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International Journal of Combinatorial Optimization Problems and Informatics.

A Quantum Inspired Particle Swarm Algorithm for Solving the Maximum Satisfiability Problem

Abdesslem Layeb

Published Feb 5, 2010• 6 citations
OpenAlex

Abstract

Abstract. In this paper we investigate the use of quantum particle swarm optimization (QPSO) principles to resolve the satisfiability problem. We describe QPSOSAT, a new iterative approach for solving the well known Maximum Satisfiability problem (MAX-SAT). This latter has been shown to be NP-hard if the number of variables per clause is greater than 3. The basic idea is to harness the optimization capabilities of QPSO algorithm to achieve good quality solutions for Max Sat problem. To enhance the efficiency of the QPSO algorithm, a local search has been used. The obtained results are very promising and show the feasibility and effectiveness of the proposed hybrid approach.

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Abstract. In this paper we investigate the use of quantum particle swarm optimization (QPSO) principles to resolve the satisfiability problem. We describe QPSOSAT, a new iterative approach for solving the well known Maximum Satisfiability problem (MAX-SAT). This latter has been shown to be NP-hard if the number of variables per clause is greater than 3. The basic idea is to harness the optimization capabilities of QPSO algorithm to achieve good quality solutions for Max Sat problem. To enhance the efficiency of the QPSO algorithm, a local search has been used. The obtained results are very promising and show the feasibility and effectiveness of the proposed hybrid approach.
Abstract: In this paper, we present a new framework for combining complete and incomplete methods in order to deal with the Max Sat problem. The objective is to find the best assignment for a set of Boolean variables, which gives the maximum of verified clauses in a Boolean formula. Unfortunately, this problem has been shown to be NP-hard (non-deterministic polynomial-time hard) if the number of variables per clause is greater than 3. The proposed approach is based on quantum inspired genetic principles and the well known exact algorithm DPLL. The underlying idea is to harness the optimization capabilities of quantum genetic algorithm to achieve good quality solutions for Max SAT problem. A new local search based on DPLL algorithm has been embodied in the quantum genetic algorithm leading to an efficient hybrid framework which achieves better balance between diversification and intensification search. The obtained results are very encouraging and show the feasibility and effectiveness of the proposed hybrid approach.
In this paper a new optimization algorithm named Adaptive Hybrid Quantum-Inspired Optimization Algorithm (AHQSOA) is presented for solving the complex optimization problems effectively. Stochastic traditional algorithms typically fail to come to be stuck in local optimum solutions and they need quite few iterations for converging. Our method integrates two quantum-inspired methodology: Quantum Particle Swarm Optimization (QPSO) for searching a large set solutions based on properties of quantum mechanics - superposition, point are located as randomly as possible, and Quantum Evolutionary Algorithms (QEA) for refining potential solutions by mutation and crossover operation. An adaptive tuning component based on the reinforcement learning dynamically adjusts the algorithm’s parameters, thus balancing the exploration in the wide interval and exploitation in the precise interval. Assessed on the commonly used benchmark functions like Sphere, Rosenbrock, Rastrigin, AHQSOA exhibits faster convergence (only 400 iterations in comparison to 1200 in standard methods), global search superiority (94% whereas 75–87% the traditional methods), and low computational simplicity. These results show all of our algorithm are nicer and faster and more efficient and robust makes for it a good candidate as for high dimensional and complex optimization problems.
Quantum-inspired algorithms (QIAs) are computationally efficient algorithms that generate a quantum model in classical hardware as an alternative to the use of quantum models. In this research paper, the researchers carried out an experimental appraisal of four quantum-inspired algorithms in quantum-inspired Evolutionary Algorithm (QEA), quantum-behaved Particle Swarm Optimization (QPSO), quantum-inspired Genetic Algorithm (QIGA) and quantum Simulated Annealing (QSA) on benchmark optimization functions. The introduction of a simulation-based methodology was done in Python to test the convergence speed, global search capability, accuracy and robustness. According to the experimental findings, QPSO always performs well compared with other methods in the achievement of faster convergence and enhanced global optimality, but QEA is highly successful in cases of discrete combinatorial problems. The paper concludes that quantum-inspired models are effective in modeling the key quantum concepts like probabilistic superposition and tunneling to attain high quality optimization results with conventional computing platforms. Such results demonstrate the opportunities of QIAs as scalable pre-quantum tools of designing, AI, and industrial optimization.
An improved quantum-inspired evolutionary algorithm is presented in this paper. Quantum angle is adopted to present the quantum bit in the proposed algorithm. A novel quantum rotation gate strategy is adopted to adjust the direction of the quantum gate which is used to update the quantum population. The step size is adaptively adjusted rather than a fixed angle. Furthermore, the particle swarm optimization is added into the improved algorithm to accelerate the convergent speed and develop the local searching ability. To demonstrate the effectiveness and applicability of the proposed approach, several experiments are performed on the 3-SAT problems. The results show that it is feasible and effective to solve the 3-SAT problem using the proposed algorithm.
Satisfiability (SAT) problem in engineering and computer science is to find the set of assignment values of input variables for the given Boolean function that evaluate this function to TRUE or prove that such satisfying values do not exist. For POS SAT Problem, we propose a novel quantum algorithm for the maximum satisfiability (MAX-SAT) which returns the maximum number of OR terms that are satisfied for the SAT-unsatisfiable function, providing us with the information how far the given Boolean function is from the SAT satisfaction. We use Grover's algorithm with a new block called quantum counter in the oracle circuit.
The K-SAT problem is a fundamental challenge in computational theory, widely used in artificial intelligence, cryptography, and optimization. Classical algorithms struggle with exponential time complexity, making them inefficient for large-scale instances. In this research, we propose an efficient quantum computing approach based on Grover’s algorithm to enhance the search process for satisfiable solutions in K-SAT problems. Our implementation leverages quantum superposition and amplitude amplification to explore multiple possible solutions simultaneously, reducing the search complexity from O (2ⁿ) in classical methods to O(√2ⁿ) in quantum computing. We design a quantum oracle that encodes the K-SAT clauses and integrates it into Grover’s iterative search framework. The performance is evaluated through Qiskit simulations, demonstrating a significant improvement in search efficiency compared to classical brute-force techniques. The results highlight the potential of quantum algorithms in solving complex combinatorial problems with enhanced speed and accuracy. This study contributes to the development of quantum-accelerated optimization methods, paving the way for real-world applications in machine learning, cryptanalysis, and large-scale data processing.