Optimization Algorithms For a Class of Engineering Design Problems

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This proposal is for the continuation of long standing efforts in developing special purpose algoritluns for the solution of important engineering optimization problems that are not tractable by standard mathematical programming or optimal control algorithms. The problems include design centering, tolerancing and post manufacture tuning, robot and vehicle path planning in the presence of obstacles with coners, described by max-min type inequalities, optimal control and pursuit-evasion problems arising in air-traffic control, various shape optimization problems, and problems of seismic resistant structural design subject reliability constraints. These problems are invariably characterized by nonsmoothness and infinite dimensionality of either variables or constraints or both, and often involve ordinary or partial differential equations. The proposed research will exploit several tools developed, such as (i) the theory of consistent approximations, (ii) reformulation techniques for converting seemingly intractable problems into tractable forms.The framework of consistent approximations ensures the convergence of local and global minimizers and stationary points of approximating problems to those of the original problem. Also, it provides master algorithm models with discretization adjustment procedures, which can be used in conjunction with highly polished, mathematical programming libraries. Furthermore, these algorithms can be made to converge superlinearly by calling superlinearly converging mathematical programming subroutines from the master algorithms. By contrast, the problem reformulation techniques that we envisage must be developed on an ad hoc basis, as we have already done for some path planning and reliability constrained problems.The chances for success of the proposal research will be considerably enhanced by the fact that we have already obtained some results on which we can build and the multidisciplinary setting provided by the ongoing interactions and collaborations of the principal investigator and others.