Optimizing Engineering Designs Using a Combined Genetic Search.
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Abstract:
In the optimization of engineering designs, traditional search and optimization methods face at least two difficulties: (i) since each is specialized in solving a particular type of problem, one method does not work well on different types of problems (ii) most of them are designed to work on continuous search spaces. Since different optimal engineering design problems give rise to objective and constraint functions of varying degree of nonlinearity and since most engineering design problems involve mixed variables (zero-one, discrete, and continuous), designers often face difficulty in using the traditional methods. In this paper, a combined genetic search technique (GeneAS) is suggested to solve mixed-integer programming problems often encountered in engineering design activities. GeneAS uses a combination of binary-coded and real-coded GAs to handle different types of variables.Keywords:
Engineering optimization
Continuous variable
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An algorithm for solving nonlinear optimization problems involving discrete, integer, zero-one, and continuous variables is presented. The augmented Lagrange multiplier method combined with Powell’s method and Fletcher and Reeves Conjugate Gradient method are used to solve the optimization problem where penalties are imposed on the constraints for integer/discrete violations. The use of zero-one variables as a tool for conceptual design optimization is also described with an example. Several case studies have been presented to illustrate the practical use of this algorithm. The results obtained are compared with those obtained by the Branch and Bound algorithm. Also, a comparison is made between the use of Powell’s method (zeroth order) and the Conjugate Gradient method (first order) in the solution of these mixed variable optimization problems.
Discrete optimization
Augmented Lagrangian method
Constraint algorithm
Constrained optimization
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Abstract This paper presents an improved particle swarm optimizer (PSO) for solving mechanical design optimization problems involving problem-specific constraints and mixed variables such as integer, discrete and continuous variables. A constraint handling method called the ‘fly-back mechanism’ is introduced to maintain a feasible population. The standard PSO algorithm is also extended to handle mixed variables using a simple scheme. Five benchmark problems commonly used in the literature of engineering optimization and nonlinear programming are successfully solved by the proposed algorithm. The proposed algorithm is easy to implement, and the results and the convergence performance of the proposed algorithm are better than other techniques. Keywords: Evolutionary algorithmsParticle swarm optimizationConstrained optimizationMechanical design Acknowledgement The authors would like to acknowledge Dr. Carlos Coello for his helpful discussions.
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The ability to mutually interact is a fundamental social behavior in all human and insect societies. Social interactions enable individuals to adapt and improve faster than biological evolution based on genetic inheritance alone. This is the driving concept behind the optimization algorithm introduced in this paper that makes use of the intra and intersociety interactions within a formal society and the civilization model to solve single objective constrained optimization problems. A society corresponds to a cluster of points in the parametric space while a civilization is a set of all such societies. Every society has its set of better performing individuals (leaders) that help others to improve through information exchange. This results in the migration of a point toward a better performing point, analogous to an intensified local search. Leaders improve only through an intersociety information exchange that results in the migration of a leader from a society to another. This helps the better performing societies to expand and flourish.
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From the Publisher:
This book brings together - in an informal and tutorial fashion - the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields.
Major concepts are illustrated with running examples, and major algorithms are illustrated by Pascal computer programs. No prior knowledge of GAs or genetics is assumed, and only a minimum of computer programming and mathematics background is required.
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Abstract This paper presents a new approach to handle constraints using evolutionary algorithms. The new technique treats constraints as objectives, and uses a multiobjective optimization approach to solve the re-stated single-objective optimization problem. The new approach is compared against other numerical and evolutionary optimization techniques in several engineering optimization problems with different kinds of constraints. The results obtained show that the new approach can consistently outperform the other techniques using relatively small sub-populations, and without a significant sacrifice in terms of performance.
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Constrained optimization problem
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There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.
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