Advances in Combinatorial Optimization:Linear Programming Formulations of the Traveling Salesman and Other Hard Combinatorial Optimization Problems by Moustapha Diaby & Mark H Karwan

Author:Moustapha Diaby & Mark H Karwan
Language: eng
Format: mobi
Publisher: World Scientific Publishing Co Pte Ltd
Published: 2016-01-27T23:00:00+00:00

are infeasible for QL. Hence, L and QL do not coincide. Hence, L and QL are distinct, and respectively, non-symmetric. The theorem follows from this directly.

The concepts used in the proof of Theorem 5.1 are illustrated in Figures 5.1 and 5.2. Figure 5.1 illustrates the case of a “swap” of constraint matrix coefficients between variables when the polytope described is non-symmetric. As can be seen from this figure, the “original” and “transformed” polytopes are congruent, but do not coincide. In Figure 5.2 (where the “original” polytope is symmetric (around the 45-degree line, specifically)), the “original” and “transformed” polytopes are congruent, and also coincide.

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