Genetic search strategies in multicriterion optimal design

Abstract

A b s t r a c tThe present paper describes an implementation of genetic search methods in multicriterion optimal designs of structural systems with a mix of continuous, integer and discrete design variables. Two distinct strategies to simultaneously generate a family of Pareto optimal designs are presented in the paper. These strategies stem from a consideration of the natural analogue, wherein distinct species of life forms share the available resources of an environment for sustenance. The efficacy of these solution strategies are examined in the context of representative structural optimization problems with multiple objective criteria and with varying dimensionality as determined by the number of design variables and constraints. I n t r o d u c t i o nMathematical nonlinear programming algorithms have been shown to be widely applicable in the automated optimal design of structural systems. They present a general approach to the problem. The more efficient of these classes of methods are gradient based (Sobieszczanski-Sobieski 1983), and require at least the first-order derivatives of both the objective function and constraints with respect to the design variables. With this "hill-climbing" or "slope-descending" ability, gradient based methods locate the relative optimum closest to the initial estimate of the optimum design. These methods do not guarantee the location of the global optimum unless the design space is known to be convex. They are also inappropriate in those applications where the design space is discontinuous, as the derivatives of the objective function or constraints may become singular across the boundary of discontinuity. Furthermore, these methods are largely designed for problems where the design space comprises of continuous real values. A modified mixed integer and discrete programming algorithm using branch-and-bound techniques has been developed (Hajela and Shih 1990), to successfully account for a mix of continuous, integer, and discrete design variables. In this approach, however, the original optimization problem is undesirably expanded to a large number of suboptimization problems.Exhaustive search and simple random search methods are among the simplest and most robust strategies for automated optimal design problems. These methods can work on almost all kinds of design spaces and without any restriction on types of design variables. An improvement on the simple enumerative techniques are methods such as random walk and random walk with direction exploitation. These methods, which require only function information, can quite often deal efficiently with nonconvex and discontinuous functions, and in many cases are capable of working with discrete type design variables. The only drawback is that they often require thousands of function evaluations to achieve the optimum, even for the simplest of problems. It is hence crucial to examine alternate strategies for optimal structural design problems, which need less computational effort than required by the enumerative search techniques, ...

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