  Metaheuristics are widely recognized gradient-free solvers to hard problems
that do not meet the rigorous mathematical assumptions of conventional solvers.
The automated design of metaheuristic algorithms provides an attractive path to
relieve manual design effort and gain enhanced performance beyond human-made
algorithms. However, the specific algorithm prototype and linear algorithm
representation in the current automated design pipeline restrict the design
within a fixed algorithm structure, which hinders discovering novelties and
diversity across the metaheuristic family. To address this challenge, this
paper proposes a general framework, AutoOpt, for automatically designing
metaheuristic algorithms with diverse structures. AutoOpt contains three
innovations: (i) A general algorithm prototype dedicated to covering the
metaheuristic family as widely as possible. It promotes high-quality automated
design on different problems by fully discovering potentials and novelties
across the family. (ii) A directed acyclic graph algorithm representation to
fit the proposed prototype. Its flexibility and evolvability enable discovering
various algorithm structures in a single run of design, thus boosting the
possibility of finding high-performance algorithms. (iii) A graph
representation embedding method offering an alternative compact form of the
graph to be manipulated, which ensures AutoOpt's generality. Experiments on
numeral functions and real applications validate AutoOpt's efficiency and
practicability.
