A problem-specific genetic algorithm (GA) is developed and demonstrated to analyze series-parallel systems and to determine the optimal design configuration when there are multiple component choices available for each of several k-out-of-n:G subsystems. The problem is to select components and redundancy-levels to optimize some objective function, given system-level constraints on reliability, cost, and/or weight. Previous formulations of the problem have implicit restrictions concerning the type of redundancy allowed, the number of available component choices, and whether mixing of components is allowed. GA is a robust evolutionary optimization search technique with very few restrictions concerning the type or size of the design problem. The solution approach was to solve the dual of a nonlinear optimization problem by using a dynamic penalty function. GA performs very well on two types of problems: (1) redundancy allocation originally proposed by Fyffe, Hines, Lee, and (2) randomly generated problem with more complex k-out-of-n:G configurations.

Reliability optimization of series-parallel systems using a genetic algorithm

This paper uses an ant colony meta-heuristic optimization method to solve the redundancy allocation problem (RAP). The RAP is a well known NP-hard problem which has been the subject of much prior work, generally in a restricted form where each subsystem must consist of identical components in parallel to make computations tractable. Meta-heuristic methods overcome this limitation, and offer a practical way to solve large instances of the relaxed RAP where different components can be placed in parallel. The ant colony method has not yet been used in reliability design, yet it is a method that is expressly designed for combinatorial problems with a neighborhood structure, as in the case of the RAP. An ant colony optimization algorithm for the RAP is devised & tested on a well-known suite of problems from the literature. It is shown that the ant colony method performs with little variability over problem instance or random number seed. It is competitive with the best-known heuristics for redundancy allocation.

An ant colony optimization algorithm for the redundancy allocation problem (RAP)

Associate member, ieee and smith, a senior member, ieee an ant colony optimization algorithm for the redundancy allocation problem (rap)

A tabu search meta-heuristic has been developed and successfully demonstrated to provide solutions to the system reliability optimization problem of redundancy allocation. Tabu search is particularly well-suited to this problem and it offers distinct advantages compared to alternative optimization methods. While there are many forms of the problem, the redundancy allocation problem generally involves the selection of components and redundancy levels to maximize system reliability given various system-level constraints. This is a common and extensively studied problem involving system design, reliability engineering and operations research. It is becoming increasingly important to develop efficient solutions to this reliability optimization problem because many telecommunications (and other) systems are becoming more complex, yet with short development schedules and very stringent reliability requirements. Tabu search can be applied to a more diverse problem domain compared to mathematical programming meth...

/pdf/efficiently-solving-the-redundancy-allocation-problem-using-3i0lnju2ny.pdf

Efficiently solving the redundancy allocation problem using tabu search

Penalty guided genetic search for reliability design optimization

This paper discusses allocating redundant components subject to resource constraints so as to optimize some measure of system performance. Two new exact algorithms are presented for the case where the objective and constraint functions are stagewise separable. Both are branch and bound algorithms. The first, BLE1, is based on an underlying knapsack structure, while the second, BLE2, exploits a multiple-choice knapsack structure. BLE1 can solve problems with 100 stages and 10 constraints in just a few seconds of CPU time on an IBM 3033. For larger problems, BLH, a heuristic procedure, is proposed. The heuristic is based on the ``slippery algorithm'' for knapsack problems. Computational testing indicates BLH often finds the optimal solution, and when it doesn't, the solutions are quite close to optimal.

Robert L. Bulfin

Papers

Optimal Allocation of Redundant Components for Large Systems