Application of boundary-tracking gradient-method for optimizing spares cost for k-out-of-n:G systems

This paper presents an application of a classical method of steepest-descent optimization coupled with a boundary-tracking technique to solve the integer spare allocation problem for k-out-of-n:G systems. The objective function for the optimization is linear and subject to a nonlinear availability constraint. The constrained problem is solved in an unconstrained manner using a multiple-gradient technique. The search along the function gradient (unit cost) aims to locate the desired optimum on the constraint boundary. A recovery move to the feasible region is carried out if the search strays into the unfeasible region. Upon re-entry into the feasible region, a new base point for the new search direction is found along the vector sum of the gradient of the objective function and the violated constraint at the recovery point. Results for this boundary tracking multi-dimensional gradient optimization method are compared with enhanced simplical optimization and other methods developed specifically for solving integer problems. The authors´ tests are carried out on systems of various numbers of subsystems. The results show appreciable improvement in execution time when compared to their earlier integer simplical optimization methods and to the Sasaki method. The improvement in CPU times is presented for comparison