Optimization of system reliability using bicriteria 0‐1 linear programming with GUB constraints

Abstract

AbstractGenerally, problems in the optimization of system reliability such as unit selection and allocation have been formulated as single‐objective nonlinear integer problems and solved by various optimization techniques. The method for solving such problems was based on an implicit enumeration method, which transformed them into 0‐1 linear programming problems. These methods have not considered the GUB constraint, which arises when transforming to 0‐1 linear programming problem, but recently, an efficient method which considers this GUB structure and introduces the AHP (Analytic Hierarchy Process) into the system constraints has been proposed. However, in such system optimization problems, there are many problems that cannot be solved by formulating them as single‐objective programming which optimizes only a single reliability or cost function. Instead, they must be solved by applying MODM methods, which handle multiple objectives that conflict with each other.In this paper, we propose an efficient algorithm that makes use of the 0‐1 LP (GUB) package, written to solve single‐objective 0‐1 linear‐programming problems, in order to solve large scale 0‐1 linear programming problems that have two conflicting objectives and GUB constraints. To illustrate the effectiveness of the method proposed here, we present two numerical examples, optimal unit selection and optimal redundancy, and compare the results with those of previous methods.