A review of the methods for global optimization rea¢ veals that most methods have been developed for unconstrained ~t problems. They need to be extended to general constrained c~ problems because most of the engineering applications have conAx(e) straints. Some of the methods can be easily extended while others need further work. It is also possible to transform a constrained D problem to an unconstrained one by using penalty or augmented det(°)Lagrangian methods and solve the problem that way. Some of the global optimization methods find all the local minimum points dj while others find only a few of them. In any case, all the methods require a very large number of calculations. Therefore, the dt computational effort to obtain a global solution is generally subdx stantial. The methods for global optimization can be divided into two broad categories: deterministic and stochastic. Some deter-~(t) ministic methods are based on certain assumptions on the cost e0 function that are not easy to check. These methods are not very exp (°)

The methods for discrete-integer-continuous variable nonlinear optimization are reviewed. They are classified into the following six categories: branch and bound, simulated annealing, sequential linearization, penalty functions, Lagrangian relaxation, and other methods. Basic ideas of each method are described and details of some of the algorithms are given. They are transcribed into a step-by-step format for easy implementation into a computer. Under "other methods", rounding-off, heuristic, cutting-plane, pure discrete, and genetic algorithms are described. For nonlinear problems, none of the methods are guaranteed to produce the global minimizer; however, "good practical" solutions can be obtained. Notation BBM D Di dij

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A genetic algorithm for engineering applications that involve sequencing of operations is proposed and demonstrated. Such applications are known as travelling salesman problems in operations research literature. The proposed algorithm uses some new operators that are different from those typically used in genetic algorithms. Some enhancements for improving performance of the algorithm are also described. Treatment of two salesmen in the problem is also discussed. Results for test problems, including a vehicle A-pillar subassembly welding sequence application, show performance of the proposed algorithm to be quite robust.

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