A Generalized SNC-BESO Method for Multi-objective Topology Optimization

Multi-objective optimization has become an invaluable tool in engineering design. One class of solutions to the multi-objective optimization problem is known as the Pareto frontier. The Pareto frontier is made up of a group of solutions known as Pareto optimal solutions. These solutions are optimal in the sense that any improvement in one design objective must come with the worsening of at least one other. Therefore, the Pareto frontier plays a vital role in engineering design, since it defines the trade-offs between conflicting objectives. Methods exist that can automatically generate a set of Pareto solutions from which the final design can be chosen. For such an approach to be successful, the generated set must truly be representative of the complete design space. This paper offers a new phase in the development of the smart normal constraint bi-directional evolutionary optimization method, which is a recently developed approach that allows the efficient and effective generation of smart Pareto sets to multi-objective topology optimization problems. Currently, only bi-objective topology optimization problems can be solved with this method. Therefore, in this paper the method is generalized to solve topology optimization problems with any number of objectives. This is demonstrated on an example having three objectives.