Recent studies have demonstrated the effectiveness of applying adaptive memory tabu search procedures to combinatorial optimization problems. In this paper we describe the development and use of such an approach to solve binary quadratic programs. Computational experience is reported, showing that the approach optimally solves the most difficult problems reported in the literature. For challenging problems of limited size, which are capable of being approached by exact procedures, we find optimal solutions considerably faster than the best reported exact method. Moreover, we demonstrate that our approach is significantly more efficient and yields better solutions than the best heuristic method reported to date. Finally, we give outcomes for larger problems that are considerably more challenging than any currently reported in the literature.Integer Programming, Heuristics, Nonlinear Optimization

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Two scheduling problems are considered: (1) scheduling n jobs non-preemptively on a single machine to minimize total weighted earliness and tardiness (WET);(2) scheduling n jobs non-preemptively on two parallel identical processors to minimize weighted mean flow time. In the second problem, a pre-ordering of the jobs is assumed that must be satisfied for any set of jobs scheduled on each specific machine. Both problems are known to be NP-complete. A 0-1 quadratic assignment formulation of the problems is presented, An equivalent 0-1 mixed integer linear programming approach for the problems are considered and a numerical example is given. The formulations presented enable one to use optimal and heuristic available algorithms of 0-1 quadratic assignment for the problems considered here.

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