domain-specific crossover operator, and a domain-specific solution repairing strategy. To make the search process computationally tractable, the proposed methodology is made suitable for parallel computing. A local search methodology is applied on the evolved non-dominated solutions found by the above-mentioned modified NSGA-II to refine the solutions further. Two case studies for tracing curvilinear and straight-line paths are performed. Results demonstrate that solutions having smaller weight than the reference design solution obtained by SOOP are found by the proposed procedure. Interesting facts and observations brought out by the study are also narrated and conclusions of the study are made.     

On the need for the use of error‐controlled finite element analyses in structural shape optimization processes

This work analyzes the influence of the discretization error associated with the finite element (FE) analyses of each design configuration proposed by the structural shape optimization algorithms over the behavior of the algorithm. The paper clearly shows that if FE analyses are not accurate enough, the final solution provided by the optimization algorithm will neither be optimal nor satisfy the constraints. The need for the use of adaptive FE analysis techniques in shape optimum design will be shown. The paper proposes the combination of two strategies to reduce the computational cost related to the use of mesh adaptivity in evolutionary optimization algorithms: (a) the use of an algorithm for the mesh generation by projection of the discretization error, which reduces the computational cost associated with the adaptive FE analysis of each geometrical configuration and (b) the successive increase of the required accuracy of the FE analyses in order to obtain a considerable reduction of the computational cost in the early stages of the optimization process. Copyright © 2011 John Wiley & Sons, Ltd.     

DISCRETE MANUFACTURING PROCESS DESIGN OPTIMIZATION USING COMPUTER SIMULATION AND GENERALIZED HILL CLIMBING ALGORITHMS

Discrete manufacturing process designs can be modelled using computer simulation. Determining optimal designs using such models is very difficult, due to the large number of manufacturing process sequences and associated parameter settings that exist. This has forced researchers to develop heuristic strategies to address such design problems. This paper introduces a new general heuristic strategy for discrete manufacturing process design optimization, called generalised hill climbing (GHC) algorithms. GHC algorithms provide a unifying approach for addressing such problems in particular, and intractable discrete optimization problems in general. Heuristic strategies such as simulated annealing, threshold accepting, Monte Carlo search, local search, and tabu search (among others) can all he formulated as GHC algorithms. Computational results are reported with various GHC algorithms applied to computer simulation models of discrete manufacturing process designs under study at the Materials Process Design Branch of Wright Laboratory, Wright Patterson Air Force Base (Dayton, Ohio, USA).     

Synthesis of near-optimal topologically constrained property-based water network using swarm intelligence

The sustainability of water resources is one of the major concerns of the world. Industries are finding ways to minimize water costs and to reduce water pollution through efficient use of supplies. One of effective solutions is the use of water pinch technology or process integration techniques. Property integration emerged as the third trend of process integration technique (aside from energy and mass integration) to solve the problem of water network synthesis by considering physical stream properties such as pH or resistivity. Various techniques have been done to solve this property-based problem. In this paper, mixed integer non-linear programming (MINLP) problems with topological constraints is studied. Nowadays, various evolutionary algorithms are also used to solve such MINLP problems. In this study, particle swarm optimization is used to solve the property integration problem. A comparison is made between this algorithm and commercial genetic algorithm (GA) applications. Particle swarm optimization is observed to perform favorably compared to GA.     

A cross-disciplinary technology transfer for search-based evolutionary computing: from engineering design to software engineering design

Although object-oriented conceptual software design is difficult to learn and perform, computational tool support for the conceptual software designer is limited. In conceptual engineering design, however, computational tools exploiting interactive evolutionary computation (EC) have shown significant utility. This article investigates the cross-disciplinary technology transfer of search-based EC from engineering design to software engineering design in an attempt to provide support for the conceptual software designer. Firstly, genetic operators inspired by genetic algorithms (GAs) and evolutionary programming are evaluated for their effectiveness against a conceptual software design representation using structural cohesion as an objective fitness function. Building on this evaluation, a multi-objective GA inspired by a non-dominated Pareto sorting approach is investigated for an industrial-scale conceptual design problem. Results obtained reveal a mass of interesting and useful conceptual software design solution variants of equivalent optimality—a typical characteristic of successful multi-objective evolutionary search techniques employed in conceptual engineering design. The mass of software design solution variants produced suggests that transferring search-based technology across disciplines has significant potential to provide computationally intelligent tool support for the conceptual software designer.     

Multiobjective design of actively controlled structures using a hybrid optimization method

A multiobjective approach to the combined structure and control optimization problem for flexible space structures is presented. The proposed formulation addresses robustness considerations for controller design, as well as a simultaneous determination of optimum actuator locations. The structural weight, controlled system energy, stability robustness index and damping augmentation provided by the active controller are considered as objective functions of the multiobjective problem which is solved using a cooperative game-theoretic approach. The actuator locations and the cross-sectional areas of structural members are treated as design variables. Since the actuator locations are spatially discrete, whereas the cross-sectional areas are continuous, the optimization problem has mixed discrete-continuous design variables. A solution approach to this problem based on a hybrid optimization scheme is presented. The hybrid optimizer is a synergetic blend of artificial genetic search and gradient-based search techniques. The computational procedure is demonstrated through the design of an ACOSS-FOUR space structure. The optimum solutions obtained using the hybrid optimizer are shown to outperform the optimum results obtained using gradient-based search techniques.     

Influence of the number and location of design parameters in the aerodynamic shape optimization of a transonic aerofoil and a wing through evolutionary algorithms and support vector machines

Surrogate-based optimization (SBO) has recently found widespread use in aerodynamic shape design owing to its promising potential to speed up the whole process by the use of a low-cost objective function evaluation, to reduce the required number of expensive computational fluid dynamics simulations. However, the application of these SBO methods for industrial configurations still faces several challenges. The most crucial challenge nowadays is the ‘curse of dimensionality’, the ability of surrogates to handle a high number of design parameters. This article presents an application study on how the number and location of design variables may affect the surrogate-based design process and aims to draw conclusions on their ability to provide optimal shapes in an efficient manner. To do so, an optimization framework based on the combined use of a surrogate modelling technique (support vector machines for regression), an evolutionary algorithm and a volumetric non-uniform rational B-splines parameterization are applied to the shape optimization of a two-dimensional aerofoil (RAE 2822) and a three-dimensional wing (DPW) in transonic flow conditions.     

A multi-objective metamodel-assisted memetic algorithm with strength-based local refinement

Metamodel-assisted evolutionary algorithms are low-cost optimization methods for CPU-demanding problems. Memetic algorithms combine global and local search methods, aiming at improving the quality of promising solutions. This article proposes a metamodel-assisted memetic algorithm which combines and extends the capabilities of the aforementioned techniques. Herein, metamodels undertake a dual role: they perform a low-cost pre-evaluation of population members during the global search and the gradient-based refinement of promising solutions. This reduces significantly the number of calls to the evaluation tool and overcomes the need for computing the objective function gradients. In multi-objective problems, the selection of individuals for refinement is based on domination and distance criteria. During refinement, a scalar strength function is maximized and this proves to be beneficial in constrained optimization. The proposed metamodel-assisted memetic algorithm employs principles of Lamarckian learning and is demonstrated on mathematical and engineering applications.     

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.     

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.     

An improved hybrid self-inertia weight adaptive particle swarm optimization algorithm with local search

As an evolutionary computing technique, particle swarm optimization (PSO) has good global search ability, but the swarm can easily lose its diversity, leading to premature convergence. To solve this problem, an improved self-inertia weight adaptive particle swarm optimization algorithm with a gradient-based local search strategy (SIW-APSO-LS) is proposed. This new algorithm balances the exploration capabilities of the improved inertia weight adaptive particle swarm optimization and the exploitation of the gradient-based local search strategy. The self-inertia weight adaptive particle swarm optimization (SIW-APSO) is used to search the solution. The SIW-APSO is updated with an evolutionary process in such a way that each particle iteratively improves its velocities and positions. The gradient-based local search focuses on the exploitation ability because it performs an accurate search following SIW-APSO. Experimental results verified that the proposed algorithm performed well compared with other PSO variants on a suite of benchmark optimization functions.     

A human‐like numerical technique for design of engineering systems

Because of the necessity for considering various creative and engineering design criteria, optimal design of an engineering system results in a highly‐constrained multi‐objective optimization problem. Major numerical approaches to such optimal design are to force the problem into a single objective function by introducing unjustifiable additional parameters and solve it using a single‐objective optimization method. Due to its difference from human design in process, the resulting design often becomes completely different from that by a human designer. This paper presents a novel numerical design approach, which resembles the human design process. Similar to the human design process, the approach consists of two steps: (1) search for the solution space of the highly‐constrained multi‐objective optimization problem and (2) derivation of a final design solution from the solution space. Multi‐objective gradient‐based method with Lagrangian multipliers (MOGM‐LM) and centre‐of‐gravity method (CoGM) are further proposed as numerical methods for each step. The proposed approach was first applied to problems with test functions where the exact solutions are known, and results demonstrate that the proposed approach can find robust solutions, which cannot be found by conventional numerical design approaches. The approach was then applied to two practical design problems. Successful design in both the examples concludes that the proposed approach can be used for various design problems that involve both the creative and engineering design criteria. Copyright © 2005 John Wiley & Sons, Ltd.     

Characterization of sequential optimization strategies in concurrent product and process design: A dual-team approach

In team-based design optimization, one type of workflow is relevant to sequential design decision-making; that is, one team's design decision goes after another team's in an alternate fashion. However, the strategies in use for sequential optimization significantly affect the final design solutions. Conventionally, the over-the-wall strategy and the Stackelberg solution strategy from game theory are extensively used for sequential optimization. In this paper, these strategies are extended to cover more design case scenarios in sequential optimization. A dual-team approach is presented to model, in particular, concurrent product and process design (CPPD) using a bi-objective optimization formalism in which a team acts as a decision maker towards a design objective. By differentiating the role of a team in sequential optimization, a set of sequential optimization strategies is provided for CPPD applications. Four CPPD models are accordingly derived to account for four case scenarios in CPPD. The implementation-related algorithms are also presented, along with an example illustration, to support computational design executions.     

基于支持向量机和重要度抽样的高强度钢板冲压成形工艺稳健设计

高强度钢板成形中噪声因素的存在造成了冲压质量不稳定.提出了基于支持向量机和重要度抽样的板料成形工艺稳健设计方法,量化了噪声因素对成形质量的影响,同时结合优化算法求解即满足质量可靠性又保证质量目标最优的工艺条件.对一高强度钢板冲压实例进行了工艺优化.按优化工艺冲压成形的零件减薄率及回弹均有所改善,验证了该方法的有效性.