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arXiv:2309.04792 · Frontiers in Computer Science

Individual subject evaluated difficulty of adjustable mazes generated using quantum annealing

Yuto Ishikawa, Takuma Yoshihara, Keita Okamura, Masayuki Ohzeki

Published Dec 7, 2023• 7 citations
arXivHTMLPDF

Abstract

In this study, the maze generation using quantum annealing is proposed. We reformulate a standard algorithm to generate a maze into a specific form of a quadratic unconstrained binary optimization problem suitable for the input of the quantum annealer. To generate more difficulty mazes, we introduce an additional cost function Qupdate to increase the difficulty. The difficulty of the mazes was evaluated by the time to solve the maze of 12 human subjects. To check the efficiency of our scheme to create the maze, we investigated the time-to-solution of a quantum processing unit, classical computer, and hybrid solver. The results show that Qupdate generates difficult mazes tailored to the individual. Furthermore, it show that the quantum processing unit is more efficient at generating mazes than other solvers. Finally, we also present applications how our results could be used in the future.

DOI
10.3389/fcomp.2023.1285962

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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 ε\varepsilonε-constraint method. Specifically, we reformulate the bi-objective problem into a single-objective formulation by restricting the second objective through adjustable ε\varepsilonε-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 ε\varepsilonε 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.
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