Metaheuristic algorithms for inverse problems

Many inverse problems in engineering can be considered as constrained optimisation, as the aim of inversion is to find the best parameter estimates so as to minimise the differences between the predicted results and the observations while satisfying all known constraints. Such optimisation problems can thus be solved by efficient optimisation techniques. As the number of degrees of freedom is usually very large, metaheuristic algorithms such as Cuckoo Search are particularly suitable for inverse problems, because metaheuristics are very efficient for solving non-linear global optimisation problems. In this paper, we will take a unified approach to inversion and optimisation and introduce a few nature-inspired metaheuristics, including genetic algorithms, differential evolution, firefly algorithm, Cuckoo Search, particle swarm optimisation and their applications in solving inverse problems.