A simulated annealing approach to the network design problem with variational inequality constraints. (English) Zbl 0764.90084

Friesz, Terry L.; Cho, Hsun-Jung; Mehta, Nihal J.; Tobin, Roger L.; Anandalingam, G.

Transp. Sci. 26, No. 1, 18-26 (1992).

Summary: The equilibrium network design problem can be formulated as a mathematical program with variational inequality constraints. We know this problem is nonconvex; hence, it is difficult to solve for a globally optimal solution. We propose a simulated annealing algorithm for the equilibrium network design problem. We demonstrate the ability of this algorithm to determine a globally optimal solution for two different networks. One of these describes an actual city in the midwestern United States.

MSC:

90C35	Programming involving graphs or networks
90C27	Combinatorial optimization
49J40	Variational inequalities
90-08	Computational methods for problems pertaining to operations research and mathematical programming
90C26	Nonconvex programming, global optimization

Keywords:

equilibrium network design; variational inequality constraints; simulated annealing; globally optimal solution