Annals of Operations Research

, Volume 238, Issue 1–2, pp 651–657 | Cite as

f-Flip strategies for unconstrained binary quadratic programming

  • Fred Glover
  • Jin-Kao Hao


Unconstrained binary quadratic programming (UBQP) provides a unifying modeling and solution framework for solving a remarkable range of binary optimization problems, including many accompanied by constraints. Current methods for solving UBQP problems customarily rely on neighborhoods consisting of flip moves that select one or more binary variables and “flip” their values to the complementary value (from 1 to 0 or from 0 to 1). We introduce a class of approaches called f-flip strategies that include a fractional value f as one of those available to the binary variables during intermediate stages of solution. A variety of different f-flip strategies, particularly within the context of multi-start algorithms, are proposed for pursuing intensification and diversification goals in metaheuristic algorithms, accompanied by special rules for evaluating and executing f-flips efficiently.


0–1 Optimization Binary quadratic programming Metaheuristics Multi-start algorithms Computational efficiency 



We are indebted to an insightful referee who discovered the omission of a variable in our formulation of Proposition 1.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.University of Colorado Leeds School of BusinessBoulderUSA
  2. 2.LERIAUniversité d’AngersAngersFrance
  3. 3.Institut Universitaire de FranceParisFrance

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