Tabu Search
A Template for Scatter Search and Path Relinking
AE '97 Selected Papers from the Third European Conference on Artificial Evolution
Efficient evaluations for solving large 0-1 unconstrained quadratic optimisation problems
International Journal of Metaheuristics
Fast two-flip move evaluations for binary unconstrained quadratic optimisation problems
International Journal of Metaheuristics
Polynomial unconstrained binary optimisation – Part 1
International Journal of Metaheuristics
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The class of problems known as quadratic zero-one (binary) unconstrained optimisation has provided access to a vast array of combinatorial optimisation problems, allowing them to be expressed within the setting of a single unifying model. A gap exists, however, in addressing polynomial problems of degree greater than 2. To bridge this gap, we provide methods for efficiently executing core search processes for the general polynomial unconstrained binary (PUB) optimisation problem. A variety of search algorithms for quadratic optimisation can take advantage of our methods to be transformed directly into algorithms for problems where the objective functions involve arbitrary polynomials. Part 1 of this paper (Glover et al., 2011) provided fundamental results for carrying out the transformations and described coding and decoding procedures relevant for efficiently handling sparse problems, where many coefficients are 0, as typically arise in practical applications. In the present part 2 paper, we provide special algorithms and data structures for taking advantage of the basic results of part 1. We also disclose how our designs can be used to enhance existing quadratic optimisation algorithms.