  Many real world optimization problems are formulated as mixed-variable
optimization problems (MVOPs) which involve both continuous and discrete
variables. MVOPs including dimensional variables are characterized by a
variable-size search space. Depending on the values of dimensional variables,
the number and type of the variables of the problem can vary dynamically. MVOPs
and variable-size MVOPs (VMVOPs) are difficult to solve and raise a number of
scientific challenges in the design of metaheuristics. Standard metaheuristics
have been first designed to address continuous or discrete optimization
problems, and are not able to tackle (V)MVOPs in an efficient way. The
development of metaheuristics for solving such problems has attracted the
attention of many researchers and is increasingly popular. However, to our
knowledge there is no well established taxonomy and comprehensive survey for
handling this important family of optimization problems.
  This paper presents a unified taxonomy for metaheuristic solutions for
solving (V)MVOPs in an attempt to provide a common terminology and
classification mechanisms. It provides a general mathematical formulation and
concepts of (V)MVOPs, and identifies the various solving methodologies than can
be applied in metaheuristics. The advantages, the weaknesses and the
limitations of the presented methodologies are discussed. The proposed taxonomy
also allows to identify some open research issues which needs further in-depth
investigations.
