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Data-Efficient Interactive Multi-Objective Optimization Using ParEGO

Arash Heidari, Sebastian Rojas Gonzalez, Tom Dhaene, Ivo Couckuyt

TL;DR

Two novel algorithms that employ Gaussian Processes and advanced discretization methods to efficiently locate the most preferred region of the Pareto front in expensive-to-evaluate problems are proposed.

Abstract

Multi-objective optimization is a widely studied problem in diverse fields, such as engineering and finance, that seeks to identify a set of non-dominated solutions that provide optimal trade-offs among competing objectives. However, the computation of the entire Pareto front can become prohibitively expensive, both in terms of computational resources and time, particularly when dealing with a large number of objectives. In practical applications, decision-makers (DMs) will select a single solution of the Pareto front that aligns with their preferences to be implemented; thus, traditional multi-objective algorithms invest a lot of budget sampling solutions that are not interesting for the DM. In this paper, we propose two novel algorithms that employ Gaussian Processes and advanced discretization methods to efficiently locate the most preferred region of the Pareto front in expensive-to-evaluate problems. Our approach involves interacting with the decision-maker to guide the optimization process towards their preferred trade-offs. Our experimental results demonstrate that our proposed algorithms are effective in finding non-dominated solutions that align with the decision-maker's preferences while maintaining computational efficiency.

Data-Efficient Interactive Multi-Objective Optimization Using ParEGO

TL;DR

Two novel algorithms that employ Gaussian Processes and advanced discretization methods to efficiently locate the most preferred region of the Pareto front in expensive-to-evaluate problems are proposed.

Abstract

Multi-objective optimization is a widely studied problem in diverse fields, such as engineering and finance, that seeks to identify a set of non-dominated solutions that provide optimal trade-offs among competing objectives. However, the computation of the entire Pareto front can become prohibitively expensive, both in terms of computational resources and time, particularly when dealing with a large number of objectives. In practical applications, decision-makers (DMs) will select a single solution of the Pareto front that aligns with their preferences to be implemented; thus, traditional multi-objective algorithms invest a lot of budget sampling solutions that are not interesting for the DM. In this paper, we propose two novel algorithms that employ Gaussian Processes and advanced discretization methods to efficiently locate the most preferred region of the Pareto front in expensive-to-evaluate problems. Our approach involves interacting with the decision-maker to guide the optimization process towards their preferred trade-offs. Our experimental results demonstrate that our proposed algorithms are effective in finding non-dominated solutions that align with the decision-maker's preferences while maintaining computational efficiency.
Paper Structure (7 sections, 5 equations, 2 figures, 3 algorithms)

This paper contains 7 sections, 5 equations, 2 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Proposed Methods
  3. Initialization Phase
  4. Triangulation-based Preferred Region Exploration (TRIPE)
  5. Weight Adjustment for Preferred Region Exploration (WAPE)
  6. Results
  7. Conclusion

Figures (2)

  • Figure 1: Triangulation in a 2-dimensional input space. Circles represent the current solutions, with the red circle indicating the solution chosen by the DM. Crosses represent the candidates generated by triangulation. The red-colored crosses, which are neighbors of the preferred solution, will be evaluated in the next iteration.
  • Figure 2: The OC during optimization for (a) TRIPE and (b) WAPE (c) benchmark Hakanen2017.