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

In general, inevitably the particular structure called generalized upper bounding (GUB) occurs when transforming the reliability optimization problem such as optimal unit selection and redundant allocation. These are formulated as the nonlinear integer programming problem and transformed to the 0‐1 linear programming problem. Recently, a method for solving the fuzzy multi‐objective 0‐1 linear programming (0‐1 FMOLP) problem which extends the efficient method considering the GUB structure to the more general MOLP problem is proposed. Also, the method is extended to deal with the fuzziness of the goal value toward the objective function. However, this method is not considered for the break‐down of the fault‐detecting and switching (FDS) device; thus, it does not sufficiently cope with the real world's reliability optimization problem. From these viewpoints, an algorithm is proposed for solving the optimal redundant unit selection problem that optimizes the system reliability with imperfect FDS device by fuzzy 0–1 MOLP. The method proposed here considers the fuzziness of the decisionmaker (DM) toward the goal value of each objective function by introducing the fuzzy goal. Further, this method enables the DM to determine the most satisfactory solution to the attainment of each goal value of the objective function and constraint and can cope with the realistic optimal design of the system reliability problems.

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“…(10) under constraints of Eqs. (ll), (12), and (13); 6, represents the width of the right-hand side (RHS) constant given by the DM.…”

Section: S-typementioning

confidence: 99%

“…(9), transform the fuzzy MOLP problem to the fuzzy 0-1 MOLP problem with GUB constraints shown as Eqs. (10) to (13); and also, by introducing the membership functions shown as Eqs. (16) and (17), transform the 0-1 LP problem with GUB constraints shown as Eqs.…”

Section: Algorithmmentioning

confidence: 99%