Improved cuckoo search for reliability optimization problems

Abstract

An efficient approach to solve engineering optimization problems is the cuckoo search algorithm. It is a recently developed meta-heuristic optimization algorithm. Normally, the parameters of the cuckoo search are kept constant. This may result in decreasing the efficiency of the algorithm. To cope with this issue, the cuckoo search parameters should be tuned properly. In this paper, an improved cuckoo search algorithm, enhancing the accuracy and convergence rate of the cuckoo search algorithm, is presented. Then, the performance of the proposed algorithm is tested on some complex engineering optimization problems. They are four well-known reliability optimization problems, a large-scale reliability optimization problem as well as a complex system, which is a 15-unit system reliability optimization problem. Finally, the results are compared with those given by several well-known methods. Simulation results demonstrate the effectiveness of the proposed algorithm.

Introduction

System reliability optimization plays a vital role in real-world applications and has been studied for decades (Aponte and Sanseverino, 2007, Chen, 2006, Chern and Jan, 1986, Coelho, 2009, Elegbede, 2005, Gen and Kim, 1999, Gen and Yun, 2006, Kuo, 2007, Kuo and Prasad, 2000, Marseguerra et al., 2004, Meziane et al., 2005, Painton and Campbell, 1995, Prasad and Kuo, 2000, Ramirez-Marquez, 2008, Salazar et al., 2006, Yin et al., 2007, Yokota et al., 1996, Zou et al., 2011). To be more competitive in the market, many designers have worked on improving the reliability of manufacturing systems or product components. The reliability problem can usually be formulated as a nonlinear programming problem with several constraints such as cost, weight, and volume. To attain higher system reliability, two main ways are usually used. The first approach is to increase the reliability of system components. It may improve the system reliability to some degree, however, the required reliability enhancement may be never achievable even though the most currently reliable elements are used. The second approach is to use redundant components in different subsystems. By using this method, however, the cost, weight, volume, etc., are also increased. This approach is named reliability redundancy allocation problem (RAP) (Kuo & Prasad, 2000).

In order to cope with optimization problems arising in system reliability, important contributions have been made since 1970 (Prasad & Kuo, 2000). To solve a category of reliability optimization problems with multiple-choice constraints, Chern and Jan (1986) developed a 2-phase solution method. They presented a general model that can be stated as the problem of finding the optimum number of redundancies maximizing the system reliability. Prasad and Kuo (2000) offered a search method (P and K-Algorithm) based on lexicographic order, and an upper bound on the objective function for solving redundancy allocation problems in coherent systems. The main advantages of the P and K-Algorithm are its simplicity and its applicability to a wide range of complex optimization problems arising in system reliability design (Zou et al., 2011). A penalty guided artificial immune algorithm to solve mixed-integer reliability design problems was proposed in (Chen, 2006). To efficiently find the feasible optimal/near optimal solution, it can search over promising feasible and infeasible regions (Zou et al., 2011). Gen and Yun (2006) employed a soft computing approach for solving a variety of reliability optimization problems. To prevent the early convergence situation of its solution, this method combined rough search and local search techniques (Zou et al., 2011). Moreover, several optimization algorithms based on swarm intelligence, such as particle swarm optimization (Coelho, 2009, Elegbede, 2005, Wu et al., 2010, Yin et al., 2007), genetic algorithm (Gen and Kim, 1999, Painton and Campbell, 1995, Marseguerra et al., 2004), evolutionary algorithm (Aponte and Sanseverino, 2007, Salazar et al., 2006, Ramirez-Marquez, 2008), ant colony algorithm (Meziane et al., 2005), harmony search algorithms (HS) (Zou et al., 2010, Zou et al., 2011) and artificial bee colony algorithm (Yeh & Hsieh, 2011), have been employed to solve reliability problems. Kuo (2007) reviewed recent advances in optimal RAP and summarized several techniques.

The Cuckoo Search (CS) developed in 2009 by Yang and Deb, 2009, Yang & Deb, 2010, is a new meta-heuristic algorithm imitating animal behavior. The optimal solutions obtained by the CS are far better than the best solutions obtained by efficient particle swarm optimizers and genetic algorithms (Yang & Deb, 2009). First, an Improved Cuckoo Search (ICS) algorithm for optimization problems is developed. Then, the performance of the proposed algorithm is tested on some complex engineering optimization problems.

The paper is organized as follows. In Section 2, the procedure of cuckoo search algorithm is briefly presented. In Section 3, the improved cuckoo search algorithm is presented. To apply it to reliability optimization problems, some preparation works are done in Section 4. In Section 5, four reliability optimization problems, a large-scale reliability optimization problem as well as a complex system are introduced. In Section 6, a number of simulations are carried out to test the performance and effectiveness of the proposed algorithm in solving complex reliability optimization problems. We end this paper with some conclusions in Section 7.