求解二元约束满足问题的混合差分进化算法研究
|
摘要
随着新技术、新方法的不断涌现,人们对于传统问题的求解提出了更高的要求,将经典的求解算法与新兴优化技术相结合,越来越成为一种解决问题的新思路,很多实践证明,混合算法能够更加灵活、更加高效的解决实际问题。本文将差分进化算法与其它传统算法相结合,提出了求解二元约束满足问题的混合差分进化算法。提出了SADE算法,将构造的自适应函数运用于差分进化算法的变异因子和交叉因子的自适应调整,算法的实验结果与近年来提出的一些算法进行了求解性能的比较和分析,分析结果显示SADE算法收敛性很好,求解成功率(SR)远远高于其他算法;提出了IMDE算法,分析在CSPs问题的求解过程中种群的不同状态,使用分段函数来针对不同的种群分布,分别进行不同的变异策略,采用公测数据集进行测试,与其他算法的测试结果进行对比后的结果显示,算法有效的预防了早熟收敛,保持了种群的多样性；提出了EEMDE算法,将类电磁机制算法(EM)的吸引-排斥机制与差分进化算法相结合,种群中每个个体看作是一个点电荷,每个点电荷根据带电量不同的比较,而受到其他点电荷的吸引或者排斥的库仑力的作用,根据点电荷所受的合力的方向来获得加速度,改变点电荷的位置,算法在不需要外在干预的情况下,就能够很好的解决局部收敛的问题,实验结果显示,算法的收敛速度接近达到其他算法的二倍,算法的物理模拟具有可行性；提出了一种SAPSO算法,将自适应思想应用于粒子群算法用于求解二元约束满足问题,将该算法应用于求解随机约束满足问题,实验结果表明,改进后的算法比原算法(PS-CSP)能以更快的速度收敛到全局解。对于本文提出的以上算法,均采用了其他作者公开的公用测试数据集进行了测试,测试结果表明,本文提出的以上算法运行结果良好。关于将差分进化算法与其它技术相结合的研究工作还处于刚起步的阶段,有很多关于解决不同问题的尝试和探索工作需要研究,本文所完成的工作对该领域的深入研究具有很好的促进作用。同时也为求解类似的问题提供了新的思路和求解手段。因此,具有一定的理论研究意义和实际应用价值。
Our daily life is filled with all kinds of constraints, for example, one week invariably includes seven days. We have to arrange our everyday work according to the timetable. Therefore, constraint is a very broad concept and Constraint Satisfaction Problems (CSPs) belong to an important research area in Artificial Intelligence. Lots of problems can be stated as CSPs. For instance, Eight-Queen problem is the most famous one, and Sudoku, Timetable, Robot Planning are all CSPs. There are many solutions to CSPs. As a result, it is a powerful tool when used to solve many complex combinatorial problems, and has aroused great attentions as well. Most of those combinatorial problems are NP-Complete problems. Generally speaking, the key targets of CSPs are to find one possible solution or all solutions. If an assignment of values to the set X makes all the constraints satisfied simultaneously, then we call these values a solution of CSPs.
Constraint satisfaction problems on finite domains are typically solvable using a form of search. The most commonly used techniques are backtracking, constraint propagation, and local search algorithm.
Backtracking is a kind of recursive algorithm. It maintains partial intermediate results of the variables when a program is being executed
Constraint propagation is a method used to modify constraint satisfaction problems. More precisely, it is a forced executed one, forcing the local compatibility, which matters the consistency of a group of variables or constraints.
Local search algorithm is incomplete. It may find a solution to a problem, but it possibly fails even if the problem is solvable. In practice, the efficiency of local search is depended by random function. Nowadays, integration of search with incomplete local search leads the world's focus to hybrid algorithms.
Differential evolution algorithm is very similar to the standard one. They are both based on the population, and have choices, intersections and mutated operations. Still, Greedy Algorithm is used in the same way. The only difference is that the differential evolution algorithm calculates the mutation rate with differential methods. So individuals may be affected by others'position and their changes and then demonstrate the social properties of swarm intelligence. There are three parameters can be used to improve the differential evolution algorithm--mutation rate F, the crossover rate CR and the size of population NP, and among them mutation rate F is the most important one. Many studies are aiming at how to improve the mutation rate F.
This paper focuses on hybrid differential evolution algorithms for binary constraint satisfaction problems. That is to make Differential Evolution Algorithms combined with other methods, and then apply them to solve binary constraint satisfaction problems. This thesis has proposed four different hybrid algorithms. Specifically, and the related research work of this thesis is carried out in the following aspects:
Firstly, a novel self-adaptive differential evolution algorithm, called SADE, has been proposed. SADE self-adaptively adjusts the mutation rate F and the crossover rate CR, and keeps the diversity of the population effectively. In order to balance individual's exploration ability, which is to solve the problem, and exploitation ability, which is to prevent the local optimization and find new space, in different stages, this paper sets two different self-adjusted nonlinear functions that vary dynamically, F and CR. SADE maintains the diversity of population and also improves the global convergence ability in the meantime. It improves the efficiency and success rate and avoids the premature convergence as well. Simulation and comparisons are based on the same test-sets of CSPs, and the results present the effectiveness, efficiency and robustness of the proposed algorithm.
Secondly, in order to solve constraint satisfaction problems, an improved differential evolution (IMDE) algorithm is proposed. With the purpose of improving the performance, bases on the different distribution of different groups, the IMDE algorithm adjust the F and CR of every individual dynamically. IMDE maintains the diversity of population and improves the global convergence ability. Experimental results prove that IMDE is effective and efficient in solving binary constraint satisfaction problems.
Thirdly, a novel hybrid elements exchange/electromagnetism meta-heuristic differential evolution algorithm (EEMDE) has been proposed. The original DE algorithm is to avoid the premature convergence effectively. The electricity charge in the electricity field is affected by the source charge'Coulombs force and that is the Coulombs Law. A individual will be like a charged particle, and a metric is defined, which is used to measure the composition of forces exerted on a point. The composition of forces is defined as to get an adaptive adjustment of the mutation rate F. EEMDE avoids the DE to the "uphill" in the wrong direction forward may produce slight disturbance on the original vector for enhancing the exploring capacity. Experiments demonstrate that the convergence of EEMDE is faster than DE and simulations based on some CSPs and it proved the effectiveness, efficiency and robustness in the same time.
Finally, a self-adaptive particle swarm algorithm, called SAPSO, has been proposed. Exploration procedure and exploitation procedure have been introduced in SAPSO. The population diversity variable, which was used to represent the diversity of population, has been defined. In addition, a metric to measure a particle's activity, which is used to choose which state it would reside in, is defined. In SAPSO, each particle has two states:exploration state and exploitation state. In order to balance a particle's exploration and exploitation capability for different evolving phase, a self-adjusted inertia weight which varies dynamically with each particle's evolution degree and the current swarm evolution degree are introduced into SAPSO algorithm. It uses the self-adaptive selection to select values from domains instead of random selection. This strategy searches in the promising solution space for global solution when the particles exploit the search space. It tests the hybrid algorithm (SAPSO) with random constraint satisfaction problems. The experimental results show that the hybrid particle swarm algorithm (SAPSO) has better global search abilities than PS-CSP, and the convergence of the algorithm is also better than other.
Three differential evolutions algorithms and one PSO algorithms have been proposed. We compared the performance of different differential evolution algorithms on binary CSPs proposed recent years. The experimental results indicate that the proposed algorithm can achieve pleasing results. However, more careful parameter tuning may improve the performance with different problem instances, and more comparative works for more problems should be performed to provide a full view. In the future, we will extend the proposed SADE algorithm for solving more comprehensive set of test problems, including real life problems.
Our daily life is filled with all kinds of constraints, for example, one week invariably includes seven days. We have to arrange our everyday work according to the timetable. Therefore, constraint is a very broad concept and Constraint Satisfaction Problems (CSPs) belong to an important research area in Artificial Intelligence. Lots of problems can be stated as CSPs. For instance, Eight-Queen problem is the most famous one, and Sudoku, Timetable, Robot Planning are all CSPs. There are many solutions to CSPs. As a result, it is a powerful tool when used to solve many complex combinatorial problems, and has aroused great attentions as well. Most of those combinatorial problems are NP-Complete problems. Generally speaking, the key targets of CSPs are to find one possible solution or all solutions. If an assignment of values to the set X makes all the constraints satisfied simultaneously, then we call these values a solution of CSPs.
Constraint satisfaction problems on finite domains are typically solvable using a form of search. The most commonly used techniques are backtracking, constraint propagation, and local search algorithm.
Backtracking is a kind of recursive algorithm. It maintains partial intermediate results of the variables when a program is being executed
Constraint propagation is a method used to modify constraint satisfaction problems. More precisely, it is a forced executed one, forcing the local compatibility, which matters the consistency of a group of variables or constraints.
Local search algorithm is incomplete. It may find a solution to a problem, but it possibly fails even if the problem is solvable. In practice, the efficiency of local search is depended by random function. Nowadays, integration of search with incomplete local search leads the world's focus to hybrid algorithms.
Differential evolution algorithm is very similar to the standard one. They are both based on the population, and have choices, intersections and mutated operations. Still, Greedy Algorithm is used in the same way. The only difference is that the differential evolution algorithm calculates the mutation rate with differential methods. So individuals may be affected by others'position and their changes and then demonstrate the social properties of swarm intelligence. There are three parameters can be used to improve the differential evolution algorithm--mutation rate F, the crossover rate CR and the size of population NP, and among them mutation rate F is the most important one. Many studies are aiming at how to improve the mutation rate F.
This paper focuses on hybrid differential evolution algorithms for binary constraint satisfaction problems. That is to make Differential Evolution Algorithms combined with other methods, and then apply them to solve binary constraint satisfaction problems. This thesis has proposed four different hybrid algorithms. Specifically, and the related research work of this thesis is carried out in the following aspects:
Firstly, a novel self-adaptive differential evolution algorithm, called SADE, has been proposed. SADE self-adaptively adjusts the mutation rate F and the crossover rate CR, and keeps the diversity of the population effectively. In order to balance individual's exploration ability, which is to solve the problem, and exploitation ability, which is to prevent the local optimization and find new space, in different stages, this paper sets two different self-adjusted nonlinear functions that vary dynamically, F and CR. SADE maintains the diversity of population and also improves the global convergence ability in the meantime. It improves the efficiency and success rate and avoids the premature convergence as well. Simulation and comparisons are based on the same test-sets of CSPs, and the results present the effectiveness, efficiency and robustness of the proposed algorithm.
Secondly, in order to solve constraint satisfaction problems, an improved differential evolution (IMDE) algorithm is proposed. With the purpose of improving the performance, bases on the different distribution of different groups, the IMDE algorithm adjust the F and CR of every individual dynamically. IMDE maintains the diversity of population and improves the global convergence ability. Experimental results prove that IMDE is effective and efficient in solving binary constraint satisfaction problems.
Thirdly, a novel hybrid elements exchange/electromagnetism meta-heuristic differential evolution algorithm (EEMDE) has been proposed. The original DE algorithm is to avoid the premature convergence effectively. The electricity charge in the electricity field is affected by the source charge'Coulombs force and that is the Coulombs Law. A individual will be like a charged particle, and a metric is defined, which is used to measure the composition of forces exerted on a point. The composition of forces is defined as to get an adaptive adjustment of the mutation rate F. EEMDE avoids the DE to the "uphill" in the wrong direction forward may produce slight disturbance on the original vector for enhancing the exploring capacity. Experiments demonstrate that the convergence of EEMDE is faster than DE and simulations based on some CSPs and it proved the effectiveness, efficiency and robustness in the same time.
Finally, a self-adaptive particle swarm algorithm, called SAPSO, has been proposed. Exploration procedure and exploitation procedure have been introduced in SAPSO. The population diversity variable, which was used to represent the diversity of population, has been defined. In addition, a metric to measure a particle's activity, which is used to choose which state it would reside in, is defined. In SAPSO, each particle has two states:exploration state and exploitation state. In order to balance a particle's exploration and exploitation capability for different evolving phase, a self-adjusted inertia weight which varies dynamically with each particle's evolution degree and the current swarm evolution degree are introduced into SAPSO algorithm. It uses the self-adaptive selection to select values from domains instead of random selection. This strategy searches in the promising solution space for global solution when the particles exploit the search space. It tests the hybrid algorithm (SAPSO) with random constraint satisfaction problems. The experimental results show that the hybrid particle swarm algorithm (SAPSO) has better global search abilities than PS-CSP, and the convergence of the algorithm is also better than other.
Three differential evolutions algorithms and one PSO algorithms have been proposed. We compared the performance of different differential evolution algorithms on binary CSPs proposed recent years. The experimental results indicate that the proposed algorithm can achieve pleasing results. However, more careful parameter tuning may improve the performance with different problem instances, and more comparative works for more problems should be performed to provide a full view. In the future, we will extend the proposed SADE algorithm for solving more comprehensive set of test problems, including real life problems.
引文
[1]谭营等译.计算群体智能基础[M].北京：清华大学出版社,2009
[2]张韵华.符号计算系统Mathematica教程[M].北京：科学出版社,2001.
[3]V. Heuveline, F. Strauf. Shape Optimization Towards Stability in Constrained Dydrodynamic Systems[J]. Computational Physics,2009,228(4):938-951.
[4]V. Heuveline, F. Strauss. Shape Optimization in Fluid Mechanics with Eigenvalue Constraints,2008. http://homes.esat.kuleuven.be/-optec/events/workshops/EIGOPT/talks/eigopt-strauss.pdf
[5]X. Han. Simulation theory Study on Urban Fire-fighting And Disp Atching Process: [PHD Thesis]. Shanghai Tongji University,1999.
[6]J.K. LENSTRA, R.K. AHG and P. BRUCKER. Complexity of machine scheduling problems [J]. Annals of Discrete Mathematics,1977,1:343-362.
[7]B. G. W. Craenen. Solving Constraint Satisfaction Problems with Evolutionary Algorithms, Ph.D. Dissertation, Vrige University,2005.
[8]C. James, Bezdek. On the relationship between neural networks, pattern recognition and intelligence [J]. Int. J. Approx. Reasoning,1992,6(2):85-107.
[9]J. C. Bezdek. On the relationship between neural networks,pattern recoginition and intelligence. The Int J of Approximate Reasooning,1992,6(2):85-107.
[10]R. Bharath and J. Drosen. Neural Network Computing [M]. McGraw-Hill,1994.
[11]L. A. Zadeh. Fuzzy Sets, Infromation and Control.1965,8:338-353.
[12]Z. Pawlk. Rough Sets. International Journal of Information and Computer Science,1982, (11):341-356.
[13]Z. Pawlk. Rough Set Theoretical Aspects of Reasoning about Data. Dordrecht:Kluer Academic Publishers,1991.
[14]J. H. Holland. Adaptation in Neural and Artificial Systems. Ann Arbor, Michigan:The University of Nichigan Press,1975; Cambridge, MA:MIT Press,1992.
[15]王飞,刘大有.基于遗传算法的动态Bayesian网结构学习的研究,电子学报,2003,31(5)：698-702.
[16]A. Daniel. Evolutionary Computation for modeling and Optimization, Publisher:Springer, 2005.
[17]X. Y. Tu. Artificial Animals for Computer Animation:Biomechanics, Locomotion, Perception, and Behavior, ACM Distinguished Ph.D Dissertation Series, (Lecture Notes in Computer Science. Eds.:G. Goos, J. Hartmanis, J.van Leeuwen. Vol. 1635) Springer-Verlag,1999.
[18]D. B. Fogel. Evolutionary Computation:Toward a New Philosophy of Machine Intelligence.2nd ed. Wiley-IEEE Press,2001.
[19]周春光,梁艳春.计算智能[M].长春：吉林大学出版社,2001.
[20]Kennedy, J.Eberhart.R.C. Particle swarm optimization[C]. In:Proc. of the 1995 IEEE International Conference on Neural Networks. Piscataway, NJ, Perth, Australia:IEEE service center,1995:1942-1948
[21]Shu-Kai S. Fan and Erwie Zahara, A hybrid simplex search and particle swarm optimization for unconstrained optimization[J]. European Journal of Operational Research,2007,181:527-548.
[22]Eric Bonabeau, Marco Dorigo and Guy Theraulaz. Swarm Intelligence:From Natural to Artificial Systems[M],Oxford University Press, USA; 1 edition,1999.
[23]M. Dorigo, V. Maniezzo, A. Colorni, The ant system:Optimization by a colony of cooperating agents[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B, 1996,26(1):29-41.
[24]M. Dorigo, V. Maniezzo, A. Colorni, Positive feedback as a search strategy[R]. Technical Report,1991a:91-016, Italy:University of Milan.
[25]J. M. Liu, K. C. Tsui. Toward Nature-Inspired Computing[M], Communications of the ACM.2006,49(10):59-64.
[26]D. David, L. Diosan, D. Dumitrescu. A New Nature-Inspired Computation Model Ising Model with Rays[C], SYNASC2005,25-29 sept.2005:315-320
[27]L.N. De Castro and J.I. Timmis, Artificial immune systems as a novel soft computing paradigm[J]. Soft Computing,2003,7:526-544.
[28]C. James, Bezdek. On the relationship between neural networks, pattern recognition and intelligence [J]. Int. J. Approx. Reasoning,1992,6(2):85-107.
[29]C. G. Langton. Studying Artificial Life with Cellular Automata [J]. Physica D,1986, 10:120-149.
[30]Daniel Ashlock, Evolutionary Computation for modeling and Optimization, Publisher: Springer,2005.
[31]孙吉贵,景沈艳.非二元约束满足问题求解[J],计算机学报.2003,(26)12：1746-1752.
[32]A. L. Davis, A. Rosenfeld. Cooperating Processes for Low-Level Vision:A Survey., Artificial Intelligence[j].1981,17:245-263.
[33]R. A. Hummel, A.Rosenfeld and S. W. Zucker. Scene Labelling by Relaxation Operations. IEEE Transactions on Systems, Man, and Cybernetics.1976,6(6):420-433.
[34]M. S.Fox. Constraint-Directed Search:A Case Study of Job Shop Scheduling.1987.
[35]V.Dhar, N.Ranganathan. Integer Programming versus Expert Systems:An Experimental Comparison, Communications of the ACM.1990,33:323-336.
[36]J. F.Rit. Propagating Temporal Constraints for Scheduling, In Proceedings of the Fifth National Conference on Artificial Intelligence.1986,383-386.
[37]E. P. K. Tsang. The Consistent Labeling Problem in Temporal Reasoning, In Proceedings of the Sixth National Conference on Artificial Intelligence.1987,251-255.
[38]M.Bruynooghe. Graph Coloring and Constraint Satisfaction, Technical Report.1985,CW 44.
[39]M. Stefik. Planning with Constraints (MOLGEN:Part Ⅰ), Artificial Intelligence.1981,16: 111-140.
[40]R.Zabih, D.McAllester. A Rearrangement Search Strategy for Determining Propositional Satisfiabilty,In Proceedings of the Seventh National Conference on Artificial Intelligence.1988,155-160.
[41]J.D. Kleer, G. J. Sussman. Propagation of Constraints Applied to Circuit Synthesis, Circuit Theory and Applications.1980,8:127-144.
[42]V. Kumar. Algorithms for constraint-satisfaction problems:a survey. AI Magazine,1992, 13(1):32-44
[43]Q. Y. Yang, J. G. Sun, J. Y. Zhang and C. J. Wang, "A Hybrid Discrete Particle Swarm Algorithm for Hard Binary CSPs," Proc. of the 2nd International Conference on Natural Computation (ICNC'06) and the 3rd International Conference on Fuzzy Systems and Knowledge Discovery,Xi'an, China, LNCS 4222,2006, pp.184-193.
[44]杨轻云,孙吉贵,张居阳.稀疏二元约束满足问题的环割集粒子群算法[J],广西师范大学学报(自然科学版).2006,24(4)：135-138
[45]B.G.W. Craenen, A.E. Eiben, J.I. van Hemert. Comparing Evolutionary Algorithms on Binary Constraint Satisfaction Problems.
[46]D. Marx. Graph Colouring Problems and Their Applications in Scheduling [J],Fperiodica Polytechnica Ser.2004,48(1):11-16.
[47]N.Karmarkar. A new polynomial time algorithm for linear programming. Combinatorica, 4,1984,373-395
[48]L.G.Khachiyan. A polynomial algorithm in linear programming. Doklady Akademia Nauk SSSR,1979,1093-1096
[49]B.M.Smith. Constructing an asymptotic phase transition in random binary constraint problems. TCS,265:265-283,2001
[50]K.Xu and W.Li. Exact phase transitions in random binary constraint satisfaction problems. TCS,265-283,2001
[51]A.M.Frieze and M.Molloy. The satisfiability threshold for randomly generated binary constraint satisfaction problems. In Proc. of Random'03, pp.275-289,2003
[52]K.Xu and W.Li. Many hard examples in exact phase transitions with application to generating hard satisfiable instances, CoRR Report cs. CC/0302001,2003
[53]R. Haralick and G. Elliot. Increasing tree search efficiency for constraintsatisfaction problems, Artificial Intelligence.1980,14(3):263-313.
[54]S. Golomb, L. Baumert. Backtrack programming. A.C.M.,1965.12(4):516-524.
[55]G. Kondrak, P. van Beek. A Theoretical Evaluation of Selected Backtracking Algorithms, Artificial Intelligence.1989,89(1-2):365-387.
[56]P. Prosser. Hybrid Algorithms for the Constraint Satisfaction Problem, Computational Intelligence.1993,9(3):268-299.
[57]A. K. Mackworth. Consistency in Networks of Relations.Arfifical Intelligence. 1977,8:99-118.
[58]R. Storn, K. Price. Differential Evolution-A simple and Efficient Heuristic for Global Optimization over Continuous Spaces, Global Optimization[J].1997, 11(4):341-359.
[59]A. P. Engelbrecht, "Fundamentals of Computational Swarm Intelligence", John Wiley & Sons Ltd,2005.
[60]K. V. Pric, R. Storn, J. Lampinen, Differential Evolution:A Practical Approach to Global Optimization, London:Springer-Verlag, UK,2005.
[61]R. Storn, K.Price. Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces[R/OL],2009-01 [2009-04-06]. ICSI, Technical Report TR-95-012,1995. ftp://ftp.icsi.berkeley.edu/pub/techreports/ 1995/tr-95-012.pdf.
[62]V. P. Kenneth, M. S. Rainer. A.LampinenJouni. Differential Evolution:A Practical Approach to Global Optimization[M]. Springer,2004:135-139.
[63]J. Lampinen and I. Zelinka, "On Stagnation of the Differential Evolution Algorithm", In: Pavel Osmera, (ed.) Proc. of MENDEL 2000,6th International Mendel Conference on Soft Computing,2000, pp.76-83.
[64]J. Lampinen and I. Zelinka, "On Stagnation of the Differential Evolution Algorithm", In: Pavel Osmera, (ed.) Proc. of MENDEL 2000,6th International Mendel Conference on Soft Computing,2000, pp.76-83.
[65]C. S. Chang, D. Y. Xu, "Differential Evolution Based Tuning of Fuzzy Automatic Train operation for Mass Rapid Transit System", IEEE Proc-Electric Power Applications,2000, 147(3):206-212
[66]J. Teo, "Exploring Dynamic Self-adaptive Populations in Differential Evolution", Soft Computing-A Fusion of Foundations,Methodologies and Applications, Vol.10 (8),2006, pp.673-686.
[67]J. Brest, B. Boskovic Boskovi'c, S. Greiner, V. Zumer Zumer and M. S. Maucec, "Performance Comparison of Self-Adaptive and Adaptive Differential Evolution Algorithms", Technical Report #2006-1-LABRAJ, University of Maribor, Faculty of Electrical Engineering and Computer Science, Slovenia,2006, http://marcel.unimb.si/janez/brest-TRl.html.
[68]J. Brest, S. Greiner, B. Bo(?)skovi'c, M. Mernik and.V. (?)Zumer, "Self-Adapting Control Parameters in Differential Evolution:A Comparative Study on Numerical Benchmark Problems", IEEE Transactions on Evolutionary Computation, Vol.10,2006, pp.646-657.
[69]Z. Yang, K. Tang and X. Yao, "Self-adaptive Differential Evolution with Neighborhood Search", In Proc. IEEE Congress on Evolutionary Computation, Hong Kong,2008, pp. 1110-1116.
[70]U. K. Chakraborty, "Advances in Differential Evolution", (Ed.) Springer-Verlag, Heidelberg,2008.
[71]陈涛,雍龙泉,邓方安等.基于差分进化算法的支持向量机参数选择[J],计算机工程与应用.2011,47(5)：24-26.
[72]刘黎黎,王诗元,汪定伟.求解交货期可变动态调度问题的差分进化算法[J],东北大学学报(自然科学版),2011,32(2)：183-187
[73]牛雪丽,刘希玉,魏欣.基于耗散结构理论的差分进化算法[J],计算机应用研究.2010,27(2)：504-505.
[74]宋敏,魏瑞轩,冯志明.基于差分进化算法的异构多无人机任务分配[J],系统仿真学报.201022(7)：1706-1710.
[75]杨启文,蔡亮,薛云灿.差分进化算法综述[J],模式识别与人工智能.2008,21(4)：506-513.
[76]贺毅朝,王熙照,刘坤起.王彦祺.差分演化的收敛性分析与算法改进,Journal of Software, Vol.21, No.5,2010,21 (5)-:875-885.
[77]R. Storn, K.Price. Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces[R/OL],2009-01 [2009-04-06]. ICSI, Technical Report TR-95-012,1995. ftp://ftp.icsi.berkeley.edu/pub/techreports/ 1995/tr-95-012.pdf.
[78]H. Y. Fan, J. Lampinen. A\trigonometric Mutation Operation to Differential Evolution[J], Global Optimization.2003,27(1):105-129.
[79]R. Mendes,A. S. Mohais. DynDE:A Differential Evolution for Dynamic Optimizatio:2005,:2808-2815.
[80]T. Blackwell, J.Branke. Multi-Swarm Optimization in Dynamic Environments,2004, 3005:489-500.
[81]卢峰,高立群.基于多种群的自适应差分进化算法[J],东北大学学报(自然科学版).2010,Vol 31(11)：1538-1541
[82]张雪霞,陈维荣,戴朝华.带局部搜索的动态多群体自适应差分进化算法及函数优化[J],电子学报.2010,38(8)：1825-1830.
[83]P. K. Bergey, C. Ragsdale. Modified Differential Evolution:A Greedy Random Strategy for Genetic Recombination[J],Management Science.2005,33(3):255-265.
[84]J. P. Chiou, C. F. Chang, C. T. Su. Ant Direction Hybrid Differential Evolution for Solving Large Capacitor Placement Problems(C), IEEE Trans on Power System,2004, 19(4):1794-1800.
[85]J. Y. Yan, Q. Ling, D. Sun. A Differential Evolution with Simulated Annealing Updating Method(C), Proc of the International Conference on Machine Learning and Cybernetics. Dalian, China.2006:2103-2106.
[86]Q. Y. Yang, J. G. Sun, J. Y. Zhang and C. J. Wang, A Hybrid Discrete Particle Swarm Algorithm for Hard Binary CSPs, Proc. of the 2nd International Conference on Natural Computation (ICNC'06) and the 3rd International Conference on Fuzzy Systems and Knowledge Discovery,Xi'an, China, LNCS 4222,2006, pp.184-193.
[87]J. Lampinen, I. Zelinka。On Stagnation of the Differential Evolution Algorithm, In: Pavel Osmera, (ed.) Proc. of MENDEL 2000,6th International Mendel Conference on Soft Computing,2000, pp.76-83.
[88]B. M. Smith. Phase transition and the mushy region in constraintsatisfaction problems, Proc. of the 11th European Conference onArtificial Intelligence. Wiley,1994, pp.100-104.
[89]Q. Y. Yang, A comparative stude of discrete differential evolution on binary constraint satisfaction problems, Proc. of the Congress on Evolutionary Computation(CEC’08), pp.330-335.
[90]Wu Lianghong,Wang Yaonan. Self-adapting control parameters modified differential evolution for trajectory planning manipulaor[J]. Control Theory Application,2007, 5(4):365-373.
[91]吴亮红.差分进化算法及应用研究[D].湖南：湖南大学电气与信息工程学院,2007.65-71.
[92]S. L. Birbil and S. C. Fang:An electromagnetism-like mechanism for global optimization, Journal of Global Optimization,(2003),25 (3):263-282.
[93]张长胜.求解规划、聚类和调度问题的混合粒子群算法研究[D].吉林大学.2009
[94]J. Kennedy, R. C. Eberhart. Particle swarm optimization. IEEE Int'I Conf. Neural Networks, Perch, Australia,1995.
[95]L. Schoofs, B. Naudts. Swarm intelligence on the binary constraint satisfaction problem. IEEE Congress on Evolutionary Com-putation (CEC 2002), Honolulu, Hawaii, USA. 2002.
[96]n-Zhong Wang, Ji-Gui Sun Particle swarm optimization for satisfiability (SAT), In: Knowledge Economy Meets Science and Technology KEST2004, the 2nd Int'I Conf. Knowledge Economy and Development of Science an Technology. Beijing:Tsinghua University Press,2004.36-41
[97]Y.Shi and R.C.Eberhart. A modified particle swarm optimizer. In:Proc. of the IEEE International Conference on Evolutionary Computation. Piscataway, NJ, Anchorage, AK USA:IEEE service center,1998,69-73
[98]Laskari, E. C., Parsopoulos, K. E., and Vrahatis, M. N:Particle swarm optimization for integer programming. In:Proc. of the IEEE Congress on Evolutionary Computation (CEC 2002), Honolulu, Hawaii, USA. (2002) 1582-1587
[99]A. Salman, I. Ahmad, S. Al-Madani. Particle Swarm optimization for task assignment Problem. Microprocessors and Microsystems,26(2002),363-371
[100]杨轻云.约束满足问题与调度问题中离散粒子群算法研究[D].吉林大学.2006
[101]E. C. Laskari, K. E. Parsopoulos, M. N:Particle swarm optimization for integer programming. In:Proc. of the IEEE Congress on Evolutionary Computation (CEC 2002), Honolulu, Hawaii, USA. (2002) 1582-1587
[102]A. Salman, I. Ahmad, S. Al-Madani. Particle Swarm optimization for task assignment Problem. Microprocessors and Microsystems,26(2002),363-371.
[103]M. Fatih Tasgetiren and Yun-Chia Liang. A Binary Particle Swarm Optimization Algorithm for Lot Sizing Problem. Journal of Economic and Social Research,5(2),2003, 1-20
[104]Maurice Clerc. Binary particle swarm optimisers:toolbox, derivations and mathematical insights. http://clerc.maurice.free.fr/pso/binary_pso
[105]HUANG Yan-Xin, ZHOU Chun-Guang, ZOU Shu-Xue, and WANG Yan.A Hybrid Algorithm on Class Cover Problems Journal of Software,16(4),2005,513-522
[106]M.Clerc:Discrete Particle Swarm Optimization:A Fuzzy Combinatorial Black Box. In.http://clerc.maurice.free.fr/pso/Fuzzy_Discrete_PSO/Fuzzy_DPSO.htm
[107]K.Rameshkumar, R.K. Suresh, and K.M.Mohanasundaram:Discrete Particle Swarm Optimization (DPSO) Algorithm for Permutation Flowshop Scheduling to Minimize Makspan. In:Proc. ICNC 2005, LNCS 3612, (2005) 572-581
[108]W. Pang, K. P. Wang, C. G, Zhou etc. Fuzzy Discrete Particle Swarm Optimization for Solving Traveling Salesman Problem. In:The Fourth International Conference on Computer and Information Technology (CIT'04),2004,796-800
[2]张韵华.符号计算系统Mathematica教程[M].北京：科学出版社,2001.
[3]V. Heuveline, F. Strauf. Shape Optimization Towards Stability in Constrained Dydrodynamic Systems[J]. Computational Physics,2009,228(4):938-951.
[4]V. Heuveline, F. Strauss. Shape Optimization in Fluid Mechanics with Eigenvalue Constraints,2008. http://homes.esat.kuleuven.be/-optec/events/workshops/EIGOPT/talks/eigopt-strauss.pdf
[5]X. Han. Simulation theory Study on Urban Fire-fighting And Disp Atching Process: [PHD Thesis]. Shanghai Tongji University,1999.
[6]J.K. LENSTRA, R.K. AHG and P. BRUCKER. Complexity of machine scheduling problems [J]. Annals of Discrete Mathematics,1977,1:343-362.
[7]B. G. W. Craenen. Solving Constraint Satisfaction Problems with Evolutionary Algorithms, Ph.D. Dissertation, Vrige University,2005.
[8]C. James, Bezdek. On the relationship between neural networks, pattern recognition and intelligence [J]. Int. J. Approx. Reasoning,1992,6(2):85-107.
[9]J. C. Bezdek. On the relationship between neural networks,pattern recoginition and intelligence. The Int J of Approximate Reasooning,1992,6(2):85-107.
[10]R. Bharath and J. Drosen. Neural Network Computing [M]. McGraw-Hill,1994.
[11]L. A. Zadeh. Fuzzy Sets, Infromation and Control.1965,8:338-353.
[12]Z. Pawlk. Rough Sets. International Journal of Information and Computer Science,1982, (11):341-356.
[13]Z. Pawlk. Rough Set Theoretical Aspects of Reasoning about Data. Dordrecht:Kluer Academic Publishers,1991.
[14]J. H. Holland. Adaptation in Neural and Artificial Systems. Ann Arbor, Michigan:The University of Nichigan Press,1975; Cambridge, MA:MIT Press,1992.
[15]王飞,刘大有.基于遗传算法的动态Bayesian网结构学习的研究,电子学报,2003,31(5)：698-702.
[16]A. Daniel. Evolutionary Computation for modeling and Optimization, Publisher:Springer, 2005.
[17]X. Y. Tu. Artificial Animals for Computer Animation:Biomechanics, Locomotion, Perception, and Behavior, ACM Distinguished Ph.D Dissertation Series, (Lecture Notes in Computer Science. Eds.:G. Goos, J. Hartmanis, J.van Leeuwen. Vol. 1635) Springer-Verlag,1999.
[18]D. B. Fogel. Evolutionary Computation:Toward a New Philosophy of Machine Intelligence.2nd ed. Wiley-IEEE Press,2001.
[19]周春光,梁艳春.计算智能[M].长春：吉林大学出版社,2001.
[20]Kennedy, J.Eberhart.R.C. Particle swarm optimization[C]. In:Proc. of the 1995 IEEE International Conference on Neural Networks. Piscataway, NJ, Perth, Australia:IEEE service center,1995:1942-1948
[21]Shu-Kai S. Fan and Erwie Zahara, A hybrid simplex search and particle swarm optimization for unconstrained optimization[J]. European Journal of Operational Research,2007,181:527-548.
[22]Eric Bonabeau, Marco Dorigo and Guy Theraulaz. Swarm Intelligence:From Natural to Artificial Systems[M],Oxford University Press, USA; 1 edition,1999.
[23]M. Dorigo, V. Maniezzo, A. Colorni, The ant system:Optimization by a colony of cooperating agents[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B, 1996,26(1):29-41.
[24]M. Dorigo, V. Maniezzo, A. Colorni, Positive feedback as a search strategy[R]. Technical Report,1991a:91-016, Italy:University of Milan.
[25]J. M. Liu, K. C. Tsui. Toward Nature-Inspired Computing[M], Communications of the ACM.2006,49(10):59-64.
[26]D. David, L. Diosan, D. Dumitrescu. A New Nature-Inspired Computation Model Ising Model with Rays[C], SYNASC2005,25-29 sept.2005:315-320
[27]L.N. De Castro and J.I. Timmis, Artificial immune systems as a novel soft computing paradigm[J]. Soft Computing,2003,7:526-544.
[28]C. James, Bezdek. On the relationship between neural networks, pattern recognition and intelligence [J]. Int. J. Approx. Reasoning,1992,6(2):85-107.
[29]C. G. Langton. Studying Artificial Life with Cellular Automata [J]. Physica D,1986, 10:120-149.
[30]Daniel Ashlock, Evolutionary Computation for modeling and Optimization, Publisher: Springer,2005.
[31]孙吉贵,景沈艳.非二元约束满足问题求解[J],计算机学报.2003,(26)12：1746-1752.
[32]A. L. Davis, A. Rosenfeld. Cooperating Processes for Low-Level Vision:A Survey., Artificial Intelligence[j].1981,17:245-263.
[33]R. A. Hummel, A.Rosenfeld and S. W. Zucker. Scene Labelling by Relaxation Operations. IEEE Transactions on Systems, Man, and Cybernetics.1976,6(6):420-433.
[34]M. S.Fox. Constraint-Directed Search:A Case Study of Job Shop Scheduling.1987.
[35]V.Dhar, N.Ranganathan. Integer Programming versus Expert Systems:An Experimental Comparison, Communications of the ACM.1990,33:323-336.
[36]J. F.Rit. Propagating Temporal Constraints for Scheduling, In Proceedings of the Fifth National Conference on Artificial Intelligence.1986,383-386.
[37]E. P. K. Tsang. The Consistent Labeling Problem in Temporal Reasoning, In Proceedings of the Sixth National Conference on Artificial Intelligence.1987,251-255.
[38]M.Bruynooghe. Graph Coloring and Constraint Satisfaction, Technical Report.1985,CW 44.
[39]M. Stefik. Planning with Constraints (MOLGEN:Part Ⅰ), Artificial Intelligence.1981,16: 111-140.
[40]R.Zabih, D.McAllester. A Rearrangement Search Strategy for Determining Propositional Satisfiabilty,In Proceedings of the Seventh National Conference on Artificial Intelligence.1988,155-160.
[41]J.D. Kleer, G. J. Sussman. Propagation of Constraints Applied to Circuit Synthesis, Circuit Theory and Applications.1980,8:127-144.
[42]V. Kumar. Algorithms for constraint-satisfaction problems:a survey. AI Magazine,1992, 13(1):32-44
[43]Q. Y. Yang, J. G. Sun, J. Y. Zhang and C. J. Wang, "A Hybrid Discrete Particle Swarm Algorithm for Hard Binary CSPs," Proc. of the 2nd International Conference on Natural Computation (ICNC'06) and the 3rd International Conference on Fuzzy Systems and Knowledge Discovery,Xi'an, China, LNCS 4222,2006, pp.184-193.
[44]杨轻云,孙吉贵,张居阳.稀疏二元约束满足问题的环割集粒子群算法[J],广西师范大学学报(自然科学版).2006,24(4)：135-138
[45]B.G.W. Craenen, A.E. Eiben, J.I. van Hemert. Comparing Evolutionary Algorithms on Binary Constraint Satisfaction Problems.
[46]D. Marx. Graph Colouring Problems and Their Applications in Scheduling [J],Fperiodica Polytechnica Ser.2004,48(1):11-16.
[47]N.Karmarkar. A new polynomial time algorithm for linear programming. Combinatorica, 4,1984,373-395
[48]L.G.Khachiyan. A polynomial algorithm in linear programming. Doklady Akademia Nauk SSSR,1979,1093-1096
[49]B.M.Smith. Constructing an asymptotic phase transition in random binary constraint problems. TCS,265:265-283,2001
[50]K.Xu and W.Li. Exact phase transitions in random binary constraint satisfaction problems. TCS,265-283,2001
[51]A.M.Frieze and M.Molloy. The satisfiability threshold for randomly generated binary constraint satisfaction problems. In Proc. of Random'03, pp.275-289,2003
[52]K.Xu and W.Li. Many hard examples in exact phase transitions with application to generating hard satisfiable instances, CoRR Report cs. CC/0302001,2003
[53]R. Haralick and G. Elliot. Increasing tree search efficiency for constraintsatisfaction problems, Artificial Intelligence.1980,14(3):263-313.
[54]S. Golomb, L. Baumert. Backtrack programming. A.C.M.,1965.12(4):516-524.
[55]G. Kondrak, P. van Beek. A Theoretical Evaluation of Selected Backtracking Algorithms, Artificial Intelligence.1989,89(1-2):365-387.
[56]P. Prosser. Hybrid Algorithms for the Constraint Satisfaction Problem, Computational Intelligence.1993,9(3):268-299.
[57]A. K. Mackworth. Consistency in Networks of Relations.Arfifical Intelligence. 1977,8:99-118.
[58]R. Storn, K. Price. Differential Evolution-A simple and Efficient Heuristic for Global Optimization over Continuous Spaces, Global Optimization[J].1997, 11(4):341-359.
[59]A. P. Engelbrecht, "Fundamentals of Computational Swarm Intelligence", John Wiley & Sons Ltd,2005.
[60]K. V. Pric, R. Storn, J. Lampinen, Differential Evolution:A Practical Approach to Global Optimization, London:Springer-Verlag, UK,2005.
[61]R. Storn, K.Price. Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces[R/OL],2009-01 [2009-04-06]. ICSI, Technical Report TR-95-012,1995. ftp://ftp.icsi.berkeley.edu/pub/techreports/ 1995/tr-95-012.pdf.
[62]V. P. Kenneth, M. S. Rainer. A.LampinenJouni. Differential Evolution:A Practical Approach to Global Optimization[M]. Springer,2004:135-139.
[63]J. Lampinen and I. Zelinka, "On Stagnation of the Differential Evolution Algorithm", In: Pavel Osmera, (ed.) Proc. of MENDEL 2000,6th International Mendel Conference on Soft Computing,2000, pp.76-83.
[64]J. Lampinen and I. Zelinka, "On Stagnation of the Differential Evolution Algorithm", In: Pavel Osmera, (ed.) Proc. of MENDEL 2000,6th International Mendel Conference on Soft Computing,2000, pp.76-83.
[65]C. S. Chang, D. Y. Xu, "Differential Evolution Based Tuning of Fuzzy Automatic Train operation for Mass Rapid Transit System", IEEE Proc-Electric Power Applications,2000, 147(3):206-212
[66]J. Teo, "Exploring Dynamic Self-adaptive Populations in Differential Evolution", Soft Computing-A Fusion of Foundations,Methodologies and Applications, Vol.10 (8),2006, pp.673-686.
[67]J. Brest, B. Boskovic Boskovi'c, S. Greiner, V. Zumer Zumer and M. S. Maucec, "Performance Comparison of Self-Adaptive and Adaptive Differential Evolution Algorithms", Technical Report #2006-1-LABRAJ, University of Maribor, Faculty of Electrical Engineering and Computer Science, Slovenia,2006, http://marcel.unimb.si/janez/brest-TRl.html.
[68]J. Brest, S. Greiner, B. Bo(?)skovi'c, M. Mernik and.V. (?)Zumer, "Self-Adapting Control Parameters in Differential Evolution:A Comparative Study on Numerical Benchmark Problems", IEEE Transactions on Evolutionary Computation, Vol.10,2006, pp.646-657.
[69]Z. Yang, K. Tang and X. Yao, "Self-adaptive Differential Evolution with Neighborhood Search", In Proc. IEEE Congress on Evolutionary Computation, Hong Kong,2008, pp. 1110-1116.
[70]U. K. Chakraborty, "Advances in Differential Evolution", (Ed.) Springer-Verlag, Heidelberg,2008.
[71]陈涛,雍龙泉,邓方安等.基于差分进化算法的支持向量机参数选择[J],计算机工程与应用.2011,47(5)：24-26.
[72]刘黎黎,王诗元,汪定伟.求解交货期可变动态调度问题的差分进化算法[J],东北大学学报(自然科学版),2011,32(2)：183-187
[73]牛雪丽,刘希玉,魏欣.基于耗散结构理论的差分进化算法[J],计算机应用研究.2010,27(2)：504-505.
[74]宋敏,魏瑞轩,冯志明.基于差分进化算法的异构多无人机任务分配[J],系统仿真学报.201022(7)：1706-1710.
[75]杨启文,蔡亮,薛云灿.差分进化算法综述[J],模式识别与人工智能.2008,21(4)：506-513.
[76]贺毅朝,王熙照,刘坤起.王彦祺.差分演化的收敛性分析与算法改进,Journal of Software, Vol.21, No.5,2010,21 (5)-:875-885.
[77]R. Storn, K.Price. Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces[R/OL],2009-01 [2009-04-06]. ICSI, Technical Report TR-95-012,1995. ftp://ftp.icsi.berkeley.edu/pub/techreports/ 1995/tr-95-012.pdf.
[78]H. Y. Fan, J. Lampinen. A\trigonometric Mutation Operation to Differential Evolution[J], Global Optimization.2003,27(1):105-129.
[79]R. Mendes,A. S. Mohais. DynDE:A Differential Evolution for Dynamic Optimizatio:2005,:2808-2815.
[80]T. Blackwell, J.Branke. Multi-Swarm Optimization in Dynamic Environments,2004, 3005:489-500.
[81]卢峰,高立群.基于多种群的自适应差分进化算法[J],东北大学学报(自然科学版).2010,Vol 31(11)：1538-1541
[82]张雪霞,陈维荣,戴朝华.带局部搜索的动态多群体自适应差分进化算法及函数优化[J],电子学报.2010,38(8)：1825-1830.
[83]P. K. Bergey, C. Ragsdale. Modified Differential Evolution:A Greedy Random Strategy for Genetic Recombination[J],Management Science.2005,33(3):255-265.
[84]J. P. Chiou, C. F. Chang, C. T. Su. Ant Direction Hybrid Differential Evolution for Solving Large Capacitor Placement Problems(C), IEEE Trans on Power System,2004, 19(4):1794-1800.
[85]J. Y. Yan, Q. Ling, D. Sun. A Differential Evolution with Simulated Annealing Updating Method(C), Proc of the International Conference on Machine Learning and Cybernetics. Dalian, China.2006:2103-2106.
[86]Q. Y. Yang, J. G. Sun, J. Y. Zhang and C. J. Wang, A Hybrid Discrete Particle Swarm Algorithm for Hard Binary CSPs, Proc. of the 2nd International Conference on Natural Computation (ICNC'06) and the 3rd International Conference on Fuzzy Systems and Knowledge Discovery,Xi'an, China, LNCS 4222,2006, pp.184-193.
[87]J. Lampinen, I. Zelinka。On Stagnation of the Differential Evolution Algorithm, In: Pavel Osmera, (ed.) Proc. of MENDEL 2000,6th International Mendel Conference on Soft Computing,2000, pp.76-83.
[88]B. M. Smith. Phase transition and the mushy region in constraintsatisfaction problems, Proc. of the 11th European Conference onArtificial Intelligence. Wiley,1994, pp.100-104.
[89]Q. Y. Yang, A comparative stude of discrete differential evolution on binary constraint satisfaction problems, Proc. of the Congress on Evolutionary Computation(CEC’08), pp.330-335.
[90]Wu Lianghong,Wang Yaonan. Self-adapting control parameters modified differential evolution for trajectory planning manipulaor[J]. Control Theory Application,2007, 5(4):365-373.
[91]吴亮红.差分进化算法及应用研究[D].湖南：湖南大学电气与信息工程学院,2007.65-71.
[92]S. L. Birbil and S. C. Fang:An electromagnetism-like mechanism for global optimization, Journal of Global Optimization,(2003),25 (3):263-282.
[93]张长胜.求解规划、聚类和调度问题的混合粒子群算法研究[D].吉林大学.2009
[94]J. Kennedy, R. C. Eberhart. Particle swarm optimization. IEEE Int'I Conf. Neural Networks, Perch, Australia,1995.
[95]L. Schoofs, B. Naudts. Swarm intelligence on the binary constraint satisfaction problem. IEEE Congress on Evolutionary Com-putation (CEC 2002), Honolulu, Hawaii, USA. 2002.
[96]n-Zhong Wang, Ji-Gui Sun Particle swarm optimization for satisfiability (SAT), In: Knowledge Economy Meets Science and Technology KEST2004, the 2nd Int'I Conf. Knowledge Economy and Development of Science an Technology. Beijing:Tsinghua University Press,2004.36-41
[97]Y.Shi and R.C.Eberhart. A modified particle swarm optimizer. In:Proc. of the IEEE International Conference on Evolutionary Computation. Piscataway, NJ, Anchorage, AK USA:IEEE service center,1998,69-73
[98]Laskari, E. C., Parsopoulos, K. E., and Vrahatis, M. N:Particle swarm optimization for integer programming. In:Proc. of the IEEE Congress on Evolutionary Computation (CEC 2002), Honolulu, Hawaii, USA. (2002) 1582-1587
[99]A. Salman, I. Ahmad, S. Al-Madani. Particle Swarm optimization for task assignment Problem. Microprocessors and Microsystems,26(2002),363-371
[100]杨轻云.约束满足问题与调度问题中离散粒子群算法研究[D].吉林大学.2006
[101]E. C. Laskari, K. E. Parsopoulos, M. N:Particle swarm optimization for integer programming. In:Proc. of the IEEE Congress on Evolutionary Computation (CEC 2002), Honolulu, Hawaii, USA. (2002) 1582-1587
[102]A. Salman, I. Ahmad, S. Al-Madani. Particle Swarm optimization for task assignment Problem. Microprocessors and Microsystems,26(2002),363-371.
[103]M. Fatih Tasgetiren and Yun-Chia Liang. A Binary Particle Swarm Optimization Algorithm for Lot Sizing Problem. Journal of Economic and Social Research,5(2),2003, 1-20
[104]Maurice Clerc. Binary particle swarm optimisers:toolbox, derivations and mathematical insights. http://clerc.maurice.free.fr/pso/binary_pso
[105]HUANG Yan-Xin, ZHOU Chun-Guang, ZOU Shu-Xue, and WANG Yan.A Hybrid Algorithm on Class Cover Problems Journal of Software,16(4),2005,513-522
[106]M.Clerc:Discrete Particle Swarm Optimization:A Fuzzy Combinatorial Black Box. In.http://clerc.maurice.free.fr/pso/Fuzzy_Discrete_PSO/Fuzzy_DPSO.htm
[107]K.Rameshkumar, R.K. Suresh, and K.M.Mohanasundaram:Discrete Particle Swarm Optimization (DPSO) Algorithm for Permutation Flowshop Scheduling to Minimize Makspan. In:Proc. ICNC 2005, LNCS 3612, (2005) 572-581
[108]W. Pang, K. P. Wang, C. G, Zhou etc. Fuzzy Discrete Particle Swarm Optimization for Solving Traveling Salesman Problem. In:The Fourth International Conference on Computer and Information Technology (CIT'04),2004,796-800