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A Quantum Framework for combinatorial optimization problem over Graphs

DATA SCIENCE AND ENGINEERING 2025年 1-12页

作者： Shi, Meng Wu, Sai Li, Ying Yuan, Gongsheng Yao, Chang Chen, Gang Bangsun Technol Hangzhou Zhejiang Peoples R China

combinatorial optimization problems over graphs, such as the traveling salesman problem, longest path problem, and maximum independent set problem, are well-known for being computationally costly, some even NP-hard problems. In this paper, we propose a general quantum algorithm framework searching for approximate solutions to combinatorial optimization problems with linear objective functions. Our framework provides APIs (application programming interfaces) that enable developers to encode weighted graph structures onto quantum circuits and utilize variational algorithms to generate approximate solutions. One key advantage of our framework is that it allows developers to design new graph algorithms for the graph problem represented as linear combinations of edge weights without requiring expertise in quantum programming. Besides, it only uses a logarithmic level of quantum bit scale, making our framework work on quantum computers with limited physical resources. Our experimental results demonstrate that our framework can provide good approximations for the traveling salesman problem compared to current quantum algorithm.

关键词： Quantum computing Variational quantum algorithms combinatorial optimization problem Traveling salesman problem

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A deterministic annealing algorithm for a combinatorial optimization problem using replicator equations

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PHYSICA D-NONLINEAR PHENOMENA 2001年第3期149卷 161-173页

作者： Tsuchiya, K Nishiyama, T Tsujita, K Kyoto Univ Grad Sch Engn Dept Aeronaut & Astronaut Kyoto 6068501 Japan

We have proposed an optimization method for a combinatorial optimization problem using replicator equations. To improve the solution further, a deterministic annealing algorithm may be applied. During the annealing process, bifurcations of equilibrium solutions will occur and affect the performance of the deterministic annealing algorithm. In this paper, the bifurcation structure of the proposed model is analyzed in detail. It is shown that only pitchfork bifurcations occur in the annealing process, and the solution obtained by the annealing is the branch uniquely connected with the uniform solution. It is also shown experimentally that in many cases, this solution corresponds to a good approximate solution of the optimization problem. Based on the results, a deterministic annealing algorithm is proposed and applied to the quadratic assignment problem to verify its performance. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： combinatorial optimization problem replicator equation bifurcation deterministic annealing algorithm

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An improved ant colony optimization algorithm for solving a complex combinatorial optimization problem

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APPLIED SOFT COMPUTING 2010年第2期10卷 653-660页

作者： Yang, Jingan Zhuang, Yanbin Hefei Univ Technol Sch Comp & Informat Sci Inst Artificial Intelligence Hefei 230009 Anhui Peoples R China Changhzou Key Lab Software Technol & Applicat Changzhou 213002 Jiangsu Peoples R China Changzhou Inst Technol Sch Comp & Informat Engn Changzhou 213002 Jiangsu Peoples R China

This paper presents an improved ant colony optimization algorithm (IACO) for solving mobile agent routing problem. The ants cooperate using an indirect form of communication mediated by pheromone trails of scent and find the best solution to their tasks guided by both information (exploitation) which has been acquired and search (exploration) of the new route. Therefore the premature convergence probability of the system is lower. The IACO can solve successfully the mobile agent routing problem, and this method has some excellent properties of robustness, self-adaptation, parallelism, and positive feedback process owing to introducing the genetic operator into this algorithm and modifying the global updating rules. The experimental results have demonstrated that IACO has much higher convergence speed than that of genetic algorithm (GA), simulated annealing (SA), and basic ant colony algorithm, and can jump over the region of the local minimum, and escape from the trap of a local minimum successfully and achieve the best solutions. Therefore the quality of the solution is improved, and the whole system robustness is enhanced. The algorithm has been successfully integrated into our simulated humanoid robot system which won the fourth place of RoboCup2008 World Competition. The results of the proposed algorithm are found to be satisfactory. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Ant colony optimization combinatorial optimization problem Mobile agent routing problem Premature convergence probability Traveling salesman problems Simulated annealing

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A new search method for combinatorial optimization problem inspired by the spin glass system

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International Congress Series 2006年 1291卷 201-204页

作者： Wakuya, Hiroshi Faculty of Science and Engineering Saga University Saga 840-8502 Honjo-machi Japan

A Hopfield network is a good tool for solving combinatorial optimization problems. Since its proposal, research activity around this area has been accelerated with the help of related ideas. But some of them are just techniques to get better solutions, so no meaningful phenomena might be observed in the field of the actual spin glass. In this paper, therefore, another search method inspired from an analogy between the Hopfield network and the spin glass is proposed. It is quite a simple idea to control a threshold of the Hopfield network corresponding to a magnetic field in the spin glass. In order to confirm its effectiveness, an N queens problem is adopted. As a result, it is found experimentally that the proposed method shows better score, e.g. a ratio of correct answer and an averaged final energy, than the conventional one. © 2006 Elsevier B.V. All rights reserved.

关键词： combinatorial optimization problem Hopfield network N queens problem Spin glass Virtual magnetic diminuendo method

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Binary Encoding Differential Evolution with Application to combinatorial optimization problem

Binary Encoding Differential Evolution with Application to C...

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Chinese Intelligent Automation Conference (CIAC)

作者： Deng, Changshou Zhao, Bingyan Yang, Yanlin Zhang, Hai Jiujiang Univ Sch Informat Sci & Technol Jiujiang Jiangxi Peoples R China

ISBN: (纸本)9783642384608;9783642384592

Differential Evolution algorithm is a new competitive heuristic optimization algorithm in the continuous field. The operators in the original Differential Evolution are simple;however, these operators make it impossible to use the Differential Evolution in the binary space directly. Based on the analysis of problems led by the mutation operator of the original Differential Evolution in the binary space, a new mutation operator was proposed to enable this optimization technique can be used in binary space. The new mutation operator, which is called semi-probability mutation operator, is a combination of the original mutation operator and a new probability-based defined operator. Initial experimental results of two different combinatorial optimization problems show its effectiveness and validity.

关键词： combinatorial optimization problem Differential evolution Binary encoding Semi-probability mutation operator

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Binary Cockroach Swarm optimization for combinatorial optimization problem

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ALGORITHMS 2016年第3期9卷 59-59页

作者： Obagbuwa, Ibidun Christiana Abidoye, Ademola Philips Univ KwaZulu Natal Sch Management Informat Technol & Governance ZA-4000 Durban South Africa Univ South Africa Sch Comp ZA-1710 Johannesburg South Africa

The Cockroach Swarm optimization (CSO) algorithm is inspired by cockroach social behavior. It is a simple and efficient meta-heuristic algorithm and has been applied to solve global optimization problems successfully. The original CSO algorithm and its variants operate mainly in continuous search space and cannot solve binary-coded optimization problems directly. Many optimization problems have their decision variables in binary. Binary Cockroach Swarm optimization (BCSO) is proposed in this paper to tackle such problems and was evaluated on the popular Traveling Salesman problem (TSP), which is considered to be an NP-hard combinatorial optimization problem (COP). A transfer function was employed to map a continuous search space CSO to binary search space. The performance of the proposed algorithm was tested firstly on benchmark functions through simulation studies and compared with the performance of existing binary particle swarm optimization and continuous space versions of CSO. The proposed BCSO was adapted to TSP and applied to a set of benchmark instances of symmetric TSP from the TSP library. The results of the proposed Binary Cockroach Swarm optimization (BCSO) algorithm on TSP were compared to other meta-heuristic algorithms.

关键词： evolutionary algorithms swarm intelligence continuous search space binary search space transfer function traveling salesman problem combinatorial optimization problem

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Binary Encoding Differential Evolution with Application to combinatorial optimization problem

Binary Encoding Differential Evolution with Application to C...

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2013年中国智能自动化学术会议

作者： Changshou Deng Bingyan Zhao Yanlin Yang Hai Zhang School of Information Science and Technology Jiujiang University

Differential Evolution algorithm is a new competitive heuristic optimization algorithm in the continuous *** operators in the original Differential Evolution are simple;however,these operators make it impossible to use the Differential Evolution in the binary space *** on the analysis of problems led by the mutation operator of the original Differential Evolution in the binary space,a new mutation operator was proposed to enable this optimization technique can be used in binary *** new mutation operator,which is called semi-probability mutation operator,is a combination of the original mutation operator and a new probability-based defined *** experimental results of two different combinatorial optimization problems show its effectiveness and validity.

关键词： combinatorial optimization problem Differential evolution Binary encoding Semi-probability mutation operator

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Building "problem solving engines" for combinatorial optimization problems

Building "problem solving engines" for combinatorial optimiz...

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International Conference on Informatics Research for Development of Knowledge Society Infrastructure

作者： Ibaraki, T Kyoto Univ Grad Sch Informat Kyoto 6068501 Japan

ISBN: (纸本)0769521509

We describe in this paper our attempts to build problem solving engines that together cover a large portion of combinatorial optimization problems encountered in real world applications. Our approach is to select a list of standard problems, and develop their solvers as engines. All the engines we developed are based on the idea of local search and metaheuristics. As standard problems, we have chosen so far CSP (constraint satisfaction problem), RCPSP (recource constrained project scheduling problem), GAP (generalized assignment problem), VRP (vehicle routing problem), SCP (set covering problem), MAX-SAT (maximum satisfiability problem), 2PP (2-dimensional packing problem) and others. In this paper we outline definitions of these problems, algorithmic contents of engines, and some computational results, putting emphasis on RCPSP and VRR.

关键词： problem solving optimisation computability computational complexity real-time systems combinatorial mathematics problem solving engines combinatorial optimization problem real world application local search metaheuristics constraint satisfaction problem recourse constrained project scheduling problem generalized assignment problem vehicle routing problem set covering problem maximum satisfiability problem 2-dimensional packing problem

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The bandpass problem: combinatorial optimization and library of problems

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JOURNAL OF combinatorial optimization 2009年第2期18卷 151-172页

作者： Babayev, Djangir A. Bell, George I. Nuriyev, Urfat G. Cox Associates Boulder CO 80301 USA Tech X Corp Boulder CO 80303 USA Ege Univ Dept Math Izmir Turkey

A combinatorial optimization problem, called the Bandpass problem, is introduced. Given a rectangular matrix A of binary elements {0,1} and a positive integer B called the Bandpass Number, a set of B consecutive non-zero elements in any column is called a Bandpass. No two bandpasses in the same column can have common rows. The Bandpass problem consists of finding an optimal permutation of rows of the matrix, which produces the maximum total number of bandpasses having the same given bandpass number in all columns. This combinatorial problem arises in considering the optimal packing of information flows on different wavelengths into groups to obtain the highest available cost reduction in design and operating the optical communication networks using wavelength division multiplexing technology. Integer programming models of two versions of the bandpass problems are developed. For a matrix A with three or more columns the Bandpass problem is proved to be NP-hard. For matrices with two or one column a polynomial algorithm solving the problem to optimality is presented. For the general case fast performing heuristic polynomial algorithms are presented, which provide near optimal solutions, acceptable for applications. High quality of the generated heuristic solutions has been confirmed in the extensive computational experiments. As an NP-hard combinatorial optimization problem with important applications the Bandpass problem offers a challenge for researchers to develop efficient computational solution methods. To encourage the further research a Library of Bandpass problems has been developed. The Library is open to public and consists of 90 problems of different sizes (numbers of rows, columns and density of non-zero elements of matrix A and bandpass number B), half of them with known optimal solutions and the second half, without.

关键词： Bandpass problem combinatorial optimization problem Binary integer programming model NP-hard problem Heuristic polynomial algorithms Library of problems

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A power optimization approach for mixed polarity Reed–Muller logic circuits based on multi-strategy fusion memetic algorithm

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Frontiers of Information Technology & Electronic Engineering 2025年第3期26卷 415-426页

作者： Mengyu ZHANG Zhenxue HE Yijin WANG Xiaojun ZHAO Xiaodan ZHANG Limin XIAO Xiang WANG Intelligent griculturalquipment RearchInstitute Hebei Agricultural UniverityBaoding 071001China Key Laboratory of Agricultural Big Data of Hebei Province Hebei Agricultural UniversityBaoding 071001China School of Computer Science and Engineering Beihang UniversityBeijing 100191China School of Electronic Information Engineering Beihang UniversityBeijing 100191China

The power optimization of mixed polarity Reed–Muller(MPRM)logic circuits is a classic combinatorial optimization *** optimization approaches often suffer from slow convergence and a propensity to converge to local optima,limiting their effectiveness in achieving optimal power ***,we propose a novel multi-strategy fusion memetic algorithm(MFMA).MFMA integrates global exploration via the chimp optimization algorithm with local exploration using the coati optimization algorithm based on the optimal position learning and adaptive weight factor(COA-OLA),complemented by population management through truncation ***,leveraging MFMA,we propose a power optimization approach for MPRM logic circuits that searches for the best polarity configuration to minimize circuit *** results based on Microelectronics Center of North Carolina(MCNC)benchmark circuits demonstrate significant improvements over existing power optimization *** achieves a maximum power saving rate of 72.30%and an average optimization rate of 43.37%;it searches for solutions faster and with higher quality,validating its effectiveness and superiority in power optimization.

关键词： Power optimization Multi-strategy fusion memetic algorithm(MFMA) Mixed polarity Reed-Muller(MPRM) combinatorial optimization problem

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