Circles packing problem is an NP-hard problem and is di?cult to solve. In this paper, ahybrid search strategy for circles packing problem is discussed. A way of generating new configurationis presented by simulating t...Circles packing problem is an NP-hard problem and is di?cult to solve. In this paper, ahybrid search strategy for circles packing problem is discussed. A way of generating new configurationis presented by simulating the moving of elastic objects, which can avoid the blindness of simulatedannealing search and make iteration process converge fast. Inspired by the life experiences of people,an e?ective personified strategy to jump out of local minima is given. Based on the simulatedannealing idea and personification strategy, an e?ective personified annealing algorithm for circlespacking problem is developed. Numerical experiments on benchmark problem instances show thatthe proposed algorithm outperforms the best algorithm in the literature.展开更多
Two personification strategies are presented, which yield a highly efficient and practical algorithm for solving one of the NP hard problems——circles packing problem on the basis of the quasi-physical algorithm. A v...Two personification strategies are presented, which yield a highly efficient and practical algorithm for solving one of the NP hard problems——circles packing problem on the basis of the quasi-physical algorithm. A very clever polynomial time complexity degree approximate algorithm for solving this problem has been reported by Dorit S.Hochbaum and Wolfgang Maass in J. ACM. Their algorithm is extremely thorough-going and of great theoretical significance. But, just as they pointed out, their algorithm is feasible only in conception and even for examples frequently encountered in everyday life and of small scale, it is the case more often than not that up to a million years would be needed to perform calculations with this algorithm. It is suggested toward the end of their paper that a heuristic algorithm of higher practical effectiveness should be sought out. A direct response to their suggestion is intented to provide.展开更多
We propose a new constructive algorithm, called HAPE3 D, which is a heuristic algorithm based on the principle of minimum total potential energy for the 3D irregular packing problem, involving packing a set of irregul...We propose a new constructive algorithm, called HAPE3 D, which is a heuristic algorithm based on the principle of minimum total potential energy for the 3D irregular packing problem, involving packing a set of irregularly shaped polyhedrons into a box-shaped container with fixed width and length but unconstrained height. The objective is to allocate all the polyhedrons in the container, and thus minimize the waste or maximize profit. HAPE3 D can deal with arbitrarily shaped polyhedrons, which can be rotated around each coordinate axis at different angles. The most outstanding merit is that HAPE3 D does not need to calculate no-fit polyhedron(NFP), which is a huge obstacle for the 3D packing problem. HAPE3 D can also be hybridized with a meta-heuristic algorithm such as simulated annealing. Two groups of computational experiments demonstrate the good performance of HAPE3 D and prove that it can be hybridized quite well with a meta-heuristic algorithm to further improve the packing quality.展开更多
Evolutionary computation techniques have mostly been used to solve various optimization problems, and it is well known that graph isomorphism problem （GIP） is a nondeterministic polynomial problem. A simulated annea...Evolutionary computation techniques have mostly been used to solve various optimization problems, and it is well known that graph isomorphism problem （GIP） is a nondeterministic polynomial problem. A simulated annealing （SA） algorithm for detecting graph isomorphism is proposed, and the proposed SA algorithm is well suited to deal with random graphs with large size. To verify the validity of the proposed SA algorithm, simulations are performed on three pairs of small graphs and four pairs of large random graphs with edge densities 0.5, 0.1, and 0.01, respectively. The simulation results show that the proposed SA algorithm can detect graph isomorphism with a high probability.展开更多
A real-life problem is the rostering of nurses at hospitals.It is a famous nondeterministic,polynomial time(NP)-hard combinatorial optimization problem.Handling the real-world nurse rostering problem(NRP)constraints i...A real-life problem is the rostering of nurses at hospitals.It is a famous nondeterministic,polynomial time(NP)-hard combinatorial optimization problem.Handling the real-world nurse rostering problem(NRP)constraints in distributing workload equally between available nurses is still a difficult task to achieve.The international shortage of nurses,in addition to the spread of COVID-19,has made it more difficult to provide convenient rosters for nurses.Based on the literature,heuristic-based methods are the most commonly used methods to solve the NRP due to its computational complexity,especially for large rosters.Heuristic-based algorithms in general have problems striking the balance between diversification and intensification.Therefore,this paper aims to introduce a novel metaheuristic hybridization that combines the enhanced harmony search algorithm(EHSA)with the simulated annealing(SA)algorithm called the annealing harmony search algorithm(AHSA).The AHSA is used to solve NRP from a Malaysian hospital.The AHSA performance is compared to the EHSA,climbing harmony search algorithm(CHSA),deluge harmony search algorithm(DHSA),and harmony annealing search algorithm(HAS).The results show that the AHSA performs better than the other compared algorithms for all the tested instances where the best ever results reported for the UKMMC dataset.展开更多
Multi-constrained Quality-of-Service (QoS) routing is a big challenge for Mobile Ad hoc Networks (MANETs) where the topology may change constantly. In this paper a novel QoS Routing Algorithm based on Simulated Anneal...Multi-constrained Quality-of-Service (QoS) routing is a big challenge for Mobile Ad hoc Networks (MANETs) where the topology may change constantly. In this paper a novel QoS Routing Algorithm based on Simulated Annealing (SA_RA) is proposed. This algorithm first uses an energy function to translate multiple QoS weights into a single mixed metric and then seeks to find a feasible path by simulated annealing. The pa- per outlines simulated annealing algorithm and analyzes the problems met when we apply it to Qos Routing (QoSR) in MANETs. Theoretical analysis and experiment results demonstrate that the proposed method is an effective approximation algorithms showing better performance than the other pertinent algorithm in seeking the (approximate) optimal configuration within a period of polynomial time.展开更多
A clonal selection based memetic algorithm is proposed for solving job shop scheduling problems in this paper. In the proposed algorithm, the clonal selection and the local search mechanism are designed to enhance exp...A clonal selection based memetic algorithm is proposed for solving job shop scheduling problems in this paper. In the proposed algorithm, the clonal selection and the local search mechanism are designed to enhance exploration and exploitation. In the clonal selection mechanism, clonal selection, hypermutation and receptor edit theories are presented to construct an evolutionary searching mechanism which is used for exploration. In the local search mechanism, a simulated annealing local search algorithm based on Nowicki and Smutnicki＇s neighborhood is presented to exploit local optima. The proposed algorithm is examined using some well-known benchmark problems. Numerical results validate the effectiveness of the proposed algorithm.展开更多
Capacitated vehicle routing problem (CVRP) is an important combinatorial optimization problem. However, it is quite difficult to achieve an optimal solution with the traditional optimization methods owing to the high ...Capacitated vehicle routing problem (CVRP) is an important combinatorial optimization problem. However, it is quite difficult to achieve an optimal solution with the traditional optimization methods owing to the high computational complexity. A hybrid algorithm was developed to solve the problem, in which an artificial immune clonal algorithm (AICA) makes use of the global search ability to search the optimal results and simulated annealing (SA) algorithm employs certain probability to avoid becoming trapped in a local optimum. The results obtained from the computational study show that the proposed algorithm is a feasible and effective method for capacitated vehicle routing problem.展开更多
Team Formation(TF)is considered one of the most significant problems in computer science and optimization.TF is defined as forming the best team of experts in a social network to complete a task with least cost.Many r...Team Formation(TF)is considered one of the most significant problems in computer science and optimization.TF is defined as forming the best team of experts in a social network to complete a task with least cost.Many real-world problems,such as task assignment,vehicle routing,nurse scheduling,resource allocation,and airline crew scheduling,are based on the TF problem.TF has been shown to be a Nondeterministic Polynomial time(NP)problem,and high-dimensional problem with several local optima that can be solved using efficient approximation algorithms.This paper proposes two improved swarm-based algorithms for solving team formation problem.The first algorithm,entitled Hybrid Heap-Based Optimizer with Simulated Annealing Algorithm(HBOSA),uses a single crossover operator to improve the performance of a standard heap-based optimizer(HBO)algorithm.It also employs the simulated annealing(SA)approach to improve model convergence and avoid local minima trapping.The second algorithm is the Chaotic Heap-based Optimizer Algorithm(CHBO).CHBO aids in the discovery of new solutions in the search space by directing particles to different regions of the search space.During HBO’s optimization process,a logistic chaotic map is used.The performance of the two proposed algorithms(HBOSA)and(CHBO)is evaluated using thirteen benchmark functions and tested in solving the TF problem with varying number of experts and skills.Furthermore,the proposed algorithms were compared to well-known optimization algorithms such as the Heap-Based Optimizer(HBO),Developed Simulated Annealing(DSA),Particle SwarmOptimization(PSO),GreyWolfOptimization(GWO),and Genetic Algorithm(GA).Finally,the proposed algorithms were applied to a real-world benchmark dataset known as the Internet Movie Database(IMDB).The simulation results revealed that the proposed algorithms outperformed the compared algorithms in terms of efficiency and performance,with fast convergence to the global minimum.展开更多
This paper presents a comparative study of evolutionary algorithms which are considered to be effective in solving the multilevel lot-sizing problem in material requirement planning(MRP)systems.Three evolutionary algo...This paper presents a comparative study of evolutionary algorithms which are considered to be effective in solving the multilevel lot-sizing problem in material requirement planning(MRP)systems.Three evolutionary algorithms(simulated annealing(SA),particle swarm optimization(PSO)and genetic algorithm(GA))are provided.For evaluating the performances of algorithms,the distribution of total cost(objective function)and the average computational time are compared.As a result,both GA and PSO have better cost performances with lower average total costs and smaller standard deviations.When the scale of the multilevel lot-sizing problem becomes larger,PSO is of a shorter computational time.展开更多
To adapt to the complex and changeable market environment,the cell formation problems(CFPs) and the cell layout problems(CLPs) with fuzzy demands were optimized simultaneously. Firstly,CFPs and CLPs were described for...To adapt to the complex and changeable market environment,the cell formation problems(CFPs) and the cell layout problems(CLPs) with fuzzy demands were optimized simultaneously. Firstly,CFPs and CLPs were described formally. To deal with the uncertainty fuzzy parameters brought,a chance constraint was introduced. A mathematical model was established with an objective function of minimizing intra-cell and inter-cell material handling cost. As the chance constraint of this problem could not be converted into its crisp equivalent,a hybrid simulated annealing(HSA) based on fuzzy simulation was put forward. Finally,simulation experiments were conducted under different confidence levels. Results indicated that the proposed hybrid algorithm was feasible and effective.展开更多
The paper describes some implementation aspects of an algorithm for approximate solution of the traveling salesman problem based on the construction of convex closed contours on the initial set of points (“cities”) ...The paper describes some implementation aspects of an algorithm for approximate solution of the traveling salesman problem based on the construction of convex closed contours on the initial set of points (“cities”) and their subsequent combination into a closed path (the so-called contour algorithm or “onion husk” algorithm). A number of heuristics related to the different stages of the algorithm are considered, and various variants of the algorithm based on these heuristics are analyzed. Sets of randomly generated points of different sizes (from 4 to 90 and from 500 to 10,000) were used to test the algorithms. The numerical results obtained are compared with the results of two well-known combinatorial optimization algorithms, namely the algorithm based on the branch and bound method and the simulated annealing algorithm. .展开更多
Recent studies employing deep learning to solve the traveling salesman problem(TSP)have mainly focused on learning construction heuristics.Such methods can improve TSP solutions,but still depend on additional programs...Recent studies employing deep learning to solve the traveling salesman problem(TSP)have mainly focused on learning construction heuristics.Such methods can improve TSP solutions,but still depend on additional programs.However,methods that focus on learning improvement heuristics to iteratively refine solutions remain insufficient.Traditional improvement heuristics are guided by a manually designed search strategy and may only achieve limited improvements.This paper proposes a novel framework for learning improvement heuristics,which automatically discovers better improvement policies for heuristics to iteratively solve the TSP.Our framework first designs a new architecture based on a transformer model to make the policy network parameterized,which introduces an action-dropout layer to prevent action selection from overfitting.It then proposes a deep reinforcement learning approach integrating a simulated annealing mechanism(named RL-SA)to learn the pairwise selected policy,aiming to improve the 2-opt algorithm's performance.The RL-SA leverages the whale optimization algorithm to generate initial solutions for better sampling efficiency and uses the Gaussian perturbation strategy to tackle the sparse reward problem of reinforcement learning.The experiment results show that the proposed approach is significantly superior to the state-of-the-art learning-based methods,and further reduces the gap between learning-based methods and highly optimized solvers in the benchmark datasets.Moreover,our pre-trained model M can be applied to guide the SA algorithm(named M-SA(ours)),which performs better than existing deep models in small-,medium-,and large-scale TSPLIB datasets.Additionally,the M-SA(ours)achieves excellent generalization performance in a real-world dataset on global liner shipping routes,with the optimization percentages in distance reduction ranging from3.52%to 17.99%.展开更多
In this paper, recent developments of some heuristic algorithms were discussed. The focus was laid on the improvements of ant-cycle (AC) algorithm based on the analysis of the performances of simulated annealing (SA) ...In this paper, recent developments of some heuristic algorithms were discussed. The focus was laid on the improvements of ant-cycle (AC) algorithm based on the analysis of the performances of simulated annealing (SA) and AC for the traveling salesman problem (TSP). The Metropolis rules in SA were applied to AC and turned out an improved AC. The computational results obtained from the case study indicated that the improved AC algorithm has advantages over the sheer SA or unmixed AC.展开更多
文摘Circles packing problem is an NP-hard problem and is di?cult to solve. In this paper, ahybrid search strategy for circles packing problem is discussed. A way of generating new configurationis presented by simulating the moving of elastic objects, which can avoid the blindness of simulatedannealing search and make iteration process converge fast. Inspired by the life experiences of people,an e?ective personified strategy to jump out of local minima is given. Based on the simulatedannealing idea and personification strategy, an e?ective personified annealing algorithm for circlespacking problem is developed. Numerical experiments on benchmark problem instances show thatthe proposed algorithm outperforms the best algorithm in the literature.
基金Project supported by the 973 National Focus Program of China on Development of Fundamental Research, 863 National HighTech Programme of China, National Natural Science Foundation of China, and Chinese Science Foundation for National Doctoral Training.
文摘Two personification strategies are presented, which yield a highly efficient and practical algorithm for solving one of the NP hard problems——circles packing problem on the basis of the quasi-physical algorithm. A very clever polynomial time complexity degree approximate algorithm for solving this problem has been reported by Dorit S.Hochbaum and Wolfgang Maass in J. ACM. Their algorithm is extremely thorough-going and of great theoretical significance. But, just as they pointed out, their algorithm is feasible only in conception and even for examples frequently encountered in everyday life and of small scale, it is the case more often than not that up to a million years would be needed to perform calculations with this algorithm. It is suggested toward the end of their paper that a heuristic algorithm of higher practical effectiveness should be sought out. A direct response to their suggestion is intented to provide.
基金supported by the Natural Science Foundation of Guangdong Province,China(No.S2013040016594)the Natural Science Foundation of Liaoning Province,China(No.201102164)the Fundamental Research Funds for the Central Universities,China(No.2013ZM0124)
文摘We propose a new constructive algorithm, called HAPE3 D, which is a heuristic algorithm based on the principle of minimum total potential energy for the 3D irregular packing problem, involving packing a set of irregularly shaped polyhedrons into a box-shaped container with fixed width and length but unconstrained height. The objective is to allocate all the polyhedrons in the container, and thus minimize the waste or maximize profit. HAPE3 D can deal with arbitrarily shaped polyhedrons, which can be rotated around each coordinate axis at different angles. The most outstanding merit is that HAPE3 D does not need to calculate no-fit polyhedron(NFP), which is a huge obstacle for the 3D packing problem. HAPE3 D can also be hybridized with a meta-heuristic algorithm such as simulated annealing. Two groups of computational experiments demonstrate the good performance of HAPE3 D and prove that it can be hybridized quite well with a meta-heuristic algorithm to further improve the packing quality.
基金the National Natural Science Foundation of China (60373089, 60674106, and 60533010)the National High Technology Research and Development "863" Program (2006AA01Z104)
文摘Evolutionary computation techniques have mostly been used to solve various optimization problems, and it is well known that graph isomorphism problem （GIP） is a nondeterministic polynomial problem. A simulated annealing （SA） algorithm for detecting graph isomorphism is proposed, and the proposed SA algorithm is well suited to deal with random graphs with large size. To verify the validity of the proposed SA algorithm, simulations are performed on three pairs of small graphs and four pairs of large random graphs with edge densities 0.5, 0.1, and 0.01, respectively. The simulation results show that the proposed SA algorithm can detect graph isomorphism with a high probability.
文摘A real-life problem is the rostering of nurses at hospitals.It is a famous nondeterministic,polynomial time(NP)-hard combinatorial optimization problem.Handling the real-world nurse rostering problem(NRP)constraints in distributing workload equally between available nurses is still a difficult task to achieve.The international shortage of nurses,in addition to the spread of COVID-19,has made it more difficult to provide convenient rosters for nurses.Based on the literature,heuristic-based methods are the most commonly used methods to solve the NRP due to its computational complexity,especially for large rosters.Heuristic-based algorithms in general have problems striking the balance between diversification and intensification.Therefore,this paper aims to introduce a novel metaheuristic hybridization that combines the enhanced harmony search algorithm(EHSA)with the simulated annealing(SA)algorithm called the annealing harmony search algorithm(AHSA).The AHSA is used to solve NRP from a Malaysian hospital.The AHSA performance is compared to the EHSA,climbing harmony search algorithm(CHSA),deluge harmony search algorithm(DHSA),and harmony annealing search algorithm(HAS).The results show that the AHSA performs better than the other compared algorithms for all the tested instances where the best ever results reported for the UKMMC dataset.
基金Supported by the National Natural Science Foundation of China (No.60472104), the Natural Science Research Program of Jiangsu Province (No.04KJB510094).
文摘Multi-constrained Quality-of-Service (QoS) routing is a big challenge for Mobile Ad hoc Networks (MANETs) where the topology may change constantly. In this paper a novel QoS Routing Algorithm based on Simulated Annealing (SA_RA) is proposed. This algorithm first uses an energy function to translate multiple QoS weights into a single mixed metric and then seeks to find a feasible path by simulated annealing. The pa- per outlines simulated annealing algorithm and analyzes the problems met when we apply it to Qos Routing (QoSR) in MANETs. Theoretical analysis and experiment results demonstrate that the proposed method is an effective approximation algorithms showing better performance than the other pertinent algorithm in seeking the (approximate) optimal configuration within a period of polynomial time.
文摘A clonal selection based memetic algorithm is proposed for solving job shop scheduling problems in this paper. In the proposed algorithm, the clonal selection and the local search mechanism are designed to enhance exploration and exploitation. In the clonal selection mechanism, clonal selection, hypermutation and receptor edit theories are presented to construct an evolutionary searching mechanism which is used for exploration. In the local search mechanism, a simulated annealing local search algorithm based on Nowicki and Smutnicki＇s neighborhood is presented to exploit local optima. The proposed algorithm is examined using some well-known benchmark problems. Numerical results validate the effectiveness of the proposed algorithm.
文摘Capacitated vehicle routing problem (CVRP) is an important combinatorial optimization problem. However, it is quite difficult to achieve an optimal solution with the traditional optimization methods owing to the high computational complexity. A hybrid algorithm was developed to solve the problem, in which an artificial immune clonal algorithm (AICA) makes use of the global search ability to search the optimal results and simulated annealing (SA) algorithm employs certain probability to avoid becoming trapped in a local optimum. The results obtained from the computational study show that the proposed algorithm is a feasible and effective method for capacitated vehicle routing problem.
文摘Team Formation(TF)is considered one of the most significant problems in computer science and optimization.TF is defined as forming the best team of experts in a social network to complete a task with least cost.Many real-world problems,such as task assignment,vehicle routing,nurse scheduling,resource allocation,and airline crew scheduling,are based on the TF problem.TF has been shown to be a Nondeterministic Polynomial time(NP)problem,and high-dimensional problem with several local optima that can be solved using efficient approximation algorithms.This paper proposes two improved swarm-based algorithms for solving team formation problem.The first algorithm,entitled Hybrid Heap-Based Optimizer with Simulated Annealing Algorithm(HBOSA),uses a single crossover operator to improve the performance of a standard heap-based optimizer(HBO)algorithm.It also employs the simulated annealing(SA)approach to improve model convergence and avoid local minima trapping.The second algorithm is the Chaotic Heap-based Optimizer Algorithm(CHBO).CHBO aids in the discovery of new solutions in the search space by directing particles to different regions of the search space.During HBO’s optimization process,a logistic chaotic map is used.The performance of the two proposed algorithms(HBOSA)and(CHBO)is evaluated using thirteen benchmark functions and tested in solving the TF problem with varying number of experts and skills.Furthermore,the proposed algorithms were compared to well-known optimization algorithms such as the Heap-Based Optimizer(HBO),Developed Simulated Annealing(DSA),Particle SwarmOptimization(PSO),GreyWolfOptimization(GWO),and Genetic Algorithm(GA).Finally,the proposed algorithms were applied to a real-world benchmark dataset known as the Internet Movie Database(IMDB).The simulation results revealed that the proposed algorithms outperformed the compared algorithms in terms of efficiency and performance,with fast convergence to the global minimum.
基金the National Natural Science Foundation of China(No.70971017)the Humanities and Social Sciences Project of Ministry of Education(No.10YJC630009)+1 种基金the Social Science Fund of Zhejiang Province(No.10CGGL21YBQ)the Natural Science Foundation of Zhejiang Province(No.Y1100854)
文摘This paper presents a comparative study of evolutionary algorithms which are considered to be effective in solving the multilevel lot-sizing problem in material requirement planning(MRP)systems.Three evolutionary algorithms(simulated annealing(SA),particle swarm optimization(PSO)and genetic algorithm(GA))are provided.For evaluating the performances of algorithms,the distribution of total cost(objective function)and the average computational time are compared.As a result,both GA and PSO have better cost performances with lower average total costs and smaller standard deviations.When the scale of the multilevel lot-sizing problem becomes larger,PSO is of a shorter computational time.
基金Supported by the National Natural Science Foundation of China(No.61273035,71471135)
文摘To adapt to the complex and changeable market environment,the cell formation problems(CFPs) and the cell layout problems(CLPs) with fuzzy demands were optimized simultaneously. Firstly,CFPs and CLPs were described formally. To deal with the uncertainty fuzzy parameters brought,a chance constraint was introduced. A mathematical model was established with an objective function of minimizing intra-cell and inter-cell material handling cost. As the chance constraint of this problem could not be converted into its crisp equivalent,a hybrid simulated annealing(HSA) based on fuzzy simulation was put forward. Finally,simulation experiments were conducted under different confidence levels. Results indicated that the proposed hybrid algorithm was feasible and effective.
文摘The paper describes some implementation aspects of an algorithm for approximate solution of the traveling salesman problem based on the construction of convex closed contours on the initial set of points (“cities”) and their subsequent combination into a closed path (the so-called contour algorithm or “onion husk” algorithm). A number of heuristics related to the different stages of the algorithm are considered, and various variants of the algorithm based on these heuristics are analyzed. Sets of randomly generated points of different sizes (from 4 to 90 and from 500 to 10,000) were used to test the algorithms. The numerical results obtained are compared with the results of two well-known combinatorial optimization algorithms, namely the algorithm based on the branch and bound method and the simulated annealing algorithm. .
基金Project supported by the National Natural Science Foundation of China(Grant Nos.72101046 and 61672128)。
文摘Recent studies employing deep learning to solve the traveling salesman problem(TSP)have mainly focused on learning construction heuristics.Such methods can improve TSP solutions,but still depend on additional programs.However,methods that focus on learning improvement heuristics to iteratively refine solutions remain insufficient.Traditional improvement heuristics are guided by a manually designed search strategy and may only achieve limited improvements.This paper proposes a novel framework for learning improvement heuristics,which automatically discovers better improvement policies for heuristics to iteratively solve the TSP.Our framework first designs a new architecture based on a transformer model to make the policy network parameterized,which introduces an action-dropout layer to prevent action selection from overfitting.It then proposes a deep reinforcement learning approach integrating a simulated annealing mechanism(named RL-SA)to learn the pairwise selected policy,aiming to improve the 2-opt algorithm's performance.The RL-SA leverages the whale optimization algorithm to generate initial solutions for better sampling efficiency and uses the Gaussian perturbation strategy to tackle the sparse reward problem of reinforcement learning.The experiment results show that the proposed approach is significantly superior to the state-of-the-art learning-based methods,and further reduces the gap between learning-based methods and highly optimized solvers in the benchmark datasets.Moreover,our pre-trained model M can be applied to guide the SA algorithm(named M-SA(ours)),which performs better than existing deep models in small-,medium-,and large-scale TSPLIB datasets.Additionally,the M-SA(ours)achieves excellent generalization performance in a real-world dataset on global liner shipping routes,with the optimization percentages in distance reduction ranging from3.52%to 17.99%.
文摘In this paper, recent developments of some heuristic algorithms were discussed. The focus was laid on the improvements of ant-cycle (AC) algorithm based on the analysis of the performances of simulated annealing (SA) and AC for the traveling salesman problem (TSP). The Metropolis rules in SA were applied to AC and turned out an improved AC. The computational results obtained from the case study indicated that the improved AC algorithm has advantages over the sheer SA or unmixed AC.
