关键词: 0-1整数规划, 可靠性分配, 线性松弛, 遗传算法, 重要度

Abstract: The requested reliability of products is allocated to the next level systems or components, is very important on the design of products and management. It is often more reasonable to consider the technological design and customer preference of the bottom components, and describe importance-reliability-cost relationships via discrete data sets, not via functions to relate cost and reliability. Considering such situations, where each component with different importance is available at several reliability levels with corresponding costs. Based on the discrete “importance-reliability-cost” data set and the minimum cost of production, the requested reliability is considered as the basic constraint conditions, and the selection identifications 0 and 1 of the bottom components are considered as the binary decision variable, the 0-1 integer programming models for reliability assignment is studied by means of the nonlinear integer programming. The optimal scheme of components which comprise the equivalent series and parallel structure system and its equivalent linear programming, and the equivalent series-parallel and parallel-series system and their linear relaxation-programming, are presented respectively. For quickly searching the optimal solutions of nonlinear programming, the search path and genetic algorithm for linear relaxations programming are given. Numerical examples are also given to illustrate the feasibility of decision program and effectiveness of presented algorithm.

Key words: 0-1 integer programming, genetic algorithm, important value, linear relaxations, reliability assignment