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-d escent optimization coupled with a boundary-tracking technique to solv e the integer spare allocation problem for kappa-out-of-n:G systems. T he objective function for the optimization is Linear and subject to a non-linear availability constraint. The constrained problem is solved in an unconstrained manner using a multiple-gradient technique. The se arch along the function gradient (unit cost) aims to locate the desire d optimum on the constraint boundary. A recovery move to the feasible region is carried out if the search strays into the infeasible region. Upon re-entry into the feasible region a new base point for the new s earch direction is found along the vector sum of the gradient of the o bjective function and the violated constraint at the recovery point. R esults for this boundary tracking multi-dimensional gradient optimizat ion method are compared with enhanced simplical optimization and other methods developed specifically for solving integer problems. Our test s are done on systems of various numbers of subsystems. The results sh ow appreciable improvement in execution time when compared to our earl ier integer simplical optimization methods and to the Sasaki method. T he improvement in CPU times is presented for comparison.