Proposal of an Algorithm for Solving the Component Assignment Problem of an Adjacent Triangle-(m, n):F Triangular Lattice System.

In this article, we investigate the component assignment problem, which involves determining the optimal component arrangement for maximizing system reliability, given individual component reliabilities. Establishing the optimal arrangement is crucial for the cost-effective design of dependable systems. We focus on the adjacent triangle-(m, n):F triangular lattice system, characterized by mn components arranged in a triangular grid. The system fails when three neighboring components located at the vertices of a triangle fail simultaneously. Applications of this system extend to surveillance camera systems, sprinkler systems, and sensing systems. To date, no algorithm has been reported for finding the optimal arrangement of the adjacent triangle-(m, n):F triangular lattice system. Therefore, this paper aims to develop an algorithm using the branch-and-bound method to determine the optimal arrangement of the adjacent triangle-(m, n):F triangular lattice system. To efficiently acquire the optimal arrangement, we derived three pruning conditions and devised an optimal arrangement search algorithm incorporating them. Computational experiments revealed that all pruning conditions decreased computation time. Specifically, the pruning condition based on necessary conditions reduced computation time on average by approximately 1/9, as demonstrated experimentally. The solutions provided by the proposed algorithm ensure optimality, enabling the assessment of approximation methods, such as metaheuristics.