Zigzag Search for Continuous Multiobjective Optimization

Abstract

A new method is proposed using a gradient-based zigzag search approach for multiobjective optimization (MOO) or vector optimization problems. The key idea of this method is searching around the Pareto front by applying an efficient local search procedure using the gradients of the objective functions. This local search zigzags along the Pareto surface guided by the gradients and iteratively returns the visited Pareto optima. Many continuous MOO problems have smooth objective functions and the set of the nondominated objective function values forms a regular surface in the image space. This fact motivates developing the zigzag search method for such relatively well-posed MOO problems. A simple implementation of this method, z-algorithm, is presented particularly for continuous bi-objective optimization (BOO) problems with well-connected Pareto optimal solutions. The efficiency of the z-algorithm is studied with a set of BOO problems and the algorithm performances are compared to those of a recently developed MOO algorithm, Pareto front approximation with adaptive weighted sum method.