Multiobjective combinatorial optimization problems with a cost and several bottleneck objective functions: An algorithm with reoptimization

2012 ◽  
Vol 39 (9) ◽  
pp. 1969-1976 ◽  
Author(s):  
Cláudio T. Bornstein ◽  
Nelson Maculan ◽  
Marta Pascoal ◽  
Leizer L. Pinto
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Objective Functions ◽  
Multiobjective Combinatorial Optimization ◽  
Combinatorial Optimization Problems

scholarly journals Computation Results of Finding All Efficient Points in Multiobjective Combinatorial Optimization

2008 ◽  
Vol 3 (4) ◽  
pp. 374 ◽  
Author(s):  
Milan Stanojevic ◽  
Mirko Vujoševic ◽  
Bogdana Stanojevic
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Efficient Points ◽  
Steiner Tree Problem ◽  
Pareto Optimal Solutions ◽  
Problem Size ◽  
Original Algorithm ◽  
Multiobjective Combinatorial Optimization ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

The number of efficient points in criteria space of multiple objective combinatorial optimization problems is considered in this paper. It is concluded that under certain assumptions, that number grows polynomially although the number of Pareto optimal solutions grows exponentially with the problem size. In order to perform experiments, an original algorithm for obtaining all efficient points was formulated and implemented for three classical multiobjective combinatorial optimization problems. Experimental results with the shortest path problem, the Steiner tree problem on graphs and the traveling salesman problem show that the number of efficient points is much lower than a polynomial upper bound.

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