Evolutionary Approaches To System Reliability Design

System reliability design (SRD) has attracted many researchers since 1960s due toreliability's critical importance in various kinds of systems, e.g., power systems, electronicsystems, hardware systems, software systems and so on. In recent years, with theincreasing levels of sophistication comprise most engineering systems in the high-techindustrial process, how to design reliable systems has become more and more important.To improving the reliability of a system, we should efficiently solve two main kinds ofproblems, while the first one is the redundancy allocation problem (RAP) and the otherone is testing resource allocation problem (TRAP). In this paper, with evolutionaryalgorithms (EAs), two difficult kinds of RAPs and TRAPs, multi-level RAP (MLRAP)and multi-objective TRAP (MOTRAP) are solved more efficiently.RAP has attracted much attention in the past thirty years due to its range of applicationsin improving the reliability of various engineering systems. In the literature,most studies on RAP have been conducted in the context of single-level systems. However,real-world engineering systems always contain multiple levels, where we havethe overall system at the highest level, subsystems at lower levels and components atthe lowest level. It is very important to study the RAP on multi-level systems, i.e.,multi-level redundancy allocation problem (MLRAP). In the previous work, the efficientlocal search process was lacked. In this paper, to exploit the searching space moreefficiently, we propose a memetic algorithm (MA) for MLRAP. As an emerging areaof evolutionary computation, MAs are population-based meta-heuristic search methodsthat combine global search strategies (e.g., crossover) with local search heuristics.They are reported to not only converge to high quality solutions, but also search moreefficiently than the conventional EAs. In our work, based on the hierarchical genotyperepresentation of the variables, we first propose two breath-first-search genetic operators(breath-first-search crossover operator and breath-first-search mutation operator),and a novel problem-specific local search operator. Then, we incorporate the aboveoperators into the MA framework, and develop a novel MA for MLRAP. Our MA performssignificantly better than the best of other previous algorithms (hierarchical geneticalgorithm, HGA) on existing systems.As the redundancy could be allocated onto each level for MLRAP, the searchingspace is much more larger than the single-level RAP. After analyzing the structure ofthe solutions obtained by the HGA and MA, we could find that the searching process is of both algorithms are focused on a special local area, which means that the globalsearching capacity of both algorithms are not strong enough. As the searching space ishuge for the MLRAP, thus, for MLRAP, the constraint handling capability is the keypoint of the problem solvers, while how to quickly getting into a potential region is thebasis of the global searching capability. To make the searching process more efficiency,we applied a global repair operator (GRO) to each solution which locates outside thepotential region. Through the experimental study, it can be concluded that GRO canimprove the global searching capability of the best of other previous algorithms (hierarchicalgenetic algorithm, HGA). Further, we incorporate the GRO into our MA, the newobtained algorithm is referred to as MA+GRO, which is the most efficient algorithm onthe evaluated systems.After efficiently solving a difficult problem (MLRAP) of the system design, wefocus on the testing resource allocation problem, which is another one of the most importantproblems in system design. In our study, we employed the software systems asthe studied model. Nowadays, as the software systems become increasingly large andcomplex, the problem of how to optimally allocate the limited testing resource duringthe testing phase has become more and more important and difficult. Traditional TRAPsseek to find an optimal allocation of a limited amount of testing resource to a number ofactivities for optimizing the only one objective (reliability or cost) under the resourceconstraint. In our work, we formulate OTRAPs as two multi-objective problems. First,we considered the reliability of the system and the testing cost as two objectives. In thesecond formulation, the total testing resource consumed was also taken into account asthe third goal. Then we adopted a well-known MOEA, namely Nondominated SortingGenetic Algorithm II (NSGA-II), to solve the formulated multi-objective problemson two parallel-series software systems. That was the first time that the OTRAPs areexplicitly formulated as multi-objective optimization problems. However, empirical resultsshowed that NSGA-II does not perform well on the second formulation. Hence,a new algorithm based on NSGA-II, Harmonic Distance Based Multi-Objective EvolutionaryAlgorithm (HaD-MOEA), is further proposed. The advantages of MOEAs overthe state-of-the-art single objectives and the HaD-MOEA over NSGA-II are empiricallydemonstrated on three parallel-series and a star-structure modular software systems.