Generalized homotopy approach to multiobjective optimization

摘要: This paper proposes a new generalized homotopy algorithm for the solution of multiobjective optimization problems with equality constraints. We consider set Pareto candidates as differentiable manifold and construct local chart which is fitted to geometry this manifold. New are generated by evaluating numerically. The method capable solving an arbitrary number k objectives, makes it possible generate all types optimal solutions, able produce homogeneous discretization set. gives necessary sufficient condition form (k-1)-dimensional manifold, provides numerical details proposed algorithm, applies two sample problems.