Algorithm for Generating the Pareto Optimal Set of Multiobjective Nonlinear Mixed-Integer Optimization Problems

Abstract

In this work we present an algorithm for solving multiobjective mixed-integer nonlinear optimization (MOMINLP) problems. The algorithm generates the complete Pareto optimal set of a given MOMINLP problem within desired numerical accuracy, i.e. an arbitrarily large number of Pareto optima can be obtained. The focus will be on bicriterion problems as we exploit some properties which are peculiar to them. The main idea of the algorithm is to iteratively identify all the discrete variable combinations values for which there exist Pareto optimal points and then to determine the continuous variable values of the Pareto optimal points of each combination. The criterion space is divided into separate search regions, which are explored for minimal points. We will demonstrate this search procedure and apply the method to a structural design problem, where the material volume and a chosen nodal displacement represent strongly conflicting and noncommensurable criteria which should be minimized simultaneously.