Backtrack programming in welded girder design

• Authors: Albert D. M. Lewis
• Venue: DAC '68 Proceedings of the 5th annual Design Automation Workshop
• Year: 1968

The object of engineering design is to satisfy some need of man with the maximization or minimization of some measure of effectiveness of the solution. Common measures of effectiveness are cost, cost-benefit ratio, and profit. In mathematical terminology an object or facility can be described by a list or vector of parameter values. The position of each element in the vector associates it with a particular parameter. The performance of the object or facility and the constraints imposed on the performance are described by a set of equalities and inequalities called the design equations. The effectiveness of the solution is indicated by the value obtained by evaluating an objective function with the design parameter values. The object of the design process is to determine the vector of parameter values, the optimum solution, which satisfies the design equations and maximizes or minimizes, as appropriate, the value of the objective function. There are a number of mathematical procedures which are useful in optimization problems. However, most methods are applicable only to particular classes of problems. The application of linear programming, for example, is limited to problems in which the design variables are involved only in linear relationships. Dynamic programming is applicable to problems in which there is a sequential flow of information. Gradient search methods are useful in many problems, but may lead to incorrect results if the function is not unimodal. Difficulties are encountered also if one or more of the parameters are defined only at discrete values. Backtrack programming, 2,3on the other hand, is generally applicable to optimization problems including those for which more specialized techniques are available. The aim of this paper is to illustrate the application of backtrack programming to the design of welded plate girders.