Structured Pareto Front Representation

Makowski, M. ORCID: https://orcid.org/0000-0002-6107-0972, Granat, J., Nahorski, Z., Shekhovtsov, A., Ren, H., & Zhao, J. (2026). Structured Pareto Front Representation. Zenodo 10.5281/zenodo.19704566. (In Press)

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Abstract

The paper presents a novel methodology for autonomous generation of the Pareto-Front Representation (PFR) of Linear Programming (LP) models. Following the Structured Modeling principles, the developed approach supports multiple-criteria analysis of independently developed diverse LP models.

The analysis is done by seamless linkage with the dedicated implementation of reusable Multiple Objective Programming (MOP) model, which represents the developed method of PFR's generation. The MOP is a small LP model, therefore the linked models are optimized by an LP solver.

The methodology enables autonomous (i.e., parametrization-free) generation of a sequence of single-objective LP optimization tasks, each providing a Pareto-efficient solution that improves the PFR distribution in terms of the distances between neighbor Pareto solutions.

Furthermore, the method's recent enhancement by the structured PFR generation has two key advantages: it dramatically decreases the computation time, and
it substantially improves the distribution of the PFR's elements. Moreover, the method properly and efficiently computes the extreme points of the~PF also when optimization of a~criterion has non-unique solution.

The approach supports objective Multiple Criteria Model Analysis (MCMA), i.e., equitable treatment of all criteria in the whole space of Pareto solutions. The paper provides examples of research projects in various fields of science, which required effective support for generation of preference-free PFR. Such analysis is also helpful for preference-guided MCMA because the provided PFR clusters are a good starting point for exploration of diverse Regions of Interest (ROI) based on diverse simultaneously reachable goals for conflicting criteria.

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