Talaván Pedro M, Yáñez Javier
Instituto Nacional de Estadística, Josefa Valcárcel 46, 28027 Madrid, Spain.
Neural Netw. 2006 May;19(4):416-28. doi: 10.1016/j.neunet.2005.10.008. Epub 2006 Feb 20.
The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.
通过连续霍普菲尔德网络（CHN）求解优化问题是基于某个能量函数或李雅普诺夫函数，该函数会随着系统的演化而减小，直至达到局部最小值。本文提出了一种新的能量函数，以便能够求解任何具有二次目标函数的0-1线性约束规划问题。这个问题被称为广义二次背包问题（GQKP），它包含一些著名的问题作为特殊情况，比如旅行商问题（TSP）和二次分配问题（QAP）。这种新的能量函数对其他作者提出的函数进行了推广。通过这个能量函数，任何GQKP都可以通过本文详细介绍的适当参数设置程序来求解。作为一个特殊情况，为了测试这种广义能量函数，还包含了一些求解旅行商问题的计算实验。
