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    STUDIA MATHEMATICA - Issue no. 4 / 2012  
         
  Article:   A KIND OF BILEVEL TRAVELING SALESMAN PROBLEM.

Authors:  . 		 
       
         
  Abstract:   The present paper highlights a type of a bilevel optimization problem on a graph. It models a real practical problem. Let N be a finite set, G = (N,E) be a weighted graph and let I ϲ N. Let C1, respectively C2, be the set of those subgraphs G1 = (N1, E1), respectively G2 = (N2, E2), of G which fulfill some given conditions in each case. Let a and b be positive numbers and let g be a natural value function defined on the set of subgraphs of G. We study the following bilevel programming problem:
where h(Gi) represents the value of a Hamiltonian circuit of minimum value corresponding to the subgraph Gi, i = 1, 2, and

Mathematics Subject Classification (2010): 90C29, 90C35, 90C90.

Keywords: Bilevel programming, lexicographic optimization, traveling salesman problem. 		 
         
     
         
         
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