Abstract: Aiming at the problem of  the high computational cost of fitness in traditional genetic algorithms for complex high-dimensional optimization problems, we proposed an improved genetic algorithm Gamma based on manifold learning and multiple linear regression.  The Gamma algorithm reduced the  dimensionality of  the population data through manifold learning, and combined AP clustering with a multiple linear regression model to reduce the calculation times of fitness function and improve algorithm optimization efficiency. Experimental results show that the Gamma algorithm achieves optimization results similar to traditional methods with fewer fitness calls in complex engineering such as the optimization of truss dome structures and multiple  classic Benchmark functions. It has a  promising application prospect in handling with complex high-dimensional optimization problems, effectively enhancing computational efficiency and reducing time costs.

Key words: genetic algorithm, manifold learning, surrogate model, complex optimization problem