自然启发的优化算法及其应用研究
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摘要
自然启发的算法是近几年来在协同进化论基础上发展起来的一种新的优化算法,为寻找复杂问题解决方案提供了新的思路。由于自然启发的优化算法具有的智能性、通用性、本质并行性和全局搜索能力,已在计算机科学、知识发现、通信网络、机器人等研究领域显示出潜力和魅力,成为智能计算领域的一个研究热点。本文对两类自然启发的优化算法:类电磁机制算法和遗传算法,进行了系统深入的研究,针对不同的优化问题提出了有效的自然启发的优化算法进行求解。
本文的主要工作如下:
1.针对标准类电磁机制算法中电荷溢出和参数敏感的问题,提出了新的电荷和粒子之间作用力的计算公式。任意两个粒子之间作用力的大小与两粒子的目标函数之差、粒子的距离有关,鼓励粒子沿着合力的方向朝邻近的局部最优解移动。在此基础上,提出了求解无约束优化问题的类电磁机制算法。用标准的Benchmark函数对算法的性能进行了测试,并和已有算法的比较结果表明,新算法能够快速的求出问题的最优解或近似最优解。
2.提出了一种基于模式搜索的类电磁机制算法求解约束优化问题。引入了粒子的违反度函数,提出了约束优化问题粒子电荷的0-1计算公式,使得可行粒子的电荷总是大于不可行粒子的电荷;新的受力公式,有利于引导不可行粒子转化为满足约束条件的粒子。理论分析表明新算法以概率1收敛到问题的全局最优解。数值实验结果表明,新算法具有收敛快、求解性能好的特点,是求解约束优化问题的一种非常有潜力的算法。
3.给出了求解多目标优化问题的一种新遗传算法。为了引导搜索向有利的方向进行,设计了有效的杂交算子和简单的变异算子,并证明了算法的全局收敛性。计算机仿真结果表明新算法可以快速的找到一组Pareto最优解。
4.研究了一种求解图着色问题的新解法。针对整数编码的冗余性,提出了有序整数编码方式,大大缩小了搜索空间。基于图着色问题的特点,设计了一种新的、有效的杂交算子。为了提高杂交算子的搜索能力,结合了一个贪婪的局部搜索技术来改进杂交算子。在此基础上提出了求解图着色问题的一种新的遗传算法,并证明了其全局收敛性。对10个国际标准算例(图的顶点从11到1000)进行了仿真实验,与以往算法的比较结果表明,新算法是有效的、有竞争力的算法。
Nature-inspired algorithm is a new method of optimization based on co-evolution of a group of individuals in recent years and provides a new tool for complex optimization problems. Due to its advantages of intelligence, wide applicability, global search ability and parallelism, nature-inspired optimization algorithm has become a hot research area and has been widely used in many fields such as computer science, telecommunication network, knowledge discovery, robots and so on. In this dissertation, studies are focused on two typical models of nature-inspired computation: electromagnetism-like mechanism (EM) algorithms and genetic algorithms (GAs). Several novel nature-inspired optimization algorithms are proposed for different optimization problems, respectively. The main contributions of this thesis can be summarized as follows:
1. In order to avoid the charge overflow and parameter sensitivity in standard electromagnetism-like mechanism algorithm, new formulas of particle charge and force between any two particles are presented, in which the magnitude of the force is related to the difference of their objective function values and the distance between two particle. The particle moves towards a local optimal solution in its neighborhood along the direction of total force. Based on these, an improved EM algorithm is proposed for unconstrained optimization problems. Simulation results on benchmark problems demonstrate that the proposed algorithm is effective and can find the global optimal solution quickly.
2. An electromagnetism-like mechanism method is proposed for solving constrained optimizations on the basis of pattern search. First, the violation degree function is introduced for the constrained optimization problems. Second, inspired from the idea that feasible particles are always better than infeasible ones, the new computational equation of the particle charge is designed. Third, a formula for computing the force between two particles is presented, which can guide infeasible particles to move towards feasible ones. Furthermore, the convergence of the new algorithm is proved and the computer simulations are made. Compared with simulation results of the existing algorithms, the proposed algorithm has the advantages of quick convergence and good performance and is very potential for constrained optimization problems.
3. For unconstrained multi-objective optimization problems (UMOP), a new algorithm is proposed. In order to guide the search along potential direction, an effective crossover operator and a simple mutation operator are presented. The convergence of the proposed algorithm is proved using the theory of probability. The simulation results show that the proposed algorithm can more quickly track the Pareto optimal solutions in comparison with other existing algorithms.
4. A novel method for graph coloring problem (GCP) is presented. A new encoding scheme is presented to avoid the redundancy of the integer representation. An effective crossover is designed according to the characteristic of the GCP. In order to enhance its ability of exploration, a greedy local search is integrated into the crossover operator. Based on these, a novel genetic algorithm for GCP is presented and its convergence to global optimal solution with probability one is proved. The proposed algorithm was tested on 10 standard test problems with the number of vertices from 11 to 1000. Experimental results indicate that the proposed algorithm performs well and is competitive with other existing algorithms.
本文的主要工作如下:
1.针对标准类电磁机制算法中电荷溢出和参数敏感的问题,提出了新的电荷和粒子之间作用力的计算公式。任意两个粒子之间作用力的大小与两粒子的目标函数之差、粒子的距离有关,鼓励粒子沿着合力的方向朝邻近的局部最优解移动。在此基础上,提出了求解无约束优化问题的类电磁机制算法。用标准的Benchmark函数对算法的性能进行了测试,并和已有算法的比较结果表明,新算法能够快速的求出问题的最优解或近似最优解。
2.提出了一种基于模式搜索的类电磁机制算法求解约束优化问题。引入了粒子的违反度函数,提出了约束优化问题粒子电荷的0-1计算公式,使得可行粒子的电荷总是大于不可行粒子的电荷;新的受力公式,有利于引导不可行粒子转化为满足约束条件的粒子。理论分析表明新算法以概率1收敛到问题的全局最优解。数值实验结果表明,新算法具有收敛快、求解性能好的特点,是求解约束优化问题的一种非常有潜力的算法。
3.给出了求解多目标优化问题的一种新遗传算法。为了引导搜索向有利的方向进行,设计了有效的杂交算子和简单的变异算子,并证明了算法的全局收敛性。计算机仿真结果表明新算法可以快速的找到一组Pareto最优解。
4.研究了一种求解图着色问题的新解法。针对整数编码的冗余性,提出了有序整数编码方式,大大缩小了搜索空间。基于图着色问题的特点,设计了一种新的、有效的杂交算子。为了提高杂交算子的搜索能力,结合了一个贪婪的局部搜索技术来改进杂交算子。在此基础上提出了求解图着色问题的一种新的遗传算法,并证明了其全局收敛性。对10个国际标准算例(图的顶点从11到1000)进行了仿真实验,与以往算法的比较结果表明,新算法是有效的、有竞争力的算法。
Nature-inspired algorithm is a new method of optimization based on co-evolution of a group of individuals in recent years and provides a new tool for complex optimization problems. Due to its advantages of intelligence, wide applicability, global search ability and parallelism, nature-inspired optimization algorithm has become a hot research area and has been widely used in many fields such as computer science, telecommunication network, knowledge discovery, robots and so on. In this dissertation, studies are focused on two typical models of nature-inspired computation: electromagnetism-like mechanism (EM) algorithms and genetic algorithms (GAs). Several novel nature-inspired optimization algorithms are proposed for different optimization problems, respectively. The main contributions of this thesis can be summarized as follows:
1. In order to avoid the charge overflow and parameter sensitivity in standard electromagnetism-like mechanism algorithm, new formulas of particle charge and force between any two particles are presented, in which the magnitude of the force is related to the difference of their objective function values and the distance between two particle. The particle moves towards a local optimal solution in its neighborhood along the direction of total force. Based on these, an improved EM algorithm is proposed for unconstrained optimization problems. Simulation results on benchmark problems demonstrate that the proposed algorithm is effective and can find the global optimal solution quickly.
2. An electromagnetism-like mechanism method is proposed for solving constrained optimizations on the basis of pattern search. First, the violation degree function is introduced for the constrained optimization problems. Second, inspired from the idea that feasible particles are always better than infeasible ones, the new computational equation of the particle charge is designed. Third, a formula for computing the force between two particles is presented, which can guide infeasible particles to move towards feasible ones. Furthermore, the convergence of the new algorithm is proved and the computer simulations are made. Compared with simulation results of the existing algorithms, the proposed algorithm has the advantages of quick convergence and good performance and is very potential for constrained optimization problems.
3. For unconstrained multi-objective optimization problems (UMOP), a new algorithm is proposed. In order to guide the search along potential direction, an effective crossover operator and a simple mutation operator are presented. The convergence of the proposed algorithm is proved using the theory of probability. The simulation results show that the proposed algorithm can more quickly track the Pareto optimal solutions in comparison with other existing algorithms.
4. A novel method for graph coloring problem (GCP) is presented. A new encoding scheme is presented to avoid the redundancy of the integer representation. An effective crossover is designed according to the characteristic of the GCP. In order to enhance its ability of exploration, a greedy local search is integrated into the crossover operator. Based on these, a novel genetic algorithm for GCP is presented and its convergence to global optimal solution with probability one is proved. The proposed algorithm was tested on 10 standard test problems with the number of vertices from 11 to 1000. Experimental results indicate that the proposed algorithm performs well and is competitive with other existing algorithms.
引文
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