In this study, a hybrid genetic algorithm/neural network with fuzzy logic controller (NN-flcGA) is proposed to find the global optimum of reliability assignment/redundant allocation problems which should be simultaneously determined two different types of decision variables. Several researchers have obtained acceptable and satisfactory results using genetic algorithms for optimal reliability assignment/redundant allocation problems during the past decade. For large-size problems, however, genetic algorithms have to enumerate numerous feasible solutions due to the broad continuous search space. Recently, a hybridized GA combined with a neural network technique (NN-hGA) has been proposed to overcome this kind of difficulty. Unfortunately, it requires a high computational cost though NN-hGA leads to a robuster and steadier global optimum irrespective of the various initial conditions of the problems. The efficacy and efficiency of the NN-flcGA is demonstrated by comparing its results with those of other traditional methods in numerical experiments. The essential features of NN-flcGA namely, 1) its combination with a neural network (NN) technique to devise initial values for the GA, 2) its application of the concept of a fuzzy logic controller when tuning strategy GA parameters dynamically, and 3) its incorporation of the revised simplex search method, make it possible not only to improve the quality of solutions but also to reduce computational cost.

The redundancy allocation problem for a series-parallel system is a well known as one of NP-hard combinatorial problems and it generally belongs to the class of nonlinear integer programming (nIP) problem. Many researchers have developed the various methods which can be roughly categorized into exact solution methods, approximate methods, and heuristic methods. Though each method has both advantages and disadvantage, the heuristic methods have been received much attention since other methods involve more computation effort and usually require larger computer memory. Genetic algorithm (GA) as one of heuristic optimization techniques is a robust evolutionary optimization search technique with very few restrictions concerning with the various design problems. However, GAs cannot guarantee the optimality and sometimes can suffer from the premature convergence situation of its solution, because it has some unknown parameters and it neither uses a priori knowledge nor exploits the local search information. To improve these problems in GA, this paper proposes an effective hybrid genetic algorithm based on, 1) fuzzy logic controller (FLC) to automatically regulate GA parameters and 2) incorporation of the iterative hill climbing method to perform local exploitation around the near optimum solution for solving redundancy allocation problem. The effectiveness of this proposed method is demonstrated by comparison results with other conventional methods on two different types of redundancy allocation problems.

In this paper, we examine an optimal reliability assignment/redundant allocation problem formulated as a nonlinear mixed integer programming (nMIP) model which should simultaneously determine continuous and discrete decision variables. This problem is more difficult than the redundant allocation problem represented by a nonlinear integer problem (nIP). Recently, several researchers have obtained acceptable and satisfactory results by using genetic algorithms (GAs) to solve optimal reliability assignment/redundant allocation problems. For large-scale problems, however, the GA has to enumerate a vast number of feasible solutions due to the broad continuous search space. To overcome this difficulty, we propose a hybridized GA combined with a neural-network technique (NN-hGA) which is suitable for approximating optimal continuous solutions. Combining a GA with the NN technique makes it easier for the GA to solve an optimal reliability assignment/redundant allocation problem by bounding the broad continuous search space by the NN technique. In addition, the NN-hGA leads to optimal robustness and steadiness and does not affect the various initial conditions of the problems. Numerical experiments and comparisons with previous results demonstrate the efficiency of our proposed method.