Software package for large-scale 0–1 linear programming on Unix system: GUB technique

Generally, 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.

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

Ida

Sato

Gen

1990

Electron Comm Jpn Pt III

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A computational algorithm for solving 0‐1 goal programming with GUB structures and its application for optimization problems in system reliability

Gen

Ida

Jae-Uk

1990

Electron Comm Jpn Pt III

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Upon to now, system optimal allocation problems such as system reliability and system availability problems have been formulated as single‐objective problems and solved through the use of various well‐developed optimization techniques. However, in this field, there are many problems that cannot be solved without applying MODM (multiple‐objective decision making) methods. These methods deal with multiple objectives that conflict with each other instead of formulating the problem as a single objective programming problem which optimizes only the reliability of the cost function, as is done in previous methods. GP (goal programming) is one of the most powerful MODM tools in this field. In practical MODM problems, many GP problems involve a large number of 0‐1 decision variables and a special type of 0‐1 variable, which arises during the transformation of non‐linear integer programming into 0‐1 linear programming. In this paper, we propose an efficient and specific algorithm for solving large‐scale 0‐1 GP problems in particular structures, which are termed GUB structures. Furthermore, to illustrate the effectiveness of the algorithm proposed here, we introduce two numerical examples from among the problems of system reliability, and compare the algorithm proposed with previous methods.

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Algorithms for solving large-scale 0–1 goal programming and its application to reliability optimization problem

Gen¹,

Sato²,

Ida³

et al. 1989

Computers & Industrial Engineering

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Software package for large-scale 0–1 linear programming on Unix system: GUB technique

Cited by 4 publications

References 9 publications

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

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

A computational algorithm for solving 0‐1 goal programming with GUB structures and its application for optimization problems in system reliability

Algorithms for solving large-scale 0–1 goal programming and its application to reliability optimization problem

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