Several versions of the devour digest tidy-up heuristic for unconstrained binary quadratic problems

The unconstrained binary quadratic optimization problem (UQP) is known to be NP-hard and due to its computational challenge and application potential, it becomes more and more considered and involved by the recent research studies, including both exact and heuristic solution approaches. Our work is in line with that of Glover, Alidaee, Rego and Kochenberger (2002) who proposed one pass heuristics as alternatives to the well-known Devour Digest Tidy-up procedure (DDT) of Boros, Hammer and Sun (1989). The “devour” step sets a term of the current representation to 0 or 1, and the “tidy-up” step substitutes the logical consequences derived from the “digest” step into the current quadratic function. We propose several versions of the DDT constructive heuristic based on the alternative representation of the quadratic function. We also present an efficient implementation of local search using r-flip moves that simultaneously change the values of r binary variables. Computational experiments performed on large scale instances show the efficiency of our implementation in terms of quality and CPU time.