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Balancing Pareto Front exploration of Non-dominated Tournament Genetic Algorithm (B-NTGA) in solving multi-objective NP-hard problems with constraints

Michał Antkiewicz, Paweł B. Myszkowski

TL;DR

The paper tackles the challenge of efficiently exploring Pareto Fronts in constrained, NP-hard multi- and many-objective optimization by introducing Balanced Non-dominated Tournament Genetic Algorithm (B-NTGA). B-NTGA augments NTGA2 with a balanced, archive-driven Gap Selection mechanism inspired by UCB to focus search on under-explored PF regions while accounting for the exploitation history of PF regions. Through extensive experiments on Travelling Thief Problem and Multi-Skill Resource-Constrained Project Scheduling Problem, B-NTGA consistently achieves superior or competitive Pareto Front approximations (measured by IGD and Purity), particularly in many-objective MS-RCPSP settings, while reducing computational overhead by simplifying selection and avoiding clone elimination. The results indicate that archive-guided, balance-aware PF exploration can significantly improve solution quality and scalability for complex, constrained MO problems, with potential applicability to other MOEAs and domains.

Abstract

The paper presents a new balanced selection operator applied to the proposed Balanced Non-dominated Tournament Genetic Algorithm (B-NTGA) that actively uses archive to solve multi- and many-objective NP-hard combinatorial optimization problems with constraints. The primary motivation is to make B-NTGA more efficient in exploring Pareto Front Approximation (PFa), focusing on 'gaps' and reducing some PFa regions' sampling too frequently. Such a balancing mechanism allows B-NTGA to be more adaptive and focus on less explored PFa regions. The proposed B-NTGA is investigated on two benchmark multi- and many-objective optimization real-world problems, like Thief Traveling Problem and Multi-Skill Resource-Constrained Project Scheduling Problem. The results of experiments show that B-NTGA has a higher efficiency and better performance than state-of-the-art methods.

Balancing Pareto Front exploration of Non-dominated Tournament Genetic Algorithm (B-NTGA) in solving multi-objective NP-hard problems with constraints

TL;DR

The paper tackles the challenge of efficiently exploring Pareto Fronts in constrained, NP-hard multi- and many-objective optimization by introducing Balanced Non-dominated Tournament Genetic Algorithm (B-NTGA). B-NTGA augments NTGA2 with a balanced, archive-driven Gap Selection mechanism inspired by UCB to focus search on under-explored PF regions while accounting for the exploitation history of PF regions. Through extensive experiments on Travelling Thief Problem and Multi-Skill Resource-Constrained Project Scheduling Problem, B-NTGA consistently achieves superior or competitive Pareto Front approximations (measured by IGD and Purity), particularly in many-objective MS-RCPSP settings, while reducing computational overhead by simplifying selection and avoiding clone elimination. The results indicate that archive-guided, balance-aware PF exploration can significantly improve solution quality and scalability for complex, constrained MO problems, with potential applicability to other MOEAs and domains.

Abstract

The paper presents a new balanced selection operator applied to the proposed Balanced Non-dominated Tournament Genetic Algorithm (B-NTGA) that actively uses archive to solve multi- and many-objective NP-hard combinatorial optimization problems with constraints. The primary motivation is to make B-NTGA more efficient in exploring Pareto Front Approximation (PFa), focusing on 'gaps' and reducing some PFa regions' sampling too frequently. Such a balancing mechanism allows B-NTGA to be more adaptive and focus on less explored PFa regions. The proposed B-NTGA is investigated on two benchmark multi- and many-objective optimization real-world problems, like Thief Traveling Problem and Multi-Skill Resource-Constrained Project Scheduling Problem. The results of experiments show that B-NTGA has a higher efficiency and better performance than state-of-the-art methods.
Paper Structure (29 sections, 24 equations, 8 figures, 9 tables, 8 algorithms)

This paper contains 29 sections, 24 equations, 8 figures, 9 tables, 8 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Non-Dominated Sorting Genetic Algorithm II
  4. Unified NSGA-III
  5. $\theta$-DEA
  6. Non-Dominated Tournament Genetic Algorithm 2
  7. Strength Pareto evolutionary algorithm 2
  8. A Multiobjective Evolutionary Algorithm Based on Decomposition
  9. Alternative exploration vs exploitation balancing
  10. The impact of multi-objectivity
  11. Problem Definition
  12. Multi-Skill Resource-Constrained Project Scheduling Problem
  13. Schedule Builder
  14. Travelling Thief Problem
  15. Balanced Non-dominated Tournament Genetic Algorithm
  16. ...and 14 more sections

Figures (8)

  • Figure 1: The example of the ‘‘gap" calculation for two objectives, used by the $Gap$$Selection$ ($GS$)
  • Figure 2: An illustration of oversampling in NTGA2 vs. B-NTGA [used: MS-RCPSP instance 200_10_84_9]
  • Figure 3: Summary of results for multi-objective TTP using Purity
  • Figure 4: Two examples of PFa for TTP instances -- with sparse (a) and dense (b) PFa.
  • Figure 5: Results for multi-objective MS-RCPSP (2obj) using Purity
  • ...and 3 more figures