Design of laminate composite layups using genetic algorithms

Fibre-reinforced laminate composites have attractively high stiffnesses and strengths and low densities. However, designing with laminate composites is more difficult than designing with metals because (a) it involves the design of the material itself, and its manufacturing route, at the same time, (b) laminates are highly anisotropic, and (c) they have complex failure modes. The failure modes and anisotropy combine to make design details unintuitively important and small detailed-design oversights have been responsible for most failures in composite structures. Design is the process of converting an idea into information from which a product can be made. Thus the central role of information processing in any design activity implies that software should be able to help. Here we show three different ways in which laminate stacking sequences can be designed.     

Genetic algorithms for optimal logical database design

The focus of this paper is database design using automated database design tools or more general CASE tools. We present a genetic algorithm for the optimization of (internal) database structures, using a multi-criterion objective function. This function expresses conflicting objectives, reflecting the well-known time/space trade-off. This paper shows how the solution space of the algorithm can be set up in the form of tree structures (forests), and how these are encoded by a simple integer assignation. Genetic operators (database transformations) defined in terms of this encoding behave as if they manipulate tree structures. Some basic experimental results produced by a research prototype are presented.     

A FORTRAN 90 genetic algorithm module for composite laminate structure design

The design of the stacking sequence for a composite laminate involves a set of discrete variables (plymaterial and ply orientation), and is thus well-suited to genetic algorithms for design optimization. Such algorithms have typically been custom-designed in FORTRAN 77 to suit specific optimization problems. Fortran 90 is a modern, powerful language with features that support important programming concepts, including those used in object-oriented programming. The Fortran 90 genetic algorithm module is used to define genetic data types, the functions which use these data types, and to provide a general framework for solving composite laminate structure design problems. The language's support of abstract data types is used to build genetic structures such as populations, subpopulations, individuals, chromosomes, and genes, and these data types are combined and manipulated by module subroutines. The use of abstract data types and long variable names makes the code useful and easily understood, while dynamic memory allocation makes the module flexible enough to be used in design problems of varying size and specification.     

Genetic algorithms in computer aided design

Design is a complex engineering activity, in which computers are more and more involved. The design task can often be seen as an optimization problem in which the parameters or the structure describing the best quality design are sought.Genetic algorithms constitute a class of search algorithms especially suited to solving complex optimization problems. In addition to parameter optimization, genetic algorithms are also suggested for solving problems in creative design, such as combining components in a novel, creative way.Genetic algorithms transpose the notions of evolution in Nature to computers and imitate natural evolution. Basically, they find solution(s) to a problem by maintaining a population of possible solutions according to the ‘survival of the fittest’ principle. We present here the main features of genetic algorithms and several ways in which they can solve difficult design problems. We briefly introduce the basic notions of genetic algorithms, namely, representation, genetic operators, fitness evaluation, and selection. We discuss several advanced genetic algorithms that have proved to be efficient in solving difficult design problems. We then give an overview of applications of genetic algorithms to different domains of engineering design.     

Genetic algorithm representations for laminate layups

The design of laminate layups using a genetic algorithm (GA) search-based function optimizer has been investigated using both a generate-and-test evaluation function and the layup-synthesis rule-base from a knowledge based design system. (The small rule-base from the laminate design was translated into a procedural evaluation function which could be called by the GA.) A simple coding of plies to genes is shown to be applicable in each case, but only when coupled with a penalty function which constrains genetic search to permissible layup candidates. Two experiments have been performed: a comparison of the GA search algorithm with a random/greedy search algorithm and a comparison of the GA with a rule based design system. Comparative tests with the rule based laminate design system are presented for four different load types. These demonstrate the robustness and accuracy of the system for the design of small scale asymmetric laminates.     

Layer reduction technique for composite laminate analysis

In this study, a layer reduction technique to decrease the number of degrees-of-freedom in composite analysis by combining a multiple-layer approach with a single-layer approach is presented. The single-layer approach is of classical laminate theory or high-order shear deformation theory while the multiple-layer approach is the interlaminar shear stress continuity theory. The layer reduction technique increases computational efficiency in composite analysis by reducing an n-layer laminate to a four-layer laminate but retaining the easiness and accuracy in calculating the transverse stresses from constitutive equations directly. The feasibility of this technique is demonstrated by numerical examples of composite laminates under both bidirectional bending and cylindrical bending.     

Multiple- and single-objective approaches to laminate optimization with genetic algorithms

In this paper an application of a genetic algorithm to a material- and sizing-optimization problem of a plate is described. This approach has obvious advantages: it does not require any derivative information and it does not impose any restriction, in terms of convexity, on the solution space. The plate optimization problem is firstly formulated as a constrained mixed-integer programming problem with a single objective function. An alternative multiobjective formulation of the problem in which some constraints are included as additional objectives is also presented. Some numerical results are included that show the appropriateness of the algorithm and of the mathematical model for the solution of this optimization problem, as well as the superiority of the multiobjective approach.     

A double-distribution statistical algorithm for composite laminate optimization

The paper proposes a new evolutionary algorithm termed Double-Distribution Optimization Algorithm (DDOA). DDOA belongs to the family of estimation of distribution algorithms (EDA) that build a statistical model of promising regions of the design space based on sets of good points and use it to guide the search. The efficiency of these algorithms is heavily dependent on the model accuracy. In this work, a generic framework for enhancing the model accuracy by incorporating statistical variable dependencies is presented. The proposed algorithm uses two distributions simultaneously: the marginal distributions of the design variables, complemented by the distribution of physically meaningful auxiliary variables. The combination of the two generates more accurate distributions of promising regions at a low computational cost. The paper demonstrates the efficiency of DDOA for three laminate optimization problems where the design variables are the fiber angles, and the auxiliary variables are integral quantities called lamination parameters. The results show that the reliability of DDOA in finding the optima is greater than that of simple EDA and a standard genetic algorithm, and that its advantage increases with the problem dimension.     

Fuzzy hybrid simulated annealing algorithms for topology design of switched local area networks

Topology design of switched local area networks (SLAN) is classified as an NP-hard problem since a number of objectives, such as monetary cost, network delay, hop count between communicating pairs, and reliability need to be simultaneously optimized under a set of constraints. This paper presents a multiobjective heuristic based on a simulated annealing (SA) algorithm for topology design of SLAN. Fuzzy logic has been incorporated in the SA algorithm to handle the imprecise multiobjective nature of the SLAN topology design problem, since the logic provides a suitable mathematical framework to address the multiobjective aspects of the problem. To enhance the performance of the proposed fuzzy simulated annealing (FSA) algorithm, two variants of FSA are also proposed. These variants incorporate characteristics of tabu search (TS) and simulated evolution (SimE) algorithms. The three proposed fuzzy heuristics are mutually compared with each other. Furthermore, two fuzzy operators, namely, ordered weighted average (OWA) and unified AND–OR (UAO) are also applied in certain steps of these algorithms. Results show that in general, the variant which embeds characteristics of SimE and TS into the fuzzy SA algorithm exhibits more intelligent search of the solution subspace and was able to find better solutions than the other two variants of the fuzzy SA. Also, the OWA and UAO operators exhibited relatively similar performance.     

Genetic algorithms with age structure

 This paper deals with genetic algorithms with age structure. Evolutionary optimization methods have been successfully applied to complex optimization problems, but the evolutionary optimization methods have a problem of bias in candidate solutions due to genetic drift in search. To solve this problem, we propose the introduction of age structure into genetic algorithms as a simple extension. In nature, an individual is removed from a population when the individual reaches lethal age. Therefore, genetic algorithms with age structure (ASGA) can maintain the genetic diversity of a population by removing aged individuals from the population. First, we conduct simple simulations of two subpopulations considering the age structure. Next, we apply the ASGA to a kanapsack problem. Finally, we discuss the optimal parameters for the age structure of the ASGA. These simulation results indicate that the ASGA can control selection pressure by aging process and relatively maintain the genetic diversity of a population. Received: 17 February 1997/Accepted: 6 May 1997     

Genetic algorithms for video segmentation

The current paper presents a new genetic algorithm (GA)-based method for video segmentation. The proposed method is specifically designed to enhance the computational efficiency and quality of the segmentation results compared to standard GAs. The segmentation is performed by chromosomes that independently evolve using distributed genetic algorithms (DGAs). However, unlike conventional DGAs, the chromosomes are initiated using the segmentation results of the previous frame, instead of random values. Thereafter, only unstable chromosomes corresponding to moving object parts are evolved by crossover and mutation. As such, these mechanisms allow for effective solution space exploration and exploitation, thereby improving the performance of the proposed method in terms of speed and segmentation quality. These advantages were confirmed based on experiments where the proposed method was successfully applied to both synthetic and natural video sequences.     

A repair operator for the preliminary design of a composite structure using genetic algorithms

This paper deals with the preliminary design of a composite structure where the design variables are the thicknesses and the percentages of fiber orientations in the zones of the structure. In this paper, we propose to include the design and manufacturing rules in the preliminary design. A stacking sequence generator is used to compute admissible stacking sequences with respect to these rules and which correspond to the design variables. Given that an admissible stacking sequence does not exist for every set of values of the design variables, a repair operator is proposed to cope with this problem. It aims at changing the values of the percentages of the fiber orientations in order to guarantee the existence of admissible stacking sequences with respect to the manufacturing rules. The repair operator is integrated into an optimization loop which uses a genetic algorithm to perform the preliminary design of a composite structure. Its efficiency is shown with a test case which involves a large number of fiber orientations and stacking sequences.     

Genetic algorithms for door-assigning and sequencing of trucks at distribution centers for the improvement of operational performance

In a supply chain, cross docking is one of the most innovative systems for improving the operational performance at distribution centers. By utilizing this cross docking system, products are delivered to the distribution center via inbound trucks and immediately sorted out. Then, products are shipped to customers via outbound trucks and thus, no inventory remains at the distribution center. In this paper, we consider the scheduling problem of inbound and outbound trucks at distribution centers. The aim is to maximize the number of products that are able to ship within a given working horizon at these centers. In this paper, a mathematical model for an optimal solution is derived and intelligent genetic algorithms are proposed. The performances of the genetic algorithms are evaluated using several randomly generated examples.     

Global control improvement algorithms

In the general vein of V.F. Krotov’s theory, we formulate an approach to nonlocal improvement based on sufficient optimality and improvement conditions. We propose constructive approaches to specifying the resolving function that realizes Krotov’s approach for arbitrary systems via linear partial differential equations and their discrete counterparts, namely linear recurrent relations. Examples are given.     

Globally convergent algorithms with local learning rates

A novel generalized theoretical result is presented that underpins the development of globally convergent first-order batch training algorithms which employ local learning rates. This result allows us to equip algorithms of this class with a strategy for adapting the overall direction of search to a descent one. In this way, a decrease of the batch-error measure at each training iteration is ensured, and convergence of the sequence of weight iterates to a local minimizer of the batch error function is obtained from remote initial weights. The effectiveness of the theoretical result is illustrated in three application examples by comparing two well-known training algorithms with local learning rates to their globally convergent modifications.