# Diversification methods for zero-one optimization

- 71 Downloads

## Abstract

We introduce new diversification methods for zero-one optimization that significantly extend strategies previously introduced in the setting of metaheuristic search. Our methods incorporate easily implemented strategies for partitioning assignments of values to variables, accompanied by processes called augmentation and shifting which create greater flexibility and generality. We then show how the resulting collection of diversified solutions can be further diversified by means of permutation mappings, which equally can be used to generate diversified collections of permutations for applications such as scheduling and routing. These methods can be applied to non-binary vectors using binarization procedures and by diversification-based learning procedures that provide connections to applications in clustering and machine learning. Detailed pseudocode and numerical illustrations are provided to show the operation of our methods and the collections of solutions they create.

## Keywords

Mathematical optimization Binary programming Metaheuristics Adaptive memory Learning## Notes

### Acknowledgements

This research has been supported in part by the Key Laboratory of International Education Cooperation of Guangdong University of Technology.

## References

- Campos, V., Glover, F., Laguna, M., Martí, R.: An experimental evaluation of a scatter search for the linear ordering problem. J. Global Optim.
**21**, 397–414 (2001)MathSciNetCrossRefzbMATHGoogle Scholar - Campos, V., Laguna, M., Martí, R.: Context-independent scatter and tabu search for permutation problems. INFORMS J. Comput.
**17**(1), 111–122 (2005)MathSciNetCrossRefzbMATHGoogle Scholar - Duarte, A., Martí, R.: Tabu search for the maximum diversity problem. Eur. J. Oper. Res.
**178**, 71–84 (2007)MathSciNetCrossRefzbMATHGoogle Scholar - Gallego, M., Laguna, M., Martí, R., Duarte, A.: Tabu search with strategic oscillation for the maximally diverse grouping problem. J. Oper. Res. Soc.
**64**(5), 724–734 (2013)CrossRefGoogle Scholar - Glover, F.: Heuristics for integer programming using surrogate constraints. Decis. Sci.
**8**, 156–166 (1977)CrossRefGoogle Scholar - Glover, F.: Tabu search for nonlinear and parametric optimization (with links to genetic algorithms). Discrete Appl. Math.
**49**, 231–255 (1994)MathSciNetCrossRefzbMATHGoogle Scholar - Glover, F.: A template for scatter search and path relinking. In: Hao J.-K., Lutton E., Ronald E., Schoenauer M., Snyers D. (eds.) Artificial Evolution, Lecture Notes in Computer Science 1363. Springer, Berlin, pp. 13–54 (1997)Google Scholar
- Glover, F.: Scatter search and path relinking. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 297–316. McGraw Hill, New York (1999)Google Scholar
- Glover, F.: Multi-start and strategic oscillation methods: principles to exploit adaptive memory. In: Laguna, M., Gonzales Velarde, J.L. (eds.) Computing Tools for Modeling, Optimization and Simulation: Interfaces in Computer Science and Operations Research, pp. 1–24. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
- Glover, F.: Adaptive memory projection methods for integer programming. In: Rego, C., Alidaee, B. (eds.) Metaheuristic Optimization Via Memory and Evolution, pp. 425–440. Kluwer Academic Publishers, Dordrecht (2005)CrossRefGoogle Scholar
- Glover, F., Hao, J.-K.: Diversification-based learning in computing and optimization. J. Heuristics (2018, in press)Google Scholar
- Glover, F., Laguna, M.: Tabu Search. In: Reeves, C. (ed.) Modern Heuristic Techniques for Combinatorial Problems, pp. 71–140. Blackwell Scientific Publishing, Oxford (1993)Google Scholar
- Laguna, M., Martí, R.: Scatter Search: Methodology and Implementations in C. Kluwer Academic Publishers, Boston (2003). ISBN 1-4020-7376-3CrossRefzbMATHGoogle Scholar
- Mayoraz, E., Moreira, M.: Combinatorial approach for data binarization. In: Principles of Data Mining and Knowledge Discovery, vol. 1704 of the Series Lecture Notes in Computer Science, pp. 442–447 (1999)Google Scholar