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第147行： − − For some versions of the algorithm, it is possible to prove that it is convergent (i.e., it is able to find the global optimum in finite time). The first evidence of convergence for an ant colony algorithm was made in 2000, the graph-based ant system algorithm, and later on for the ACS and MMAS algorithms. Like most [[metaheuristic]]s, it is very difficult to estimate the theoretical speed of convergence. A performance analysis of a continuous ant colony algorithm with respect to its various parameters (edge selection strategy, distance measure metric, and pheromone evaporation rate) showed that its performance and rate of convergence are sensitive to the chosen parameter values, and especially to the value of the pheromone evaporation rate.<ref>V.K.Ojha, A. Abraham and V. Snasel, [https://arxiv.org/abs/1707.01812 ACO for Continuous Function Optimization: A Performance Analysis], 14th International Conference on Intelligent Systems Design and Applications (ISDA), Japan, Page 145 - 150, 2017, 978-1-4799-7938-7/14 2014 IEEE.</ref> In 2004, Zlochin and his colleagues<ref name="Zlochin model-based search">M. Zlochin, M. Birattari, N. Meuleau, et M. Dorigo, ''Model-based search for combinatorial optimization: A critical survey'', Annals of Operations Research, vol. 131, pp. 373-395, 2004.</ref> showed that COAC-type algorithms could be assimilated methods of [[stochastic gradient descent]], on the [[cross-entropy]] and [[estimation of distribution algorithm]]. They proposed these [[metaheuristic]]s as a "[[research-based model]]". − − For some versions of the algorithm, it is possible to prove that it is convergent (i.e., it is able to find the global optimum in finite time). The first evidence of convergence for an ant colony algorithm was made in 2000, the graph-based ant system algorithm, and later on for the ACS and MMAS algorithms. Like most metaheuristics, it is very difficult to estimate the theoretical speed of convergence. A performance analysis of a continuous ant colony algorithm with respect to its various parameters (edge selection strategy, distance measure metric, and pheromone evaporation rate) showed that its performance and rate of convergence are sensitive to the chosen parameter values, and especially to the value of the pheromone evaporation rate. In 2004, Zlochin and his colleagues showed that COAC-type algorithms could be assimilated methods of stochastic gradient descent, on the cross-entropy and estimation of distribution algorithm. They proposed these metaheuristics as a "research-based model". −
→收敛 Convergence
==收敛 Convergence==
==收敛 Convergence==
对于某些版本的算法，可以证明它是收敛的（也就是说，它能在有限时间内找到全局最优解）。蚁群算法的收敛性在2000年首次得到证实，然后是基于图的蚂蚁系统算法，以及后来的 ACS 和 MMAS 算法。和大多数启发式算法一样，很难估计理论上的收敛速度。对连续蚁群算法相关各参数（边的选择策略、距离测度方法和信息素蒸发率）的性能分析表明，蚁群算法的性能和收敛速度对参数值，特别是信息素蒸发率的参数选择非常敏感。<ref>V.K.Ojha, A. Abraham and V. Snasel, [https://arxiv.org/abs/1707.01812 ACO for Continuous Function Optimization: A Performance Analysis], 14th International Conference on Intelligent Systems Design and Applications (ISDA), Japan, Page 145 - 150, 2017, 978-1-4799-7938-7/14 2014 IEEE.</ref> 在2004年，Zlochin 和他的同事<ref name="Zlochin model-based search">M. Zlochin, M. Birattari, N. Meuleau, et M. Dorigo, ''Model-based search for combinatorial optimization: A critical survey'', Annals of Operations Research, vol. 131, pp. 373-395, 2004.</ref>们展示了COAC类型的算法在[[交叉熵 cross-entropy]]和[[分布估计算法 estimation of distribution algorithm]]中可以同化为随机梯度下降方法。他们提出这些元启发式算法作为一个“基于研究的模型”。
对于某些版本的算法，可以证明它是收敛的（也就是说，它能在有限时间内找到全局最优解）。蚁群算法的收敛性在2000年首次得到证实，然后是基于图的蚂蚁系统算法，以及后来的 ACS 和 MMAS 算法。和大多数启发式算法一样，很难估计理论上的收敛速度。对连续蚁群算法相关各参数（边的选择策略、距离测度方法和信息素蒸发率）的性能分析表明，蚁群算法的性能和收敛速度对参数值，特别是信息素蒸发率的参数选择非常敏感。<ref>V.K.Ojha, A. Abraham and V. Snasel, [https://arxiv.org/abs/1707.01812 ACO for Continuous Function Optimization: A Performance Analysis], 14th International Conference on Intelligent Systems Design and Applications (ISDA), Japan, Page 145 - 150, 2017, 978-1-4799-7938-7/14 2014 IEEE.</ref> 在2004年，Zlochin 和他的同事<ref name="Zlochin model-based search">M. Zlochin, M. Birattari, N. Meuleau, et M. Dorigo, ''Model-based search for combinatorial optimization: A critical survey'', Annals of Operations Research, vol. 131, pp. 373-395, 2004.</ref>们展示了COAC类型的算法在[[交叉熵 cross-entropy]]和[[分布估计算法 estimation of distribution algorithm]]中可以同化为随机梯度下降方法。他们提出这些元启发式算法作为一个“基于研究的模型”。
==应用==
==应用==