Quafu-Qcover:Explore combinatorial optimization problems on cloud-based quantum computers

We introduce Quafu-Qcover,an open-source cloud-based software package developed for solving combinatorial optimization problems using quantum simulators and hardware backends.Quafu-Qcover provides a standardized and comprehensive workflow that utilizes the quantum approximate optimization algorithm(QAOA).It facilitates the automatic conversion of the original problem into a quadratic unconstrained binary optimization(QUBO)model and its corresponding Ising model,which can be subsequently transformed into a weight graph.The core of Qcover relies on a graph decomposition-based classical algorithm,which efficiently derives the optimal parameters for the shallow QAOA circuit.Quafu-Qcover incorporates a dedicated compiler capable of translating QAOA circuits into physical quantum circuits that can be executed on Quafu cloud quantum computers.Compared to a general-purpose compiler,our compiler demonstrates the ability to generate shorter circuit depths,while also exhibiting superior speed performance.Additionally,the Qcover compiler has the capability to dynamically create a library of qubits coupling substructures in real-time,utilizing the most recent calibration data from the superconducting quantum devices.This ensures that computational tasks can be assigned to connected physical qubits with the highest fidelity.The Quafu-Qcover allows us to retrieve quantum computing sampling results using a task ID at any time,enabling asynchronous processing.Moreover,it incorporates modules for results preprocessing and visualization,facilitating an intuitive display of solutions for combinatorial optimization problems.We hope that Quafu-Qcover can serve as an instructive illustration for how to explore application problems on the Quafu cloud quantum computers.

Learning to Branch in Combinatorial Optimization With Graph Pointer Networks

Traditional expert-designed branching rules in branch-and-bound(B&B) are static, often failing to adapt to diverse and evolving problem instances. Crafting these rules is labor-intensive, and may not scale well with complex problems.Given the frequent need to solve varied combinatorial optimization problems, leveraging statistical learning to auto-tune B&B algorithms for specific problem classes becomes attractive. This paper proposes a graph pointer network model to learn the branch rules. Graph features, global features and historical features are designated to represent the solver state. The graph neural network processes graph features, while the pointer mechanism assimilates the global and historical features to finally determine the variable on which to branch. The model is trained to imitate the expert strong branching rule by a tailored top-k Kullback-Leibler divergence loss function. Experiments on a series of benchmark problems demonstrate that the proposed approach significantly outperforms the widely used expert-designed branching rules. It also outperforms state-of-the-art machine-learning-based branch-and-bound methods in terms of solving speed and search tree size on all the test instances. In addition, the model can generalize to unseen instances and scale to larger instances.

A Predator-prey Particle Swarm Optimization Approach to Multiple UCAV Air Combat Modeled by Dynamic Game Theory

Dynamic game theory has received considerable attention as a promising technique for formulating control actions for agents in an extended complex enterprise that involves an adversary. At each decision making step, each side seeks the best scheme with the purpose of maximizing its own objective function. In this paper, a game theoretic approach based on predatorprey particle swarm optimization (PP-PSO) is presented, and the dynamic task assignment problem for multiple unmanned combat aerial vehicles (UCAVs) in military operation is decomposed and modeled as a two-player game at each decision stage. The optimal assignment scheme of each stage is regarded as a mixed Nash equilibrium, which can be solved by using the PP-PSO. The effectiveness of our proposed methodology is verified by a typical example of an air military operation that involves two opposing forces: the attacking force Red and the defense force Blue. © 2014 Chinese Association of Automation.

Time Complexity of Evolutionary Algorithms for Combinatorial Optimization:A Decade of Results

Computational time complexity analyzes of evolutionary algorithms （EAs） have been performed since the mid-nineties. The first results were related to very simple algorithms, such as the （1＋1）-EA, on toy problems. These efforts produced a deeper understanding of how EAs perform on different kinds of fitness landscapes and general mathematical tools that may be extended to the analysis of more complicated EAs on more realistic problems. In fact, in recent years, it has been possible to analyze the （1＋1）-EA on combinatorial optimization problems with practical applications and more realistic population-based EAs on structured toy problems. This paper presents a survey of the results obtained in the last decade along these two research lines. The most common mathematical techniques are introduced, the basic ideas behind them are discussed and their elective applications are highlighted. Solved problems that were still open are enumerated as are those still awaiting for a solution. New questions and problems arisen in the meantime are also considered.

SOME COMBINATORIAL OPTIMIZATION PROBLEMS ARISING FROM VLSI CIRCUIT DESIGN

This paper is basically a survey to show a number of combinatorial optimization problems arising from VLSI circuit design. Some of them including the existence problem, minimax problem, net representation, bend minimization, area minimization, placement problem, routing problem, etc. are especially discussed with new results and theoretical ideas for treating them. Finally, a number of problems for further research are mentioned.

Combinatorial Optimization Based Analog Circuit Fault Diagnosis with Back Propagation Neural Network

Electronic components' reliability has become the key of the complex system mission execution. Analog circuit is an important part of electronic components. Its fault diagnosis is far more challenging than that of digital circuit. Simulations and applications have shown that the methods based on BP neural network are effective in analog circuit fault diagnosis. Aiming at the tolerance of analog circuit,a combinatorial optimization diagnosis scheme was proposed with back propagation( BP) neural network( BPNN).The main contributions of this scheme included two parts:( 1) the random tolerance samples were added into the nominal training samples to establish new training samples,which were used to train the BP neural network based diagnosis model;( 2) the initial weights of the BP neural network were optimized by genetic algorithm( GA) to avoid local minima,and the BP neural network was tuned with Levenberg-Marquardt algorithm( LMA) in the local solution space to look for the optimum solution or approximate optimal solutions. The experimental results show preliminarily that the scheme substantially improves the whole learning process approximation and generalization ability,and effectively promotes analog circuit fault diagnosis performance based on BPNN.

Vertex Cover Optimization Using a Novel Graph Decomposition Approach

The minimum vertex cover problem(MVCP)is a well-known combinatorial optimization problem of graph theory.The MVCP is an NP(nondeterministic polynomial)complete problem and it has an exponential growing complexity with respect to the size of a graph.No algorithm exits till date that can exactly solve the problem in a deterministic polynomial time scale.However,several algorithms are proposed that solve the problem approximately in a short polynomial time scale.Such algorithms are useful for large size graphs,for which exact solution of MVCP is impossible with current computational resources.The MVCP has a wide range of applications in the fields like bioinformatics,biochemistry,circuit design,electrical engineering,data aggregation,networking,internet traffic monitoring,pattern recognition,marketing and franchising etc.This work aims to solve the MVCP approximately by a novel graph decomposition approach.The decomposition of the graph yields a subgraph that contains edges shared by triangular edge structures.A subgraph is covered to yield a subgraph that forms one or more Hamiltonian cycles or paths.In order to reduce complexity of the algorithm a new strategy is also proposed.The reduction strategy can be used for any algorithm solving MVCP.Based on the graph decomposition and the reduction strategy,two algorithms are formulated to approximately solve the MVCP.These algorithms are tested using well known standard benchmark graphs.The key feature of the results is a good approximate error ratio and improvement in optimum vertex cover values for few graphs.

Whale Optimization Algorithm Strategies for Higher Interaction Strength T-Way Testing

Much of our daily tasks have been computerized by machines and sensors communicating with each other in real-time.There is a reasonable risk that something could go wrong because there are a lot of sensors producing a lot of data.Combinatorial testing(CT)can be used in this case to reduce risks and ensure conformance to specifications.Numerous existing metaheuristic-based solutions aim to assist the test suite generation for combinatorial testing,also known as t-way testing(where t indicates the interaction strength),viewed as an optimization problem.Much previous research,while helpful,only investigated a small number of interaction strengths up to t=6.For lightweight applications,research has demonstrated good fault-finding ability.However,the number of interaction strengths considered must be higher in the case of interactions that generate large amounts of data.Due to resource restrictions and the combinatorial explosion challenge,little work has been done to produce high-order interaction strength.In this context,the Whale Optimization Algorithm(WOA)is proposed to generate high-order interaction strength.To ensure that WOA conquers premature convergence and avoids local optima for large search spaces(owing to high-order interaction),three variants of WOA have been developed,namely Structurally Modified Whale Optimization Algorithm(SWOA),Tolerance Whale Optimization Algorithm(TWOA),and Tolerance Structurally Modified Whale Optimization Algorithm(TSWOA).Our experiments show that the third strategy gives the best performance and is comparable to existing state-of-thearts based strategies.

Optimization Techniques in University Timetabling Problem:Constraints,Methodologies,Benchmarks,and Open Issues

University timetabling problems are a yearly challenging task and are faced repeatedly each semester.The problems are considered nonpolynomial time(NP)and combinatorial optimization problems(COP),which means that they can be solved through optimization algorithms to produce the aspired optimal timetable.Several techniques have been used to solve university timetabling problems,and most of them use optimization techniques.This paper provides a comprehensive review of the most recent studies dealing with concepts,methodologies,optimization,benchmarks,and open issues of university timetabling problems.The comprehensive review starts by presenting the essence of university timetabling as NP-COP,defining and clarifying the two formed classes of university timetabling:University Course Timetabling and University Examination Timetabling,illustrating the adopted algorithms for solving such a problem,elaborating the university timetabling constraints to be considered achieving the optimal timetable,and explaining how to analyze and measure the performance of the optimization algorithms by demonstrating the commonly used benchmark datasets for the evaluation.It is noted that meta-heuristic methodologies are widely used in the literature.Additionally,recently,multi-objective optimization has been increasingly used in solving such a problem that can identify robust university timetabling solutions.Finally,trends and future directions in university timetabling problems are provided.This paper provides good information for students,researchers,and specialists interested in this area of research.The challenges and possibilities for future research prospects are also explored.

Application of the edge of chaos in combinatorial optimization

Many problems in science,engineering and real life are related to the combinatorial optimization.However,many combinatorial optimization problems belong to a class of the NP-hard problems,and their globally optimal solutions are usually difficult to solve.Therefore,great attention has been attracted to the algorithms of searching the globally optimal solution or near-optimal solution for the combinatorial optimization problems.As a typical combinatorial optimization problem,the traveling salesman problem(TSP)often serves as a touchstone for novel approaches.It has been found that natural systems,particularly brain nervous systems,work at the critical region between order and disorder,namely,on the edge of chaos.In this work,an algorithm for the combinatorial optimization problems is proposed based on the neural networks on the edge of chaos(ECNN).The algorithm is then applied to TSPs of 10 cities,21 cities,48 cities and 70 cities.The results show that ECNN algorithm has strong ability to drive the networks away from local minimums.Compared with the transiently chaotic neural network(TCNN),the stochastic chaotic neural network(SCNN)algorithms and other optimization algorithms,much higher rates of globally optimal solutions and near-optimal solutions are obtained with ECNN algorithm.To conclude,our algorithm provides an effective way for solving the combinatorial optimization problems.

A COMBINAT0RIAL ALGORITHM FOR THE DISCRETE OPTIMIZATION OF STRUCTURES

The definition of local optimum solution of the discrete optimization is first given.and then a comprehensive combinatorial algorithm is proposed in this paper. Two-leveloptimum method is used in the algorithm. In the first level optimization, anapproximate local optimum solution X is found by using the heuristic algorithm,relative difference quotient algorithm. with high computational efficiency and highperformance demonstrated by the performance test of random samples. In the secondlevel, a mathematical model of (- 1, 0, 1) programming is established first, and then itis changed into (0, 1) programming model. The local optimum solution X will befrom the (0. 1) programming by using the delimitative and combinatorial algorithm orthe relative difference quotient algorithm. By this algorithm, the local optimumsolution can be obtained certainly, and a method is provnded to judge whether or notthe approximate optimum solution obtained by heuristic algorithm is an optimumsolution. The above comprehensive combinatorial algorithm has higher computationalefficiency.

Formulation of the Social Workers’ Problem in Quadratic Unconstrained Binary Optimization Form and Solve It on a Quantum Computer

The problem of social workers visiting their patients at home is a class of combinatorial optimization problems and belongs to the class of problems known as NP-Hard. These problems require heuristic techniques to provide an efficient solution in the best of cases. In this article, in addition to providing a detailed resolution of the social workers’ problem using the Quadratic Unconstrained Binary Optimization Problems (QUBO) formulation, an approach to mapping the inequality constraints in the QUBO form is given. Finally, we map it in the Hamiltonian of the Ising model to solve it with the Quantum Exact Solver and Variational Quantum Eigensolvers (VQE). The quantum feasibility of the algorithm will be tested on IBMQ computers.

Combinatorial Discovery and Optimization of New Materials

The concept of the combinatorial discovery and optimization of new materials, and its background,importance, and application, as well as its current status in the world, are briefly reviewed in this paper.

Original optimal method to solve the all-pairs shortest path problem: Dhouib-matrix-ALL-SPP

The All-pairs shortest path problem(ALL-SPP)aims to find the shortest path joining all the vertices in a given graph.This study proposed a new optimal method,Dhouib-matrix-ALL-SPP(DM-ALL-SPP)to solve the ALL-SPP based on column-row navigation through the adjacency matrix.DM-ALL-SPP is designed to generate in a single execution the shortest path with details among all-pairs of vertices for a graph with positive and negative weighted edges.Even for graphs with a negative cycle,DM-ALL-SPP reported a negative cycle.In addition,DM-ALL-SPP continues to work for directed,undirected and mixed graphs.Furthermore,it is characterized by two phases:the first phase consists of adding by column repeated(n)iterations(where n is the number of vertices),and the second phase resides in adding by row executed in the worst case(n∗log(n))iterations.The first phase,focused on improving the elements of each column by adding their values to each row and modifying them with the smallest value.The second phase is emphasized by rows only for the elements modified in the first phase.Different instances from the literature were used to test the performance of the proposed DM-ALL-SPP method,which was developed using the Python programming language and the results were compared to those obtained by the Floyd-Warshall algorithm.

A Genetic Algorithm-based Approach to Scheduling of Batch Production with Maximum Profit

The optimal scheduling of multi-product batch process is studied and a new mathematics model targeting the maximum profit is proposed, which can be solved by the modified genetic algorithm (MGA) with mixed coding (sequence coding and decimal coding) developed by us. In which, the partially matched cross over (PMX) and reverse mutation are used for the sequence coding, whereas the arithmetic crossover and heteropic mutation are used for the decimal coding. In addition, the relationship between production scale and production cost is analyzed and the maximum profit is always a trade-off of the production scale and production cost. Two examples are solved to demonstrate the effectiveness of the method.

A Gene-Pool Based Genetic Algorithm for TSP

Based on the analysis of previous genetic algorithms (GAs) for TSP, a novel method called Ge- GA is proposed. It combines gene pool and GA so as to direct the evolution of the whole population. The core of Ge- GA is the construction of gene pool and how to apply it to GA. Different from standard GAs, Ge- GA aims to enhance the ability of exploration and exploitation by incorporating global search with local search. On one hand a local search called Ge- Lo-calSearch operator is proposed to improve the solution quality, on the other hand the modified Inver-Over operator called Ge InverOver is considered as a global search mechanism to expand solution space of local minimal. Both of these operators are based on the gene pool. Our algorithm is applied to 11 well-known traveling salesman problems whose numbers of cities are from 70 to 1577 cities. The experiments results indicate that Ge- GA has great robustness for TSP. For each test instance, the average value of solution quality, found in accepted time, stays within 0. 001% from the optimum.

Hopfield neural network based on ant system

Hopfield neural network is a single layer feedforward neural network. Hopfield network requires some control parameters to be carefully selected, else the network is apt to converge to local minimum. An ant system is a nature inspired meta heuristic algorithm. It has been applied to several combinatorial optimization problems such as Traveling Salesman Problem, Scheduling Problems, etc. This paper will show an ant system may be used in tuning the network control parameters by a group of cooperated ants. The major advantage of this network is to adjust the network parameters automatically, avoiding a blind search for the set of control parameters. This network was tested on two TSP problems, 5 cities and 10 cities. The results have shown an obvious improvement.

A DEGREE SEQUENCE METHOD FOR THE CUTWIDTH PROBLEM OF GRAPHS

The cutwidth problem fora graph G is to embed G into a path such thatthe maximum number of overlap edges is minimized.This paperpresents an approach based on the degree se- quence of G for determining the exact value of cutwidth of typical graphs (e.g.,n- cube,cater- pillars) .Relations between the cutwidth and other graph- theoretic parameters are studied as wel

Smart Cities in Europe and the ALMA Logistics Project

In this paper, a brief survey of smart citiy projects in Europe is presented. This survey shows the extent of transport and logistics in smart cities. We concentrate on a smart city project we have been working on that is related to A Logistic Mobile Application （ALMA）. The application is based on Internet of Things and combines a communication infrastructure and a High Performance Computing infrastructure in order to deliver mobile logistic services with high quality of service and adaptation to the dynamic nature of logistic operations.

Optimizing combination of aircraft maintenance tasks by adaptive genetic algorithm based on cluster search

It is significant to combine multiple tasks into an optimal work package in decision-making of aircraft maintenance to reduce cost,so a cost rate model of combinatorial maintenance is an urgent need.However,the optimal combination under various constraints not only involves numerical calculations but also is an NP-hard combinatorial problem.To solve the problem,an adaptive genetic algorithm based on cluster search,which is divided into two phases,is put forward.In the first phase,according to the density,all individuals can be homogeneously scattered over the whole solution space through crossover and mutation and better individuals are collected as candidate cluster centres.In the second phase,the search is confined to the neighbourhood of some selected possible solutions to accurately solve with cluster radius decreasing slowly,meanwhile all clusters continuously move to better regions until all the peaks in the question space is searched.This algorithm can efficiently solve the combination problem.Taking the optimization on decision-making of aircraft maintenance by the algorithm for an example,maintenance which combines multiple parts or tasks can significantly enhance economic benefit when the halt cost is rather high.