Global optimization via neural network approximation of inverse coordinate mappings with evolutionary parameter control

A hybrid method of global optimization NNAICM-PSO is presented. It uses neural network approximation of inverse mappings of objective function values to coordinates combined with particle swarm optimization to find the global minimum of a continuous objective function of multiple variables with bound constraints. The objective function is viewed as a black box.
The method employs groups of moving probe points attracted by goals like in particle swarm optimization. One of the possible goals is determined via mapping of decreased objective function values to coordinates by modified Dual Generalized Regression Neural Networks constructed from probe points.
The parameters of the search are controlled by an evolutionary algorithm. The algorithm forms a population of evolving rules each containing a tuple of parameter values. There are two measures of fitness: short-term (charm) and long-term (merit). Charm is used to select rules for reproduction and application. Merit determines survival of an individual. This two-fold system preserves potentially useful individuals from extinction due to short-term situation changes.
Test problems of 100 variables were solved. The results indicate that evolutionary control is better than random variation of parameters for NNAICM-PSO. With some problems, when rule bases are reused, error progressively decreases in subsequent runs, which means that the method adapts to the problem.