Pareto Front Identification via Objective Vector Jacobian Matrix Singularity

This paper presents a method to identify the exact Pareto front for a multi-objective optimization problem. The developed technique addresses the identification of the Pareto frontier in the cost space and the Pareto set in the design space for both constrained and unconstrained optimization problems. The proposed approach identifies a n – 1 dimensional hypersurface for a multi-objective problem with n cost functions, a subset of which constitute the Pareto front. The n – 1 dimensional hypersurface is identified by enforcing a singularity constraint on the Jacobian of the cost vector with respect to the optimization parameters. Since the boundary is identified in the design space, the relation of design points to the exact Pareto front in the cost space is known. The proposed method is proven effective in the Pareto identification for a set of previously released challenge problems. Six of these examples are included in this paper; 3 unconstrained and 3 constrained.

Evaluated Preference Genetic Algorithm and its Engineering Applications

This paper proposes a novel multiobjective genetic algorithm (MOGA), Evaluated Preference Genetic Algorithm (EPGA), for efficiently solving engineering multiobjective optimization problems. EPGA utilizes a preferred objective vector to perform a fast multiobjective ranking schema within a low computation complexity O(MNlogN) where N is the size of genetic population and M is the number of objectives. For verifying the proposed algorithms, this paper studies two engineering problems in which multiple mutual-conflicted objectives should be considered. According to the experimental results, the proposed EPGA can efficiently explore the Pareto front and provide very good solution capabilities for the engineering optimization problems.