Computational aspects of simplex and MBU-simplex algorithms using different anti-cycling pivot rules

Illés, Tibor and Nagy, Adrienn (2014) Computational aspects of simplex and MBU-simplex algorithms using different anti-cycling pivot rules. Optimization, 63 (1). pp. 49-66. ISSN 0233-1934

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Abstract

Several variations of index selection rules for simplex-type algorithms for linear programming, like the Last-In-First-Out or the Most-Often-Selected-Variable are rules not only theoretically finite, but also provide significant flexibility in choosing a pivot element. Based on an implementation of the primal simplex and the monotonic build-up (MBU) simplex method, the practical benefit of the flexibility of these anti-cycling pivot rules is evaluated using public benchmark LP test sets. Our results also provide numerical evidence that the MBU-simplex algorithm is a viable alternative to the traditional simplex algorithm.