Geometrical con...guration of the Pareto frontier of bi-criteria {0,1}-knapsack problems
نویسندگان
چکیده
This paper deals with three particular models of the bi-criteria {0,1}-knapsack problem: equal weighted items, constant sum of the criteria coe¢cients, and the combination of the two previous models. The con...guration of the Pareto frontier is presented and studied. Several properties on the number and the composition of the e¢cient solutions are devised. The connectedness of the e¢cient solutions is investigated and observed for the entire set of e¢cient solutions of the third model. The models are highly structured and induce singular properties in the geometry of Pareto frontiers when compared with the ones of randomly generated instances. This aspect can increase the knowledge about the generation of e¢cient solutions for general bi-criteria {0,1}-knapsack problems. The models can also be useful in generic {0,1}-multiple criteria problems. Key-words: Bi-criteria knapsack problems, Pareto frontier, Connectedness, Combinatorial Optimization.
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