Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Lipschitzian optimization without the Lipschitz constant
Journal of Optimization Theory and Applications
Geometric approach to Fletcher's ideal penalty function
Journal of Optimization Theory and Applications
Automatic differentiation of algorithms
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Using DIRECT to Solve an Aircraft Routing Problem
Computational Optimization and Applications
Global Optimization by Multilevel Coordinate Search
Journal of Global Optimization
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We deal with the problem of scheduling preventive maintenance (PM) for a system so that, over its operating life, we minimize a performance function which reflects repair and replacement costs as well as the costs of the PM itself. It is assumed that a hazard rate model is known which predicts the frequency of system failure as a function of age. It is also assumed that each PM produces a step reduction in the effective age of the system.We consider some variations and extensions of a PM scheduling approach proposed by Lin et al. [6]. In particular we consider numerical algorithms which may be more appropriate for hazard rate models which are less simple than those used in [6] and we introduce some constraints into the problem in order to avoid the possibility of spurious solutions. We also discuss the use of automatic differentiation (AD) as a convenient tool for computing the gradients and Hessians that are needed by numerical optimization methods.The main contribution of the paper is a new problem formulation which allows the optimal number of occurrences of PM to be determined along with their optimal timings. This formulation involves the global minimization of a non-smooth performance function. In our numerical tests this is done via the algorithm DIRECT proposed by Jones et al. [19]. We show results for a number of examples, involving different hazard rate models, to give an indication of how PM schedules can vary in response to changes in relative costs of maintenance, repair and replacement.