Amplitude-Ensemble Quantum-Inspired Tabu Search Algorithm for Solving 0/1 Knapsack Problems

Konsep Inti

Enhancing QTS with AE-QTS for improved search performance in solving knapsack problems.

Abstrak

In this paper, an enhanced version of the Quantum-inspired Tabu Search (QTS) algorithm is introduced as the "amplitude-ensemble" QTS (AE-QTS). This modification aims to improve the utilization of population information, resembling the Grover Search Algorithm while maintaining algorithm simplicity. The AE-QTS is applied to solve the classical combinatorial optimization 0/1 knapsack problem. Experimental results demonstrate that AE-QTS outperforms other algorithms, including QTS, by an average of 20% and up to 30% in some cases. Even with increasing problem complexity, AE-QTS consistently provides superior solutions compared to QTS. The study highlights that AE-QTS exhibits better search performance and efficiency.
Metaheuristics have been a popular research area due to their ability to solve complex problems like NP-complete and NP-hard problems. Quantum Algorithms have also shown significant advancements, leading researchers to integrate quantum characteristics into metaheuristic algorithms. Among these quantum-inspired algorithms, QEA and QTS are mainly conceived from a quantum perspective. While QEA leans towards traditional population-based thinking, QTS mirrors the Grover Search Algorithm conceptually.
The basic unit of a quantum computer is a qubit, which can exist in superposition states representing infinite information possibilities. Quantum logic gates perform reversible operations using rotation matrices for unitary operations. The 0/1 knapsack problem involves selecting items within weight constraints to maximize profit. Three cases categorize different methods of generating weights and profits for items.
The AE-QTS method expands on QTS by incorporating all explored information into qubits' amplitude adjustments across the entire population of each iteration. Experiments comparing AE-QTS with classical algorithms like GA, TS, DE show superior convergence results with increased efficiency over time. Performance improvements are notable across different item quantities and complexities.
The study concludes that incorporating population concepts from the Grover Search Algorithm into all qubits of AE-QTS enhances search performance compared to QTS. The proposed method maintains simplicity without adding parameters or complexity to existing implementations based on QTS.

Statistik

Experimental results show that AE-QTS outperforms other algorithms by at least an average of 20% in all cases and even by 30% in some cases.

Kutipan

"AE-QTS demonstrates better search performance and efficiency compared to other algorithms."
"Results prove that our method has better search performance."
"The 'amplitude-ensemble' mechanism increases the performance of QTS by approximately 20-30%."

Wawasan Utama Disaring Dari

Amplitude-Ensemble Quantum-Inspired Tabu Search Algorithm for Solving 0/1 Knapsack Problems

by Kuo-Chun Tse... pada arxiv.org 03-19-2024

https://arxiv.org/pdf/2311.12867.pdf

Pertanyaan yang Lebih Dalam

How can quantum-inspired algorithms be further optimized beyond incorporating population concepts

To further optimize quantum-inspired algorithms beyond incorporating population concepts, researchers can explore hybrid approaches that combine quantum computing principles with classical optimization techniques. One approach could involve integrating machine learning algorithms to enhance the adaptability and efficiency of quantum-inspired metaheuristics. By leveraging the strengths of both quantum and classical methods, such hybrid models could potentially achieve superior performance in solving complex problems. Additionally, advancements in hardware technology, such as the development of more powerful quantum processors or specialized hardware accelerators, could significantly boost the computational capabilities of these algorithms.

What potential drawbacks or limitations might arise from relying heavily on quantum characteristics in metaheuristic algorithms

Relying heavily on quantum characteristics in metaheuristic algorithms may introduce certain drawbacks or limitations. One potential limitation is the sensitivity of quantum systems to noise and errors, which can impact the reliability and accuracy of computations. Quantum decoherence and environmental interference pose significant challenges in maintaining coherent superposition states necessary for quantum computation. Moreover, implementing complex quantum operations may require substantial computational resources and expertise, making it challenging for practical applications at scale. Additionally, interpreting results from quantum-inspired algorithms might be inherently probabilistic due to measurement uncertainties inherent in qubit-based calculations.

How can the principles behind quantum computing be applied in unconventional problem-solving scenarios beyond optimization tasks

The principles behind quantum computing can be applied in unconventional problem-solving scenarios beyond traditional optimization tasks by exploring novel domains where parallelism and superposition offer unique advantages. For instance:

Cryptography: Quantum principles like entanglement can revolutionize secure communication protocols by enabling unbreakable encryption through techniques like Quantum Key Distribution.
Drug Discovery: Quantum simulations can model molecular interactions with unprecedented accuracy, accelerating drug discovery processes by predicting compound behaviors more efficiently.
Climate Modeling: Leveraging qubits' ability to represent multiple states simultaneously allows for faster climate modeling simulations that consider a multitude of variables concurrently.
By harnessing these capabilities effectively across diverse fields, innovative solutions to complex real-world problems can be developed using insights from quantum computing principles.