Cellular Gradient Algorithm for Solving Complex Mechanical Optimization Design Problems

Abstract

In mechanical optimization design problems, there are often some non-continuous or non-differentiable objective functions. For these non-continuous and non-differentiable optimization objectives, it is often difficult for existing optimal design algorithms to find the desired optimal solutions. In this paper, we incorporate the idea of gradient descent into cellular automata and propose a Cellular Gradient (CG) method. First, we have given the basic rules and algorithmic framework of CG and designed three kinds of growth and extinction rules respectively. Then, the three evolutionary rules for cellular within a single cycle are analyzed separately for form and ordering. The best expressions for the cellular jealous neighbor rule and the solitary regeneration rule are given, and the most appropriate order in which the rules are run is selected. Finally, the solution results of the cellular gradient algorithm and other classical optimization design algorithms are compared with a multi-objective multi-parameter mechanical optimization design problem as an example. The computational results show that the cellular gradient algorithm has an advantage over other algorithms in solving global and dynamic mechanical optimal design problems. The novelty of CG is to provide a new way of thinking for solving optimization problems with global discontinuities.