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A new non-monotonic infeasible simplex-type algorithm for Linear Programming.

Charalampos P Triantafyllidis1, Nikolaos Samaras2

  • 1Computational Biology & Integrative Genomics, Department of Oncology, Medical Sciences Division, University of Oxford, Oxford, United Kingdom.

Peerj. Computer Science
|April 5, 2021
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Summary
This summary is machine-generated.

A novel simplex-type algorithm for Linear Programming offers competitive performance against state-of-the-art solvers. This new method achieves convergence comparable to commercial optimizers like CPLEX and Gurobi.

Keywords:
Exterior pointInfeasibleInterior point methodLinear programmingMathematical programmingNon-monotonicOptimizationSimplex-type

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Area of Science:

  • Operations Research
  • Computer Science
  • Applied Mathematics

Background:

  • Linear Programming (LP) is a fundamental optimization technique with wide applications.
  • Existing simplex-type algorithms often rely on primal or dual feasibility and monotonic improvement.
  • The need for more efficient and robust LP solvers persists.

Purpose of the Study:

  • To introduce a new simplex-type algorithm for Linear Programming.
  • To address limitations of traditional simplex methods by allowing non-feasible and non-improving basic solutions.
  • To evaluate the performance of the proposed algorithm against leading commercial solvers.

Main Methods:

  • The algorithm computes basic solutions that are neither primal nor dual feasible, nor monotonically improving.
  • It constructs a feasible direction at each iteration by connecting basic solutions with interior points.
  • Performance comparison was conducted using 93 well-known benchmark problems.

Main Results:

  • The proposed algorithm demonstrates competitive performance against state-of-the-art commercial solvers (CPLEX, Gurobi).
  • The number of iterations required for convergence is comparable to established Primal-Simplex optimizers.
  • Results indicate promising efficiency for the new simplex-type algorithm.

Conclusions:

  • The novel simplex-type algorithm presents a viable alternative for solving Linear Programming problems.
  • Its unique approach to basic solutions and feasible directions contributes to its competitive performance.
  • Further research may explore its scalability and application to larger-scale optimization challenges.