Implicit representation in genetic algorithms using redundancy

A new representation combining redundancy and implicit fitness constraints is introduced that performs better than a simple genetic algorithm (GA) and a structured GA in experiments. The implicit redundant representation (IRR) consists of a string that is over-specified, allowing for sections of the string to remain inactive during function evaluation. The representation does not require the user to prespecify the number of parameters to evaluate or the location of these parameters within the string. This information is obtained implicitly by the fitness function during the GA operations. The good performance of the IRR can be attributed to several factors: less disruption of existing fit members due to the increased probability of crossovers and mutation affecting only redundant material; discovery of fit members through the conversion of redundant material into essential information; and the ability to enlarge or reduce the search space dynamically by varying the number of variables evaluated by the fitness function. The IRR GA provides a more biologically parallel representation that maintains a diverse population throughout the evolution process. In addition, the IRR provides the necessary flexibility to represent unstructured problem domains that do not have the explicit constraints required by fixed representations.     

Target-matching test problem for multiobjective topology optimization using genetic algorithms

This paper describes the multiobjective topology optimization of continuum structures solved as a discrete optimization problem using a multiobjective genetic algorithm (GA) with proficient constraint handling. Crucial to the effectiveness of the methodology is the use of a morphological geometry representation that defines valid structural geometries that are inherently free from checkerboard patterns, disconnected segments, or poor connectivity. A graph- theoretic chromosome encoding, together with compatible reproduction operators, helps facilitate the transmission of topological/shape characteristics across generations in the evolutionary process. A multicriterion target-matching problem developed here is a novel test problem, where a predefined target geometry is the known optimum solution, and the good results obtained in solving this problem provide a convincing demonstration and a quantitative measure of how close to the true optimum the solutions achieved by GA methods can be. The methodology is then used to successfully design a path-generating compliant mechanism by solving a multicriterion structural topology optimization problem.     

An Unstructured Finite Volume Approach for Structural Dynamics in Response to Fluid Motions

A new cell-vortex unstructured finite volume method for structural dynamics is assessed for simulations of structural dynamics in response to fluid motions. A robust implicit dual-time stepping method is employed to obtain time accurate solutions. The resulting system of algebraic equations is matrix-free and allows solid elements to include structure thickness, inertia, and structural stresses for accurate predictions of structural responses and stress distributions. The method is coupled with a fluid dynamics solver for fluid-structure interaction, providing a viable alternative to the finite element method for structural dynamics calculations. A mesh sensitivity test indicates that the finite volume method is at least of second-order accuracy. The method is validated by the problem of vortex-induced vibration of an elastic plate with different initial conditions and material properties. The results are in good agreement with existing numerical data and analytical solutions. The method is then applied to simulate a channel flow with an elastic wall. The effects of wall inertia and structural stresses on the fluid flow are investigated.     

Structural topology optimization using a genetic algorithm with a morphological geometric representation scheme

This paper describes a versatile methodology for solving topology design optimization problems using a genetic algorithm (GA). The key to its effectiveness is a geometric representation scheme that works by specifying a skeleton which defines the underlying topology/connectivity of a structural continuum together with segments of material surrounding the skeleton. The required design variables are encoded in a chromosome which is in the form of a directed graph that embodies this underlying topology so that appropriate crossover and mutation operators can be devised to recombine and help preserve any desirable geometry characteristics of the design through succeeding generations in the evolutionary process. The overall methodology is first tested by solving ‘target matching’ problems—simulated topology optimization problems in each of which a ‘target’ geometry is first created and predefined as the optimum solution, and the objective of the optimization problem is to evolve design solutions to converge towards this target shape. The methodology is then applied to design two path-generating compliant mechanisms—large-displacement flexural structures that undergo some desired displacement paths at some point when given a straight line input displacement at some other point—by an actual process of topology/shape optimization.     

Immune network simulations in multicriterion design

A modification to the genetic algorithm (GA) based search procedure, based on the modeling of a biological immune system, is proposed as an approach to solving the multicriterion design problem. Such problems have received considerable attention, given that decisions in engineering design practice typically require allocation of resources to satisfy multiple, and frequently conflicting requirements. The approach is particularly amenable to problems with a mix of continuous, discrete, and integer design variables, where the GA has been shown to perform in an effective manner. The approach considered in the present work is based on the concept of converting the multicriterion problem into one with a scalar objective through the use of the utility function. The strength of the approach is in its ability to generate the Pareto-Edgeworth front of compromise solutions in a single execution of the GA. A characteristic feature of biological immune systems which allows for the generation of multiple specialist antibodies, is shown to be an effective approach to facilitate the generation of the Pareto-Edgeworth front. Solutions to problems in structural design are presented in support of the proposed approach.     

CGD-GA: A graph-based genetic algorithm for sensor network design

The foundations and implementation of a genetic algorithm (GA) for instrumentation purposes are presented in this paper. The GA constitutes an initialization module of a decision support system for sensor network design. The method development entailed the definition of the individual’s representation as well as the design of a graph-based fitness function, along with the formulation of several other ad hoc implemented features. The performance and effectiveness of the GA were assessed by initializing the instrumentation design of an ammonia synthesis plant. The initialization provided by the GA succeeded in accelerating the sensor network design procedures. It also accomplished a great improvement in the overall quality of the resulting instrument configuration. Therefore, the GA constitutes a valuable tool for the treatment of real industrial problems.     

Fast structural optimization with frequency constraints by genetic algorithm using adaptive eigenvalue reanalysis methods

Structural optimization with frequency constraints is highly nonlinear dynamic optimization problems. Genetic algorithm (GA) has greater advantage in global optimization for nonlinear problem than optimality criteria and mathematical programming methods, but it needs more computational time and numerous eigenvalue reanalysis. To speed up the design process, an adaptive eigenvalue reanalysis method for GA-based structural optimization is presented. This reanalysis technique is derived primarily on the Kirsch’s combined approximations method, which is also highly accurate for case of repeated eigenvalues problem. The required number of basis vectors at every generation is adaptively determined and the rules for selecting initial number of basis vectors are given. Numerical examples of truss design are presented to validate the reanalysis-based frequency optimization. The results demonstrate that the adaptive eigenvalue reanalysis affects very slightly the accuracy of the optimal solutions and significantly reduces the computational time involved in the design process of large-scale structures.     

A hybrid AI/OR decision support tool for backbone communications network design

Much of existing DSS literature views the role of human expertise as primarily that of selecting appropriate formal models for solving a problem or synthesizing sequences thereof. Once a model (or model sequence) is determined, values of decision variables are determined by the model(s) alone. Hence, automated methods for facilitating model selection and synthesis have received considerable attention. However, a single model is often not an accurate abstraction of reality. Also, results from multiple formal models often have to be combined heuristically to obtain practical solutions. Thus, in this paper we explore the premise that human expertise needs to interact with formal models during the process of searching for solution values. Specifically, we describe a hybrid decision support tool for the design of backbone communication networks, a problem recognized as being of considerable complexity. An internal representation of the design process that employs a blackboard, a truth maintainence system and dependency directed backtracking, allows human expertise and formal models to jointly determine decision variable values in a uniform manner. The design tool has been implemented using a combination of Lisp and Fortran. Computational experiments indicate that incorporating human expertise during the search process results in superior complete solutions and added flexibility in satisfying ad hoc requirements. We conjecture that this hybrid search approach is not limited to the telecommunication network design problem and can be extended to other applications.     

An AHP-based decision-making tool for the solution of multiproduct batch plant design problem under imprecise demand

This paper addresses the problem of the optimal design of batch plants with imprecise demands in product amounts. The design of such plants necessarily involves the way that equipment may be utilized, which means that plant scheduling and production must form an integral part of the design problem. This work relies on a previous study, which proposed an alternative treatment of the imprecision (demands) by introducing fuzzy concepts, embedded in a multi-objective Genetic Algorithm (GA) that takes into account simultaneously maximization of the net present value (NPV) and two other performance criteria, i.e. the production delay/advance and a flexibility criterion. The results showed that an additional interpretation step might be necessary to help the managers choosing among the non-dominated solutions provided by the GA. The analytic hierarchy process (AHP) is a strategy commonly used in Operations Research for the solution of this kind of multicriteria decision problems, allowing the apprehension of manager subjective judgments. The major aim of this study is thus to propose a software integrating the AHP theory for the analysis of the GA Pareto-optimal solutions, as an alternative decision-support tool for the batch plant design problem solution.     

A genetic algorithm approach for solving the daily photograph selection problem of the SPOT5 satellite

This article addresses the combinatorial optimization problem of managing earth observation satellites (EOSs) such as the French SPOT5, which is concerned with selecting on each day a subset of a set of candidate photographs. The problem has a significant economic importance due to its high initial investment cost that exists in these instruments and its solution difficulty resulting from the large solution space, making it an attractive research area. This article proposes a genetic algorithm (GA) for solving the SPOT5 selection problem using a new genome representation for maximizing not only a single objective as profit but a multi-criteria objective that includes the number of acquired photographs. Test results of our proposed GA show that it finds optimal solutions effectively for moderate size problems and obtains better results for two large benchmark instances coded 1403 and 1504 in the literature. Also, we verify the result that the best known value in the literature for problem coded 1401 is an optimal value.     

A new optimality criteria method for shape optimization of natural frequency problems

A new shape optimization method for natural frequency problems is presented. The approach is based on an optimality criterion for general continuum solids, which is derived in this paper for the maximization of the first natural frequency with a volume constraint. An efficient redesign rule for frequency problems is developed to achieve the required shape modifications. The optimality criterion is extended to volume minimization problems with multiple frequency constraints. The nonparametric geometry representation creates a complete design space for the optimization problem, which includes all possible solutions for the finite element discretization. The combination with the optimality criteria approach results in a robust and fast convergence, which is independent of the number of design variables. Sensitivity information of objective function and constraints are not required, which allows to solve the structural analysis task using fast and reliable industry standard finite element solvers like ABAQUS, ANSYS, I-DEAS, MARC, NASTRAN, or PERMAS. The new approach is currently being implemented in the optimization system TOSCA.     

Structural topology design optimization using Genetic Algorithms with a bit-array representation

In this paper, a bit-array representation method for structural topology optimization using the Genetic Algorithm (GA) is implemented. The importance of structural connectivity in a design is further emphasized by considering the total number of connected objects of each individual explicitly in an equality constraint function. To evaluate the constrained objective function, Deb’s constraint handling approach is further developed to ensure that feasible individuals are always better than infeasible ones in the population to improve the efficiency of the GA. A violation penalty method is proposed to drive the GA search towards the topologies with higher structural performance, less unusable material and fewer separate objects in the design domain. An identical initialization method is also proposed to improve the GA performance in dealing with problems with long narrow design domains. Numerical results of structural topology optimization problems of minimum weight and minimum compliance designs show the success of this bit-array representation method and suggest that the GA performance can be significantly improved by handling the design connectivity properly.     

Structural application of a shape optimization method based on a genetic algorithm

This paper presents a structural application of a shape optimization method based on a Genetic Algorithm (GA). The method produces a sequence of fixed-distance step-wise movements of the boundary nodes of a finite element model to derive optimal shapes from an arbitrary initial design space. The GA is used to find the optimal or near-optimal combination of boundary nodes to be moved for a given step movement. The GA uses both basic and advanced operators. For illustrative purposes, the method has been applied to structural shape-optimization. The shape-optimization methodology presented allows local optimization, where only crucial parts of a structure are optimized as well as global shape-optimization which involves finding the optimal shape of the structure as a whole for a given environment as described by its loading and freedom conditions. Material can be removed or added to reach the optimal shape. Two examples of structural shape optimization are included showing local and global optimization through material removal and addition. Received October 14, 1999     

Main Effect Fine-tuning of the Mutation Operator and the Neighbourhood Function for Uncapacitated Facility Location Problems

In both genetic algorithms (GAs) and simulated annealing (SA), solutions can be represented by gene representation. Mutation operator in GA and neighborhood function in SA are used to explore the solution space. They usually select genes for performing mutation. The rate of selection of genes can be called mutation rate. However, randomly selecting genes may not be the best way for both algorithms. This paper describes how to estimate the main effect in genes representation. The resulting estimates cannot only be used to understand the domination of gene representation, but also employed to fine-tune the mutation rate in both the mutation operator in the GA and the neighborhood function in the SA. It has been demonstrated the use of the proposed methods for solving uncapacitated facility location problems and discuss the examination of the proposed methods with some useful comparisons with both the latest developed GA and SA for solving this problem. For many well-known benchmark problems, the proposed methods yield better results in solution quality than the previously used methods.     

Combining genetic algorithms with BESO for topology optimization

This paper proposes a new algorithm for topology optimization by combining the features of genetic algorithms (GAs) and bi-directional evolutionary structural optimization (BESO). An efficient treatment of individuals and population for finite element models is presented which is different from traditional GAs application in structural design. GAs operators of crossover and mutation suitable for topology optimization problems are developed. The effects of various parameters used in the proposed GA on the optimization speed and performance are examined. Several 2D and 3D examples of compliance minimization problems are provided to demonstrate the efficiency of the proposed new approach and its capability of obtaining convergent solutions. Wherever possible, the numerical results of the proposed algorithm are compared with the solutions of other GA methods and the SIMP method.     

An improved adaptive genetic algorithm based on hormone modulation mechanism for job-shop scheduling problem

An improved adaptive genetic algorithm (IAGA) for solving the minimum makespan problem of job-shop scheduling problem (JSP) is presented. Though the traditional genetic algorithm (GA) exhibits implicit parallelism and can retain useful redundant information about what is learned from previous searches by its representation in individuals in the population, yet GA may lose solutions and substructures due to the disruptive effects of genetic operators and is not easy to regulate GA’s convergence. The proposed IAGA is inspired from hormone modulation mechanism, and then the adaptive crossover probability and adaptive mutation probability are designed. The proposed IAGA is characterized by simplifying operations, high search precision, overcoming premature phenomenon and slow evolution. The proposed method by employing operation-based encoding is effectively applied to solve a dynamic job-shop scheduling problem (DJSP) and a complicated contrastive experiment of JSP in manufacturing system. Meanwhile, in order to ensure to create a feasible solution, a new method for crossover operation is adopted, named, partheno-genetic operation (PGO). The computational results validate the effectiveness of the proposed IAGA, which can not only find optimal or close-to-optimal solutions but can also obtain both better and more robust results than the existing genetic algorithms reported recently in the literature. By employing IAGA, machines can be used more efficiently, which means that tasks can be allocated appropriately, production efficiency can be improved, and the production cycle can be shortened efficiently.     

A mixed GA-PSO-based approach for performance-based design optimization of 2D reinforced concrete special moment-resisting frames

A mixed genetic algorithm and particle swarm optimization in conjunction with nonlinear static and dynamic analyses as a smart and simple approach is introduced for performance-based design optimization of two-dimensional (2D) reinforced concrete special moment-resisting frames. The objective function of the problem is considered to be total cost of required steel and concrete in design of the frame. Dimensions and longitudinal reinforcement of the structural elements are considered to be design variables and serviceability, special moment-resisting and performance conditions of the frame are constraints of the problem. First, lower feasible bond of the design variables are obtained via analyzing the frame under service gravity loads. Then, the joint shear constraint has been considered to modify the obtained minimum design variables from the previous step. Based on these constraints, the initial population of the genetic algorithm (GA) is generated and by using the nonlinear static analysis, values of each population are calculated. Then, the particle swarm optimization (PSO) technique is employed to improve keeping percent of the badly fitted populations. This procedure is repeated until the optimum result that satisfies all constraints is obtained. Then, the nonlinear static analysis is replaced with the nonlinear dynamic analysis and optimization problem is solved again between obtained lower and upper bounds, which is considered to be optimum result of optimization solution with nonlinear static analysis. It has been found that by mixing the analyses and considering the hybrid GA-PSO method, the optimum result can be achieved with less computational efforts and lower usage of materials.     

Design of distributed compliant micromechanisms with an implicit free boundary representation

In this paper, a parameterization approach is presented for structural shape and topology optimization of compliant mechanisms using a moving boundary representation. A level set model is developed to implicitly describe the structural boundary by embedding into a scalar function of higher dimension as zero level set. The compactly supported radial basis function of favorable smoothness and accuracy is used to interpolate the level set function. Thus, the temporal and spatial initial value problem is now converted into a time-separable parameterization problem. Accordingly, the more difficult shape and topology optimization of the Hamilton–Jacobi equation is then transferred into a relatively easy size optimization with the expansion coefficients as design variables. The design boundary is therefore advanced by applying the optimality criteria method to iteratively evaluate the size optimization so as to update the level set function in accordance with expansion coefficients of the interpolation. The optimization problem of the compliant mechanism is established by including both the mechanical efficiency as the objective function and the prescribed material usage as the constraint. The design sensitivity analysis is performed by utilizing the shape derivative. It is noted that the present method is not only capable of simultaneously addressing shape fidelity and topology changes with a smooth structural boundary but also able to avoid some of the unfavorable numerical issues such as the Courant–Friedrich–Levy condition, the velocity extension algorithm, and the reinitialization procedure in the conventional level set method. In particular, the present method can generate new holes inside the material domain, which makes the final design less insensitive to the initial guess. The compliant inverter is applied to demonstrate the availability of the present method in the framework of the implicit free boundary representation.