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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.

SUMMARYThe Uncapacitated Facility Location Problem (UFLP) is a fundamental optimization problem involving the selection of locations at which facilities supplying the same service are to be placed. Since it has been shown that the UFLP is NP-hard, it has generally been thought that there is no hope of finding a polynomial time algorithm by which an optimal solution is always obtained. In this paper, we propose a genetic algorithm for solving the UFLP. In the UFLP, according to the ratio of the cost of facility placement and the cost to users of the facility, the number of facility locations can be roughly estimated. Therefore, partial solution spaces that are likely to contain a good solution can be predicted to some extent on the basis of the classification index. By using mutation with the operation that searches the solution space that is likely to contain a good solution, the proposed method can search the whole space of solutions efficiently. Its effectiveness is shown by a numerical experiment in which our method is compared with existing methods.