CONTINUOUS EQUILIBRIUM NETWORK DESIGN MODELS
CONTINUOUS EQUILIBRIUM NETWORK DESIGN MODELS
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DOI：
10.1016/0191-2615(79)90004-3
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发表时间：
1979-01-01
影响因子：
6.8
通讯作者：
LEBLANC, LJ
中科院分区：
文献类型：
--
作者：
ABDULAAL, M;LEBLANC, LJ
在用户最优流量假设下的网络设计问题可以建模为0-1混合整数规划问题。相反，我们制定的网络设计问题与连续投资变量的均衡分配作为一个非线性优化问题。我们表明，这个优化问题是等价的，我们解决了直接搜索技术的无约束问题。对于凸投资成本函数，鲍威尔的方法和胡克和吉夫斯的方法的性能是近似相同的计算要求为24节点，76弧网络。对于凹投资函数的情况，胡克和吉夫斯是上级。凹连续模型的解与0-1模型的解非常相似。而且，所需的求解时间远小于相同网络的相应离散模型所需的求解时间。讨论了连续方法的优点和缺点以及计算要求。
It is known that the network design problem with the assumption of user optimal flows can be modeled as a 0–1 mixed integer programming problem. Instead, we formulate the network design problem with continuous investment variables subject to equilibrium assignment as a nonlinear optimization problem. We show that this optimization problem is equivalent to an unconstrained problem which we solve by direct search techniques. For convex investment cost functions, the performance of both Powell's method and the method of Hooke and Jeeves is approximately the same with respect to computational requirements for a 24 node, 76 arc network. For the case of concave investment functions, Hooke and Jeeves was superior. The solution to the concave continuous model was very similar to that of the 0–1 model. Furthermore, the required solution time was far less than that required by the corresponding discrete model of the same network. The advantages and disadvantages of the continuous approach as well as the computational requirements are discussed.