Abstract
This paper presents a new simplex-type algorithm for Linear Programming with the following two main characteristics: (i) the algorithm computes basic solutions which are neither primal or dual feasible, nor monotonically improving and (ii) the sequence of these basic solutions is connected with a sequence of monotonically improving interior points to construct a feasible direction at each iteration. We compare the proposed algorithm with the state-of-the-art commercial CPLEX and Gurobi Primal-Simplex optimizers on a collection of 93 well known benchmarks. The results are promising, showing that the new algorithm competes versus the state-of-the-art solvers in the total number of iterations required to converge.
Highlights
Linear Programming (LP) constitutes one of the most fundamental classes of mathematical programming models which is widely used in many scientific areas since many real world problems can be formulated as Linear Programs (LPs) (Triantafyllidis & Papageorgiou, 2018; Gkioulekas & Papageorgiou, 2019; Yang et al, 2016; Amin & Emrouznejad, 2011; Janssens & Ramaekers, 2011; Fernndez & Borrajo, 2012; Burdett et al, 2017)
The majority of these algorithms can be divided into two main categories: (i) simplex-type or pivoting algorithms and (ii) Interior Point Methods (IPMs)
In this paper we proposed a new non-monotonic simplex-type algorithm for solving LPs. interior Exterior Primal Simplex Algorithm (iEPSA) does not maintain monotonicity on the basic solutions but only on the interior point solutions
Summary
Linear Programming (LP) constitutes one of the most fundamental classes of mathematical programming models which is widely used in many scientific areas since many real world problems can be formulated as Linear Programs (LPs) (Triantafyllidis & Papageorgiou, 2018; Gkioulekas & Papageorgiou, 2019; Yang et al, 2016; Amin & Emrouznejad, 2011; Janssens & Ramaekers, 2011; Fernndez & Borrajo, 2012; Burdett et al, 2017). Many algorithms have been invented for the solution of LPs. Many algorithms have been invented for the solution of LPs The majority of these algorithms can be divided into two main categories: (i) simplex-type or pivoting algorithms and (ii) Interior Point Methods (IPMs). The Primal Simplex Algorithm (PSA) (Dantzig, 1949) had been the most efficient method for solving LPs until the 80’s. PSA ranked as one of the top 10 algorithms of the 20th century (Dongarra & Sullivan, 2000). It performs well in practice, on LPs of small or medium size.
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