網路可靠性設計之整數規劃問題全域最佳化

Abstract

系統可靠性問題在各種領域中都廣受利用，如電信領域、運輸規劃、機械系統，甚至積體電路設計。本類問題其決策變數多為正整數，其目標函數及限制式則多為非線性式，解題有相當之困難度。過去文獻多以連續性方式漸進之，或以啟發式演算法計算，前者忽略決策變數為正整數之限制，後者則不能保證求得全域最佳解。 本論文提出一演算法求解此一混合整數規劃問題，可求得最佳解。本演算法引進零壹變數、及分段式方法求解。

System reliability design problems, including redundancy allocation problems, and decision variables are constrained to positive integer values. Since the objective function and the constraints are of ten nonlinear, past algorithms often treat it as continuous or use a heuristic without guaranteeing the global optimum. In this paper, we presented an algorithm for the global optimization of the integer-programming problems arising in system-reliability design. The algorithm is based on the piecewise method and the introduction of 0-1 variables.