Cross entropy for multiobjective combinatorial optimization problems with linear relaxations

2015 ◽  
Vol 243 (2) ◽  
pp. 362-368 ◽  
Author(s):  
Rafael Caballero ◽  
Alfredo G. Hernández-Díaz ◽  
Manuel Laguna ◽  
Julián Molina
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Cross Entropy ◽  
Multiobjective Combinatorial Optimization ◽  
Combinatorial Optimization Problems ◽  
Linear Relaxations

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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