  Nature-inspired metaheuristic algorithms are important components of
artificial intelligence, and are increasingly used across disciplines to tackle
various types of challenging optimization problems. We apply a newly proposed
nature-inspired metaheuristic algorithm called competitive swarm optimizer with
mutated agents (CSO-MA) and demonstrate its flexibility and out-performance
relative to its competitors in a variety of optimization problems in the
statistical sciences. In particular, we show the algorithm is efficient and can
incorporate various cost structures or multiple user-specified nonlinear
constraints. Our applications include (i) finding maximum likelihood estimates
of parameters in a single cell generalized trend model to study pseudotime in
bioinformatics, (ii) estimating parameters in a commonly used Rasch model in
education research, (iii) finding M-estimates for a Cox regression in a Markov
renewal model and (iv) matrix completion to impute missing values in a two
compartment model. In addition we discuss applications to (v) select variables
optimally in an ecology problem and (vi) design a car refueling experiment for
the auto industry using a logistic model with multiple interacting factors.
