Advanced Quantum Annealing for the Bi-Objective Traveling Thief Problem: An $\varepsilon$-Constraint-based Approach

2026-03-13

AI Summary

This work addresses the challenge posed by the strong coupling between route planning and item selection in the bi-objective Traveling Thief Problem (BI-TTP), which hinders the scalability of conventional approaches. To overcome this, the study introduces a novel integration of the ε-constraint method with quantum annealing: by tuning the ε parameter, the bi-objective problem is transformed into a single-objective QUBO model, which is effectively formulated through fractional-term reformulation and auxiliary variables. The resulting model is solved via quantum annealing, followed by a tailored heuristic refinement. Evaluated on standard benchmark instances, the proposed approach significantly outperforms existing baselines, efficiently generating high-quality, diverse Pareto-optimal solutions while effectively expanding the Pareto front and enhancing overall solution efficiency.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Satisfiability
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

This paper addresses the Bi-Objective Traveling Thief Problem (BI-TTP), a challenging multi-objective optimization problem that requires the simultaneous optimization of travel cost and item profit. Conventional methods for the BI-TTP often face severe scalability issues due to the complex interdependence between routing and packing decisions, as well as the inherent complexity and large problem size. These difficulties render classical computing approaches increasingly inapplicable. To tackle this, we propose an advanced hybrid approach that combines quantum annealing (QA) with the $\varepsilon$-constraint method. Specifically, we reformulate the bi-objective problem into a single-objective formulation by restricting the second objective through adjustable $\varepsilon$-levels, determined within established upper and lower bounds. The resulting subproblem involves a sum of fractional terms, which is reformulated with auxiliary variables into an equivalent form. Subsequently, the equivalent formulation is transformed into a Quadratic Unconstrained Binary Optimization (QUBO) model, enabling direct solution via a quantum annealing (QA) solver. The solutions obtained from the quantum annealer are subsequently refined using a tailored heuristic procedure to further enhance overall performance. By leveraging the flexibility in selecting $\varepsilon$ parameters, our approach effectively captures a broad Pareto front, enhancing solution diversity. Experimental results on benchmark instances demonstrate that the proposed method effectively balances two objectives and outperforms baseline approaches in time efficiency.

Problem

• Bi-Objective Traveling Thief Problem
• multi-objective optimization
• scalability
• routing and packing interdependence
• large-scale combinatorial optimization

Innovation

• Quantum Annealing
• ε-constraint method
• QUBO formulation
• Bi-Objective Optimization
• Traveling Thief Problem