A scalable, black-box hybrid genetic algorithm for continuous multimodal optimization in moderate dimensions

Sammendrag

Optimization problems can be found in many areas of science
and technology. Not only the global optimum, but also a
(large) number of near-optima are often of interest. This
gives rise to what are referred to as multimodal optimization
problems. In most cases, the number and quality of the optima
are unknown and assumptions cannot be made about the
objective functions. In this paper, we focus on continuous,
unconstrained optimization in moderately high-dimensional
continuous spaces (d ≤ 10).
We present a scalable
algorithm with virtually no parameters, which performs well
for general objective functions (non-convex, discontinuous).
It is based on two well-established algorithms (CMA-ES,
deterministic crowding). Novel elements of the algorithm
include the detection of seed points for local searches and
collision avoidance, both based on nearest neighbors, and a
strategy for semi-sequential optimization to realize scalability.
The performance of the proposed algorithm is numerically
evaluated using the CEC2013 niching benchmark suite for
1 − 20 dimensional functions, and a 9 dimensional real-world
problem from constraint optimization in climate research.
The algorithm performs well in relation to the CEC2013
benchmarks and only falls short on higher dimensional and
strongly inisotropic problems. In the case of the climate-
related problem, the algorithm is able to find a high number
(> 150) of optima of relevance to climate research. The
proposed algorithm does not require special configuration for
the optimization problems considered in this paper, i.e., it
shows good black-box behavior.