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A well-regarded as well as powerful method named the ‘analytic hierarchy process’ (AHP) uses mathematics and psychology for making and analysing complex decisions. This article aims to present a brief review of the consistency measure of the judgments in AHP. Judgments should not be random or illogical. Several researchers have developed different consistency measures to identify the rationality of judgments. This article summarises the consistency measures which have been proposed so far in the literature. Moreover, this paper describes briefly the functional relationships established in the literature among the well-known consistency indices. At last, some thoughtful research directions that can be helpful in further research to develop and improve the performance of AHP are provided as well.

For the past two decades, nature-inspired optimization algorithms have gained enormous popularity among the researchers. On the other hand, complex system reliability optimization problems, which are nonlinear programming problems in nature, are proved to be non-deterministic polynomial-time hard (NP-hard) from a computational point of view. In this work, few complex reliability optimization problems are solved by using a very recent nature-inspired metaheuristic called gray wolf optimizer (GWO) algorithm. GWO mimics the chasing, hunting, and the hierarchal behavior of gray wolves. The results obtained by GWO are compared with those of some recent and popular metaheuristic such as the cuckoo search algorithm, particle swarm optimization, ant colony optimization, and simulated annealing. This comparative study shows that the results obtained by GWO are either superior or competitive to the results that have been obtained by these well-known metaheuristic mentioned earlier.SA =simulated annealing; GA = genetic algorithm; TS = tabu search; PSO = particle swarm optimization; CSA = cuckoo search algorithm; DP = dynamic programming.A. KUMAR, S. PANT AND M. RAM