Solving binary semidefinite programming problems and binary linear programming problems via multi-objective programming

Document Type : Research Paper

Authors

Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran

Abstract

‎In recent years the binary quadratic program has grown in‎ ‎combinatorial optimization‎. ‎Quadratic programming can‎ ‎be formulated as a semidefinite programming problem‎. ‎In this paper‎, ‎we consider the general form of‎ ‎binary semidefinite programming problems (BSDP)‎.‎ ‎We show the optimal solutions of the BSDP belong to the efficient set of a semidefinite multiobjective programming problem (SDMOP)‎. ‎Although‎ ‎finding all efficient points for multiobjective is not an easy problem‎, ‎but‎
‎solving a continuous problem would be easier than a discrete variable problem‎. ‎In this paper‎, ‎we solve an SDMOP‎, ‎as an auxiliary‎, ‎instead of BSDP‎. We show the performance of our method by generating and solving random problems.

Keywords

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Volume 13, Issue 1
March 2022
Pages 297-304
  • Receive Date: 02 February 2018
  • Revise Date: 21 July 2018
  • Accept Date: 13 February 2019