A Method for Integration of Preferences to a Multi-Objective Evolutionary Algorithm Using Ordinal Multi-Criteria Classification

Alejandro Castellanos-Alvarez,Nelson Rangel-Valdez,Hector Fraire,Laura Cruz-Reyes,Eduardo Fernandez,José Alfredo Brambila-Hernández,Claudia Gómez-Santillán

doi:10.3390/mca26020027

Abstract

Most real-world problems require the optimization of multiple objective functions simultaneously, which can conflict with each other. The environment of these problems usually involves imprecise information derived from inaccurate measurements or the variability in decision-makers’ (DMs’) judgments and beliefs, which can lead to unsatisfactory solutions. The imperfect knowledge can be present either in objective functions, restrictions, or decision-maker’s preferences. These optimization problems have been solved using various techniques such as multi-objective evolutionary algorithms (MOEAs). This paper proposes a new MOEA called NSGA-III-P (non-nominated sorting genetic algorithm III with preferences). The main characteristic of NSGA-III-P is an ordinal multi-criteria classification method for preference integration to guide the algorithm to the region of interest given by the decision-maker’s preferences. Besides, the use of interval analysis allows the expression of preferences with imprecision. The experiments contrasted several versions of the proposed method with the original NSGA-III to analyze different selective pressure induced by the DM’s preferences. In these experiments, the algorithms solved three-objectives instances of the DTLZ problem. The obtained results showed a better approximation to the region of interest for a DM when its preferences are considered.

Highlights

Many industrial domains are concerned with multi-objective optimization problems (MOPs), which in general have conflicting objectives to handle [1]
MOPs with metaheuristics, like multi-objective evolutionary algorithms (MOEAs); they obtain an approximation of the Pareto optimal set
We propose a new method to integrate the DM’s preferences to NSGA-III, which can deal with many objectives and is based on non-dominated fronts’ ordering

Summary

Introduction

Many industrial domains are concerned with multi-objective optimization problems (MOPs), which in general have conflicting objectives to handle [1]. A MOPs is to find a set of solutions defined as Pareto optimal solutions. They represent the best compromise between the conflicting objectives. MOPs with metaheuristics, like multi-objective evolutionary algorithms (MOEAs); they obtain an approximation of the Pareto optimal set. The decision-maker (DM) has to choose the best compromise solution, which satisfies his preferences, from the set of solutions obtained (non-dominated by each other)

Objectives

Methods

Results

Conclusion